| Network-distance band | Barangays covered | Barangays covered (%) | Population covered | Population covered (%) |
|---|---|---|---|---|
| Within 800 m | 36 | 25.4 | 452,646 | 14.7 |
| Within 1,600 m | 93 | 65.5 | 1,534,802 | 49.8 |
| Within 2,400 m | 121 | 85.2 | 2,271,786 | 73.7 |
| Beyond 2,400 m | 21 | 14.8 | 812,484 | 26.3 |
Network-Constrained Public-Library Accessibility and Spatial Equity in Quezon City
A Barangay-Level Population-Weighted Analysis
Abstract
Public libraries function as civic and social infrastructure whose value depends partly on residents’ ability to physically reach them. This study evaluates whether the spatial allocation of Quezon City Public Library (QCPL) branches aligns with barangay-level population demand under pedestrian-network constraints. Rather than treating branch presence or straight-line proximity as sufficient evidence of access, the study conceptualizes public-library equity as the distribution of potential service exposure produced by the interaction of branch supply, population concentration, and network impedance. Barangay-level pedestrian accessibility is measured using shortest network distance to the nearest QCPL branch, cumulative distance thresholds, population-weighted coverage, geodesic-network comparison, district disparity analysis, and spatial clustering diagnostics. Accessibility burden is operationalized through population-distance exposure and evaluated using Moran’s I, Local Moran’s I (LISA), and Getis-Ord Gi* statistics. Results indicate substantial inequities in pedestrian accessibility. Only 36 of 142 barangays, representing 452,646 residents or 14.7% of the city population, fall within an 800 m network-distance catchment. Coverage increases to 49.8% of the population within 1,600 m and 73.7% within 2,400 m, leaving 812,484 residents beyond the 2,400 m threshold. Mean network distance (1,441.3 m) substantially exceeds mean geodesic distance (918.2 m), and 87.3% of barangays exhibit network distances more than 25% longer than their geodesic equivalents, demonstrating that straight-line proximity systematically overestimates practical pedestrian access. Spatial autocorrelation analysis reveals statistically significant clustering of accessibility burden, with high-burden hot spots concentrated in northern Quezon City, particularly Districts 2, 5, and 6. The findings demonstrate that branch counts and circular buffers alone are insufficient indicators of equitable public-library provision. The study contributes a network-based, population-weighted, and spatially explicit framework for evaluating urban public-service accessibility and offers an applied methodology for infrastructure-equity planning in Global South cities.
Keywords
Public-library accessibility, spatial equity, network accessibility, pedestrian-network analysis, GIS; Moran’s I, Local Moran’s I, Getis-Ord Gi*, population-weighted accessibility, urban service allocation, Quezon City, public-service infrastructure, spatial clustering, accessibility burden, Global South urban planning
1 Introduction
Public libraries are place-based public institutions whose value depends not only on collections, staffing, and programming, but also on whether residents can physically reach them. In contemporary library research, public libraries are increasingly understood as civic and social infrastructure: everyday spaces for information access, digital support, learning, encounter, and local public life (Audunson et al., 2019; Lenstra and Carlos, 2019; McShane, 2011). This social-infrastructure role gives spatial access a planning significance. If public libraries are expected to support civic participation and community life, then their branch locations must be evaluated not only as points on a map but as opportunities that are more or less reachable through the urban movement network.
Accessibility offers a way to translate this concern into measurable spatial evidence. In transport and urban planning research, accessibility is commonly defined as the relationship between opportunities and the effort required to reach them (Geurs and Wee, 2004; Hansen, 1959). For public facilities, accessibility is also an equity issue because the spatial distribution of facilities may align poorly with population demand, leaving some residents with substantially greater travel burdens than others (Cheng et al., 2021; Taleai et al., 2014). The relevant question is therefore not simply whether a city has public-library branches, but whether those branches are distributed in ways that provide comparable potential exposure to residents across neighborhoods.
Distance measurement is central to this question. Straight-line or geodesic buffers are easy to communicate, but they simplify pedestrian movement by ignoring the street network, barriers, block structure, crossings, and indirect routes. GIS accessibility research shows that distance-measure choices can materially change service-area estimates and spatial interpretation (Boscoe et al., 2012; Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008). For walkable public services, this matters because a barangay that appears near a library in geometric space may still face a much longer network route. When geodesic proximity is treated as practical access, public-service coverage may appear more extensive and more equitable than it is.
This study evaluates these issues in Quezon City, Philippines, using the Quezon City Public Library (QCPL) branch system as an urban public-service case. Quezon City is an appropriate setting because it combines a large population, heterogeneous districts, 142 barangays, and uneven urban form. The barangay scale is useful for local planning because it is fine-grained enough to capture intra-urban variation while still corresponding to administrative units used in service delivery. The study treats barangays as planning units and measures potential pedestrian accessibility, not individual library use.
The study combines nearest-branch pedestrian-network distance, population-weighted threshold coverage, geodesic-network comparison, district disparity analysis, and spatial clustering diagnostics. It is deliberately framed as a spatial allocation and equity diagnostic rather than as a full optimization or behavioral model. The aim is to determine whether the existing branch geography produces an allocation mismatch: high or clustered population exposure to network-distance burden that is not visible from branch counts or circular buffers alone.
1.1 Research Problem
Despite the presence of multiple QCPL branches, pedestrian-accessible library services may not be distributed in proportion to barangay-level population demand. A branch network can appear adequate if assessed through branch counts, administrative presence, or circular buffers, yet still leave large populations outside reasonable walking access when pedestrian-network impedance is considered. This creates a risk that conventional proximity measures will overstate practical accessibility and obscure high-burden barangays.
The problem is not simply that some barangays are farther from branches than others. The more specific research problem is that branch supply, population concentration, and pedestrian-network structure may interact to produce unequal accessibility burden. If high-population barangays are also network-distant from the nearest QCPL branch, then the spatial distribution of library services may be misaligned with resident demand. If high-burden barangays are spatially clustered, then the access gap is not only an isolated local issue but an area-based public-service equity concern.
This study therefore evaluates whether network-based pedestrian accessibility to QCPL branches is equitably distributed across Quezon City barangays when accessibility is measured through network distance, weighted by resident population exposure, compared against geodesic distance, and tested for spatial clustering. Equity is operationalized in a limited and measurable sense: unequal distribution of potential service exposure and population-distance burden. The normative benchmark is not equal branch counts across districts, but a weaker and more defensible distributive criterion: large populations should not be systematically exposed to higher network-distance burden, and high burdens should not be spatially concentrated without compensating service provision. The study does not claim to measure all dimensions of library equity, such as branch quality, opening hours, collection adequacy, socioeconomic vulnerability, digital exclusion, or actual user behavior.
1.2 Research Questions
This study addresses five research questions:
What is the spatial distribution of network-based pedestrian accessibility to QCPL branches across Quezon City barangays?
How substantially do geodesic distance measures underestimate pedestrian-network travel burden across barangays?
To what extent is network-based accessibility associated with barangay population concentration and district location?
Are accessibility disadvantages spatially clustered across barangays?
Which barangays exhibit the greatest population-weighted accessibility burden under network-constrained conditions?
These questions create a focused analytical sequence: baseline accessibility, measurement validity, demand-location association, spatial structure, and equity-oriented prioritization. A sixth question, concerning how alternative branch-siting or mobile-library scenarios would change population-weighted equity, is treated as a necessary next-stage extension rather than as an answered question in the present article. This distinction matters because the current dataset can identify spatial accessibility burdens and statistically significant clustering, but it cannot determine optimal branch sites or explain actual library use without additional data on branch capacity, candidate locations, user preferences, socioeconomic vulnerability, and multimodal travel behavior.
1.3 Significance
The study contributes to public-library planning by treating libraries as spatially distributed public infrastructure rather than only as institutional service points. Prior research has emphasized the civic and social-infrastructure roles of libraries (Audunson et al., 2019; Lenstra and Carlos, 2019), and public-library accessibility research shows that the physical location of branches is an equity issue in its own right (Cheng et al., 2021). This study extends that concern to Quezon City by identifying where pedestrian access is weakest and where large populations are exposed to long network distances.
The study also contributes methodologically by combining three accessibility diagnostics that are often reported separately: network-distance measurement, population-weighted coverage, and spatial clustering analysis. Network distance provides a more realistic representation of pedestrian impedance than geodesic distance for walkable services (Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008). Population weighting prevents small barangays and large barangays from being treated as equivalent service units. Moran’s I, Local Moran’s I, and Getis-Ord Gi* add a spatial-statistical test of whether accessibility burden is clustered rather than merely uneven (Anselin, 1995; Getis and Ord, 1992; Ord and Getis, 1995).
For local planning, the significance of the study lies in its ability to distinguish different kinds of access problems. Some barangays may be severely distant from the nearest branch, while others may combine moderate distance with very large populations. Still others may form part of a wider high-burden cluster. These distinctions matter because they imply different responses: new branch feasibility assessment, mobile-library deployment, partnerships with barangay facilities or schools, pedestrian-network improvements, or more detailed capacity-sensitive modeling.
Finally, the study contributes to urban-service equity research in a Global South context. Much of the accessibility literature is methodologically transferable, but local planning problems depend on administrative geography, urban form, data availability, and institutional capacity. By producing a reproducible barangay-level analysis for Quezon City, the study offers an applied framework that can be adapted to other Philippine cities and other public-service systems where branch counts or straight-line buffers may conceal population-weighted accessibility burdens.
2 Literature Review
2.2 Spatial Accessibility and Urban Service Equity
Spatial accessibility research provides the methodological bridge between facility provision and service equity. Rather than treating public services as evenly available once they exist within a city, accessibility analysis asks how the location of facilities interacts with the location of residents, the cost of movement, and the distribution of demand. In this sense, accessibility is not simply a measure of distance. It is an index of how urban opportunities are spatially arranged relative to the populations expected to use them (Geurs and Wee, 2004; Hansen, 1959; Jin et al., 2019; Zheng et al., 2019).
This distinction is central to equity analysis. A facility network can appear adequate in aggregate while still producing localized under-provision if branches, service points, or other public resources are poorly matched to residential concentrations. Taleai, Sliuzas, and Flacke argue that spatial-equity evaluation helps planners identify areas of under-provision, assess the effectiveness of service policies, and guide the allocation of scarce public facilities (Taleai et al., 2014). Their broader point applies directly to library planning: the equity question is not only whether a city has public libraries, but whether the spatial arrangement of those libraries allows different neighborhoods to reach them with comparable ease.
Public-service accessibility studies have developed several families of measures, including nearest-distance approaches, cumulative-opportunity measures, gravity models, and two-step floating catchment area methods (Jin et al., 2019; Tao et al., 2020). These methods differ in complexity, but they share a common concern with the spatial relationship between supply and demand. For facility systems such as libraries, schools, parks, health centers, and transit stations, the relevant planning question is often practical rather than abstract: which residents are within a reasonable access threshold, which areas remain outside it, and how large is the affected population? This makes threshold-based and population-weighted measures especially useful when communicating findings to planners and public agencies.
Library-accessibility research increasingly shows why this allocation perspective matters. Cheng, Wu, and Moen examine the spatial accessibility and spatial equity of public-library locations, while Higgs, Jones, and Langford show that library accessibility analysis can incorporate catchments, supply-side parameters, and competition among service points (Cheng et al., 2021; Higgs et al., 2017). Their work positions libraries within a broader family of public-service accessibility problems: service value is not exhausted by institutional presence, because residents experience the system through the geography of reachable opportunities.
The equity implications become sharper when accessibility is evaluated at small geographic units. District-level or citywide summaries can obscure localized deficits because they average high-access and low-access areas into a single figure, while areal aggregation can also alter observed spatial patterns through the modifiable areal unit problem (Buzzelli, 2020; Openshaw, 1984). Barangay-level analysis is therefore appropriate for the present study because it retains neighborhood-scale variation while still allowing aggregation to districts and population groups. This scale also aligns with public-service planning concerns: branch expansion, mobile-library scheduling, outreach programs, and pedestrian improvements are typically implemented in relation to identifiable local service areas rather than citywide averages alone (Taleai et al., 2014).
The literature also cautions that spatial accessibility should not be conflated with realized service use. Accessibility measures estimate the potential ease of reaching a service; they do not directly capture user preferences, institutional quality, opening hours, disability access, perceived safety, or social barriers. Studies of public-service facilities increasingly recognize this distinction by combining spatial measures with demand, capacity, transport mode, and equity indicators (Liu et al., 2023; Tao et al., 2020). For this study, the implication is methodological modesty: the analysis can identify the geography of potential pedestrian access to QCPL branches, but it cannot by itself explain all dimensions of library use. Its contribution is to establish whether the spatial precondition for equitable use is present across Quezon City barangays.
2.3 Network-Based Accessibility Versus Geodesic Buffers
The distinction between geodesic and network-based accessibility is central to the present study. Geodesic distance measures the straight-line separation between an origin and a destination. It is computationally simple and useful for broad exploratory analysis, but it assumes that movement can occur directly across space. Pedestrian access rarely works this way. Residents move through a street network shaped by block structure, intersections, barriers, crossings, route availability, and the location of entrances. For this reason, a straight-line service area can include residents who are physically near a branch but must walk substantially farther to reach it (Boscoe et al., 2012; Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008; Nesbitt et al., 2014).
GIS-based accessibility studies commonly distinguish buffer analysis from network analysis. Buffer analysis identifies areas within a fixed distance from a facility, while network analysis estimates reachability through connected transport links and associated travel costs (Yhee et al., 2021). Both approaches can be useful, but they answer different questions. A circular buffer asks who is near a facility in geometric space; a network service area asks who can reach it through the available mobility system. For pedestrian access to public libraries, the second question is more consistent with the everyday meaning of accessibility.
The methodological literature shows that the choice of distance metric can materially affect service-area estimates. Gutierrez Puebla and Garcia Palomares demonstrate that distance measures influence the calculation of transport service areas in GIS (Gutierrez Puebla and Garcia Palomares, 2008). Buczkowska and colleagues similarly argue that the choice among Euclidean distance, travel time, and network distance is often treated too casually, even though it can affect spatial modeling outcomes (Buczkowska et al., 2019). More directly, Chen and Chen show that straight-line distance can bias spatial analysis and that public-facility service areas may be overestimated when Euclidean distance is used instead of actual network distance (Chen and Chen, 2021). These findings support the premise that geodesic buffers should be treated as approximations, not definitive evidence of walkable access.
This issue is particularly important for equity analysis. If straight-line buffers overstate access, the error will not necessarily be evenly distributed. Areas with fragmented street networks, large blocks, gated parcels, watercourses, major roads, or disconnected pedestrian routes may appear adequately served in geometric space while remaining less accessible in practice. The resulting bias can be policy-relevant: underserved areas may be missed, facility performance may be overstated, and the apparent distribution of public-service benefits may look more equitable than the network actually permits (Boscoe et al., 2012; Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008).
The present study therefore uses network distance as the primary measure of pedestrian accessibility and treats geodesic distance as a comparison case. This design is intentionally conservative. It does not assume that every resident will walk to a library, nor that distance is the only determinant of library use. It asks a narrower and more defensible question: how much does the measured accessibility of QCPL branches change when the analysis moves from straight-line proximity to pedestrian-network distance? The answer matters because any planning standard based on walkable catchments should be evaluated against the routes residents can actually use.
2.4 Spatial Equity and Facility Allocation
The equity claim in this study is grounded in distributive spatial-equity theory rather than in distance description alone. Spatial justice scholarship argues that the distribution of urban resources is not neutral: infrastructure, public facilities, and mobility systems shape residents’ practical opportunities (Fainstein, 2010; Harvey, 1973; Soja, 2010). Transport-equity scholarship makes the same point in more operational terms: accessibility is central to distributive justice because it describes how easily people can reach opportunities, while broad theories of justice require explicit translation into measurable equity criteria (Pereira et al., 2017). The present study therefore uses justice theory in a deliberately limited way. It does not test a full theory of justice, deprivation, or capability. Instead, it operationalizes spatial equity as the distribution of potential service exposure across barangays and residents. Under this definition, an accessibility pattern is more equitable when pedestrian-network burden is not concentrated among high-population barangays or particular districts.
This framing also distinguishes spatial accessibility from service adequacy. Accessibility measures the effort required to reach an opportunity; adequacy also requires evidence on capacity, quality, opening hours, staffing, collection depth, digital services, and user demand. Public facility models such as two-step floating catchment area methods respond to this distinction by linking supply capacity, population demand, and distance decay (Delamater, 2013; Luo and Wang, 2003; Tao et al., 2020). The present study cannot estimate a full capacity-sensitive E2SFCA model because comparable branch-capacity data are not available. It nevertheless adopts the same demand-supply logic by weighting coverage by population, ranking high-burden barangays, and treating threshold coverage as an equity diagnostic rather than as a complete service-adequacy measure.
The spatial unit also shapes the interpretation of equity. Barangay-level analysis is useful for planning communication, but it remains vulnerable to the modifiable areal unit problem and ecological fallacy because within-barangay population distribution is not observed (Buzzelli, 2020; Openshaw, 1984). Spatial clustering and autocorrelation methods can test whether disadvantage is geographically concentrated rather than randomly distributed. Global Moran’s I evaluates whether high or low values are spatially patterned across the full study area, Local Moran’s I or LISA identifies local clusters and spatial outliers, and Getis-Ord Gi* identifies hot spots and cold spots of unusually high or low local concentration (Anselin, 1995; Bivand and Wong, 2018; Getis and Ord, 1992; Ord and Getis, 1995). The present study therefore combines district comparison, non-parametric district tests, mapped patterns, and formal spatial clustering diagnostics as complementary evidence of accessibility-burden concentration.
2.5 Conceptual Framework
This study is guided by a Network-Constrained Public Service Equity Model. The model treats library accessibility as an intermediate mechanism between urban form and spatial equity outcomes, not as equity itself. Public-library equity is defined here as the distribution of potential service exposure across residents and barangays: high-population areas should not carry systematically higher pedestrian-network burden simply because branch supply and street connectivity are poorly aligned with where people live (Geurs and Wee, 2004; Hansen, 1959; Soja, 2010; Taleai et al., 2014).
The framework has six core constructs. Library supply refers to QCPL branch locations and, in a fuller model, branch capacity. Population demand refers to the number of residents represented by each barangay. Network morphology refers to the connective structure of the street system, including the degree to which routes are direct or fragmented. Network impedance refers to the pedestrian-network distance that results from that morphology. Accessibility exposure refers to threshold-based access to branch opportunities under network conditions. Accessibility burden refers to the combination of resident population and network distance. The spatial equity outcome refers to the unequal distribution of accessibility burden across barangays and districts (Boeing, 2017; Boisjoly et al., 2020; Geurs and Wee, 2004; Hansen, 1959; Luo and Wang, 2003).
| Construct | Operational definition in this study |
|---|---|
| Library supply | QCPL branch locations; branch capacity is identified as an advanced-model requirement |
| Population demand | Barangay resident population; population density is identified as an advanced-model requirement |
| Network morphology | Street-network structure that shapes route directness; represented indirectly through observed network distance |
| Network impedance | Shortest pedestrian-network distance to the nearest branch |
| Accessibility exposure | Barangay and population coverage within cumulative network-distance thresholds; continuous network distance |
| Accessibility burden | Population multiplied by network distance, expressed as person-kilometers; Gini coefficient and underserved population |
| Spatial equity outcome | Unequal distribution of exposure and burden across barangays and districts |
The directional logic is that facility allocation and urban morphology jointly shape network impedance; network impedance shapes pedestrian accessibility; pedestrian accessibility shapes population-weighted service exposure; and the distribution of exposure across residents produces the spatial equity outcome. This logic avoids treating unequal distance as automatically equivalent to inequity. Distance becomes equity-relevant when it is systematically misaligned with population demand or concentrated in particular districts and high-population barangays (Boisjoly et al., 2020; Geurs and Wee, 2004; Pereira et al., 2017; Soja, 2010).
Figure 1 summarizes this framework. It positions network distance as the measurable constraint, population as the demand weight, and equity as a distributional outcome evaluated through threshold coverage, district disparities, high-burden barangays, spatial clustering, and geodesic-network measurement bias. The figure also identifies optional extensions–capacity-sensitive E2SFCA or gravity models, spatial regression, and location-allocation scenarios–that are required before making stronger claims about service adequacy or optimal intervention design (Delamater, 2013; He and Xie, 2022; LeSage, 2015; Luo and Wang, 2003; Tao et al., 2020).
Four hypotheses follow from the framework.
\(H_1\): barangay population is not aligned with lower network-distance burden; instead, higher-population barangays are expected to have equal or greater network-distance burden under the current branch allocation.
\(H_2\): network-distance estimates of pedestrian travel burden are significantly greater than geodesic-distance estimates when pedestrian movement is constrained by the street network.
\(H_3\): accessibility burden exhibits positive spatial autocorrelation and forms identifiable local high-burden clusters.
\(H_4\): high-population barangays outside the 800 m threshold contribute disproportionately to citywide accessibility inequity. These hypotheses organize the empirical analysis while remaining appropriately scoped to the available data. A stronger future hypothesis would test whether intersection density, circuity, land-use mix, peripheral location, or deprivation indicators predict burden, but those explanatory variables are not yet available in the present dataset.
3 Methods
The empirical dataset contains 142 barangay origins, each linked to district and population attributes, and measures each barangay’s distance to the nearest QCPL branch using both network and geodesic distance metrics. It combines barangay-level accessibility classifications, distance-comparison measures, cumulative coverage summaries, district-level coverage indicators, underserved-area summaries, and barangay polygon geometry from the HDX PSA-NAMRIA Philippine administrative boundary dataset (National Mapping and Resource Information Authority and Philippine Statistics Authority, 2023). At the barangay level, the data identify each barangay’s district, population, nearest QCPL branch, network distance to that branch, and resulting accessibility category. A paired distance-comparison dataset records geodesic and network distance for each barangay, together with the absolute and percentage differences between the two measures.
The workflow begins with three empirical inputs: barangay-level demand, QCPL branch locations, and the pedestrian network. These inputs are used to construct a nearest-branch network-distance dataset that identifies the shortest network distance from each barangay to its nearest library branch. The resulting distances are classified using multiple distance thresholds and aggregated into barangay, population, and district-level coverage summaries. A parallel geodesic-distance comparison is retained as a measurement-validity test, allowing the study to quantify how much straight-line measures overstate pedestrian accessibility. The figures used in the study show network-based accessibility, district coverage, underserved barangays, and geodesic overestimation of pedestrian access.
The dataset supports a population-weighted accessibility analysis but has clear scope limits. It measures potential pedestrian access from barangay origins to library branches; it does not measure individual travel behavior, library visits, perceived safety, sidewalk condition, opening hours, collection quality, or program capacity. It also does not include candidate branch sites, branch service capacity, or a complete origin-destination matrix from every barangay to every branch, which are needed for optimization or E2SFCA modeling (Delamater, 2013; Luo and Wang, 2003; Tao et al., 2020). For this reason, the analysis should be interpreted as an assessment of spatial opportunity and demand exposure rather than realized library use or final service adequacy (Nesbitt et al., 2014).
Six assumptions follow from these data constraints. First, the nearest branch is treated as the relevant available branch, although residents may choose a farther branch because of collections, opening hours, school or work trips, transit access, or familiarity. Second, the barangay origin represents resident location, although large barangays may contain substantial internal population variation. Third, the 800 m threshold is used as a planning benchmark rather than as an observed behavioral cutoff. Fourth, distance burden is interpreted as a necessary but incomplete indicator of service inequity. Fifth, population size is used as the main demand measure because household-level socioeconomic need, age structure, student population, and digital-exclusion indicators are not integrated into the current dataset. Sixth, QCPL branches are treated as equivalent service opportunities because comparable capacity indicators are unavailable. These assumptions are not treated as harmless; they define the boundary between the present accessibility diagnostic and the stronger capacity-sensitive, vulnerability-sensitive, and behavior-sensitive models recommended for future work.
3.1 Network-Distance Accessibility Analysis
The primary accessibility measure is the shortest pedestrian-network distance from each barangay origin to the nearest QCPL branch. This measure follows the accessibility logic established in the conceptual framework: library access is evaluated as a relation among residential demand, facility supply, and the impedance imposed by the urban movement network. Network distance is used as the main impedance measure because it better represents feasible pedestrian movement than straight-line proximity, particularly in urban settings where block structure, road hierarchy, barriers, and route connectivity shape actual walking paths (Buczkowska et al., 2019; Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008).
For each of the 142 barangays, the barangay-level accessibility dataset identifies the nearest QCPL branch, the computed network distance to that branch, the barangay’s district, its population, and its resulting accessibility category. The analysis treats each barangay as an origin and each QCPL branch as a potential destination, then assigns the barangay to the branch with the minimum network-distance value. This nearest-facility specification is appropriate for a first-order public-service accessibility analysis because the core question is whether residents of each barangay have a nearby branch available within the pedestrian network, not whether they choose among multiple branches or optimize by collection type, opening hours, or program availability.
This nearest-network-distance procedure also establishes the spatial unit for all subsequent summaries. Barangay-level distances are retained for identifying specific underserved areas, while population and district attributes allow the same results to be aggregated into citywide and district-level indicators. The method therefore avoids treating coverage as a purely geometric property of branch locations. Instead, it links branch proximity to the number of residents represented by each barangay and to the district structure through which local planning priorities are often organized.
The network-distance approach is intentionally paired with, but analytically prioritized over, geodesic distance. The paired distance-comparison dataset preserves both measures for each barangay so that the study can quantify the difference between straight-line and network-based access. This design follows GIS accessibility research showing that the choice of distance metric can affect service-area estimates and may overstate practical access when Euclidean or geodesic measures are substituted for network distance (Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008). In the present study, geodesic distance is therefore not used as the main measure of walkable service access. It is used as a benchmark for evaluating how much apparent accessibility changes when movement is measured through the pedestrian network.
All empirical claims derived from this procedure are interpreted as potential spatial access. The analysis does not infer observed library use, individual walking routes, or subjective willingness to walk. It estimates whether each barangay is spatially positioned within a plausible network-distance catchment of a QCPL branch. This narrower interpretation is important because accessibility is a necessary but incomplete condition for equitable service use: residents may be near a branch and still face non-spatial barriers, while residents beyond the threshold may use other modes of transport. The value of the method is that it establishes the spatial opportunity structure within which those other factors operate (Geurs and Wee, 2004; Nesbitt et al., 2014).
3.2 Distance Thresholds and Service Categories
Barangays are classified using a cumulative network-distance threshold scheme centered on 800 m. The 800 m band is used as the principal accessibility threshold because it represents a conservative walking-access standard for a neighborhood-scale public service and is consistent with GIS-based social-infrastructure studies that classify facilities through walkable distance bands rather than through administrative availability alone (Yhee et al., 2021). The threshold is not treated as a universal behavioral cutoff. Instead, it functions as a transparent planning standard that allows the study to distinguish barangays with proximate pedestrian access from those where reaching a branch requires a longer network trip.
The analysis uses four cumulative service bands: within 800 m, within 1,600 m, within 2,400 m, and beyond 2,400 m. These bands translate the continuous network-distance measure into categories that are interpretable for planning. Barangays within 800 m are classified as having proximate pedestrian access to a QCPL branch. Barangays beyond 800 m are classified as underserved for the main equity analysis, with the 1,600 m and 2,400 m bands used to differentiate moderate from more severe distance burdens. This tiered structure is important because the binary 800 m classification identifies the principal access gap, while the wider bands show whether excluded barangays are near the threshold or substantially distant from the branch network.
The cumulative coverage results provide the empirical basis for these categories. Across the 142 barangays, 36 barangays fall within 800 m network distance of a QCPL branch. Coverage expands to 93 barangays within 1,600 m and 121 barangays within 2,400 m, leaving 21 barangays beyond 2,400 m. Because these categories are cumulative, each wider band includes barangays already counted in the shorter band. This design supports both accessibility interpretation and policy prioritization: the 800 m threshold identifies the main served population, while the wider bands identify where interventions may require different responses, such as branch expansion, mobile-library service, outreach programming, or pedestrian-network improvements.
The threshold categories are also population-weighted in the results. A barangay count alone can understate the significance of access gaps if low-access barangays contain large populations. For this reason, each distance band is evaluated both by the number of barangays and by the number and percentage of residents represented in those barangays. This population-weighted interpretation is consistent with the study’s spatial-equity framework: service access is not only a matter of how many places are covered, but how many residents are positioned within or beyond the relevant pedestrian catchments.
3.3 Population-Weighted Coverage
Coverage is calculated in two complementary ways: by barangay and by population. Barangay coverage measures the share of spatial units within a given network-distance threshold, while population coverage measures the share of residents represented by those barangays. The distinction is necessary because barangays vary substantially in population size. A threshold may cover many small barangays while excluding fewer but more populous barangays, producing a misleading impression of service reach if only unit counts are reported.
For each threshold \(t\), barangay coverage is calculated as:
\[ C_b(t) = \frac{\sum_{i=1}^{n} I(d_i \leq t)}{n} \times 100 \]
where \(C_b(t)\) is the percentage of barangays covered at threshold \(t\), \(d_i\) is the network distance from barangay \(i\) to its nearest QCPL branch, \(I(d_i \leq t)\) is an indicator equal to 1 when the barangay is within the threshold and 0 otherwise, and \(n\) is the total number of barangays. In this study, \(n = 142\).
Population-weighted coverage is calculated as:
\[ C_p(t) = \frac{\sum_{i=1}^{n} P_i I(d_i \leq t)}{\sum_{i=1}^{n} P_i} \times 100 \]
where \(C_p(t)\) is the percentage of residents covered at threshold \(t\) and \(P_i\) is the population of barangay \(i\). This measure gives greater analytical weight to barangays with larger resident populations and is therefore more appropriate for evaluating public-service equity than an unweighted count alone. The study reports both indicators because they answer different planning questions: barangay coverage identifies the spatial extent of the branch network, while population coverage estimates how many residents are positioned within the relevant pedestrian catchments.
The same logic is applied to the 800 m, 1,600 m, and 2,400 m thresholds. The 800 m threshold is used to define the main served population, while wider thresholds identify secondary catchment conditions and the remaining population beyond 2,400 m. This cumulative design allows the results to show not only whether residents are underserved at the main walking threshold, but also whether they are just outside proximate access or located far beyond the existing library network. In equity terms, the latter distinction matters because different levels of distance burden imply different planning responses.
3.4 Equity Operationalization and Sensitivity Analysis
Equity is operationalized as the distributional fairness of potential pedestrian exposure to QCPL branches. The study therefore evaluates accessibility through four linked indicators: cumulative population coverage, district-level underserved population, a high-burden barangay index, and an accessibility inequality statistic. This use of distributional and population-weighted indicators follows accessibility-equity studies that use metrics such as Gini coefficients, Lorenz curves, and correlations between need and access to evaluate horizontal and vertical equity (Boisjoly et al., 2020). The high-burden index is calculated as a simple demand-distance exposure measure:
\[ B_i = \frac{P_i d_i}{1000} \]
where \(B_i\) is person-kilometers of network-distance burden, \(P_i\) is barangay population, and \(d_i\) is the network distance from barangay \(i\) to the nearest QCPL branch. This index does not represent actual trips. It is a prioritization diagnostic that identifies barangays where large populations coincide with long network distances.
Accessibility inequality is summarized using the Gini coefficient of barangay network distances:
\[ G = \frac{\sum_{i=1}^{n}\sum_{j=1}^{n}|d_i-d_j|}{2n^2\bar{d}} \]
where \(d_i\) and \(d_j\) are barangay network distances and \(\bar{d}\) is the mean network distance. A higher value indicates a more unequal distribution of distance burden across barangays. Because the underlying observations are barangay-level rather than household-level, this statistic is interpreted as an areal inequality measure.
The study also tests the sensitivity of coverage estimates to alternative network-distance thresholds. In addition to the principal 800 m standard, the results report 400 m, 1,200 m, 1,600 m, and 2,400 m thresholds. This does not eliminate threshold dependence, but it shows whether the substantive interpretation changes when the walking-access standard is tightened or relaxed; threshold sensitivity is important because catchment-size assumptions can affect accessibility estimates (Ni et al., 2015; Zhu et al., 2018).
3.5 District-Level Equity Analysis
District-level analysis is used to evaluate whether network-based library access is evenly distributed across Quezon City’s six districts. The district is not treated as the primary unit of measurement; barangays remain the base observations. Districts are used as an aggregation level because they provide an interpretable planning geography for comparing service outcomes across larger sections of the city. This approach is consistent with spatial-equity analysis of public facilities, where fine-grained accessibility measures are often summarized across administrative or planning units to identify areas of relative under-provision (Muhaimin et al., 2022; Taleai et al., 2014).
For each district \(j\), the analysis aggregates barangay-level threshold classifications into district-specific coverage counts and population totals. District barangay coverage at threshold \(t\) is calculated as:
\[ C_{bj}(t) = \frac{\sum_{i \in j} I(d_i \leq t)}{n_j} \times 100 \]
where \(C_{bj}(t)\) is the percentage of barangays in district \(j\) covered at threshold \(t\), \(n_j\) is the number of barangays in that district, and \(i \in j\) denotes barangays located within district \(j\). District population coverage is calculated as:
\[ C_{pj}(t) = \frac{\sum_{i \in j} P_i I(d_i \leq t)}{\sum_{i \in j} P_i} \times 100 \]
where \(C_{pj}(t)\) is the share of district population represented by barangays within the threshold. The same calculations are applied to the 800 m, 1,600 m, and 2,400 m bands, allowing the analysis to compare both proximate access and wider catchment conditions across districts.
The 800 m threshold is used to define district-level underserved populations. A barangay is counted as underserved when its nearest QCPL branch is more than 800 m away by network distance. For each district, the analysis sums the number of underserved barangays and the population represented by those barangays. The district-level underserved summary used in the analysis was selected because it is aligned with the same 800 m threshold used in the main barangay classification, ensuring consistency between the citywide, barangay-level, and district-level results.
District comparisons are interpreted with two cautions. First, districts differ substantially in the number of barangays and resident population, so percentage coverage and absolute affected population must be read together. A district may have a small number of barangays but a large affected population, or a high count of underserved barangays with a smaller total population. Second, district aggregation can conceal variation among barangays within the same district. For that reason, the results section reports district-level disparities alongside barangay-level priority areas rather than treating district averages as complete descriptions of local access conditions (Buzzelli, 2020; Openshaw, 1984).
3.6 Statistical Analysis
Four inferential diagnostics are added to strengthen the descriptive GIS analysis while staying within the limits of the available data. First, the association between barangay population and nearest-branch network distance is tested using Spearman’s rank correlation, with Pearson’s correlation reported as a supplementary linear diagnostic. This evaluates whether population demand is aligned with lower pedestrian-network burden.
Second, the network-geodesic comparison is tested using paired-sample procedures because each barangay has both a network-distance and geodesic-distance estimate. A one-sided paired \(t\) test evaluates whether mean network distance exceeds mean geodesic distance, and a Wilcoxon signed-rank test provides a non-parametric robustness check for the same paired comparison.
Third, district differences in barangay network distance are evaluated using the Kruskal-Wallis rank-sum test. This non-parametric test is used because district sample sizes differ and because distance distributions are not assumed to be normally distributed. The test does not identify causal mechanisms; it evaluates whether the distribution of network-distance burden differs across district groups.
Fourth, spatial clustering is tested using barangay polygon geometry from the PSA-NAMRIA administrative boundary dataset distributed through HDX. Barangay names in the boundary layer are normalized and joined to the accessibility dataset, producing 142 matched Quezon City barangay polygons. A queen-contiguity spatial weights matrix is then constructed from the barangay polygons and row-standardized for analysis. The matrix has no islands, meaning every barangay has at least one spatial neighbor.
Global Moran’s I is estimated for both nearest-branch network distance and the population-distance burden index. This tests whether similar accessibility burdens are spatially clustered across the city rather than randomly arranged. Local Moran’s I is then estimated for the population-distance burden index to classify high-high burden clusters, low-low clusters, and spatial outliers (Anselin, 1995). Getis-Ord Gi* is estimated for the same burden index to identify statistically significant hot spots and cold spots of local burden concentration (Getis and Ord, 1992; Ord and Getis, 1995). Because local spatial statistics involve multiple local tests, the results report both nominal p values and Benjamini-Hochberg adjusted q values. The local results are interpreted as exploratory cluster diagnostics rather than as causal evidence (Bivand and Wong, 2018).
3.7 Geodesic-Network Distance Comparison
The final methodological step compares geodesic and network distance for each barangay. This comparison is included because straight-line buffers remain common in exploratory service-area analysis, but they can overstate practical access when the street network requires indirect routes (Buczkowska et al., 2019; Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008). The comparison does not treat geodesic distance as an alternative preferred measure. Instead, it uses geodesic distance as a benchmark for estimating how much accessibility would be overstated if pedestrian movement were approximated by straight-line proximity.
For each barangay \(i\), the absolute distance difference is calculated as:
\[ \Delta_i = d_{n,i} - d_{g,i} \]
where \(d_{n,i}\) is the network distance from barangay \(i\) to the nearest QCPL branch and \(d_{g,i}\) is the corresponding geodesic distance. A positive value indicates that the network route is longer than the straight-line distance, while a negative value indicates that the measured network distance is shorter than the geodesic value. The latter can occur in spatial datasets because origin and destination representations, snapping procedures, or centroid placement may not align perfectly across distance measures.
Percentage distance inflation is calculated as:
\[ \delta_i = \frac{d_{n,i} - d_{g,i}}{d_{g,i}} \times 100 \]
where \(\delta_i\) expresses the network-distance burden relative to the geodesic distance. The analysis summarizes this measure using the mean network distance, mean geodesic distance, mean and median difference, and the number and percentage of barangays where network distance exceeds geodesic distance by more than 25%, 50%, and 100%. These thresholds are not interpreted as behavioral cutoffs. They are diagnostic indicators of how strongly straight-line measurement understates the walking distance implied by the pedestrian network.
This comparison strengthens the study’s methodological contribution. If network and geodesic distances were similar, then a simpler buffer-based approach might provide a reasonable approximation for strategic planning. If the differences are large and widespread, however, geodesic buffers may materially misrepresent the accessibility landscape. The geodesic-network comparison therefore evaluates whether the choice of distance metric changes the substantive interpretation of library service equity in Quezon City (Boscoe et al., 2012; Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008).
3.8 Methodological Scope
The study is designed as a network-based spatial equity diagnostic rather than as a full public-facility optimization model. A capacity-sensitive E2SFCA model would estimate:
\[ A_i=\sum_j \frac{S_j f(d_{ij})}{\sum_k P_k f(d_{kj})} \]
where \(A_i\) is accessibility at barangay \(i\), \(S_j\) is service capacity at branch \(j\), \(P_k\) is population demand near branch \(j\), and \(f(d)\) is a distance-decay function. This model is methodologically attractive because it accounts for demand competition and branch capacity (Delamater, 2013; Luo and Wang, 2003; Tao et al., 2020; Xiao et al., 2022). It is not estimated here because the available project data contain nearest-branch distances rather than a complete barangay-to-branch distance matrix and do not include comparable branch-capacity measures. The study therefore uses nearest-network-distance, population-weighted coverage, and spatial clustering diagnostics as transparent, reproducible evidence, while treating E2SFCA, multimodal accessibility, and siting optimization as necessary next-stage analyses (Zhu et al., 2018).
The same boundary applies to explanatory modeling. A stronger explanatory design would estimate OLS or logistic models for network distance, underserved status, population-distance burden, or geodesic-network inflation, then evaluate whether spatial lag or spatial error specifications are needed when residuals remain spatially dependent (Elhorst, 2010; LeSage, 2015). Candidate predictors would include population density, district, distance from the city center, intersection density, road density, circuity, land-use mix, deprivation proxies, and public-transport proximity. Those variables are identified in Figure 1 as geospatial-context inputs, but they are not yet available in the present analytic dataset. A final planning extension would use location-allocation or scenario modeling to compare one new branch, multiple mobile-library stops, pedestrian-network improvements, or hybrid interventions; public-facility location models are specifically designed to balance accessibility, capacity, cost, and equity objectives (He and Xie, 2022). The present article therefore stops at statistically structured diagnosis and does not claim to estimate determinants or optimal allocation scenarios.
4 Results
4.1 Overall Service Coverage
The network-distance results show that pedestrian access to QCPL branches is limited at the principal 800 m threshold. As shown in Table 2, only 36 of 142 barangays are within 800 m network distance of a branch. This represents 25.4% of barangays but only 14.7% of the city population, indicating that proximate branch access covers a smaller share of residents than of administrative units. In population terms, the 800 m catchment includes 452,646 residents, leaving most residents outside the main walking-access threshold.
Coverage expands substantially when wider network-distance bands are considered, but the broader pattern remains one of constrained pedestrian reach. Within 1,600 m, 93 barangays and 1,534,802 residents are covered, equivalent to 65.5% of barangays and 49.8% of the population. Within 2,400 m, coverage rises to 121 barangays and 2,271,786 residents, or 85.2% of barangays and 73.7% of the population. Even at this wider threshold, however, 21 barangays remain beyond 2,400 m, representing 812,484 residents or 26.3% of the city population. This final group is especially important for planning because it identifies residents whose barangays are not merely outside proximate access but substantially distant from the existing branch network.
Figure 2 maps the network-based accessibility pattern and reinforces the interpretation of Table 2. The figure shows that accessible and underserved barangays are not randomly distributed; rather, branch proximity creates localized zones of relatively strong access while leaving larger peripheral or network-distant areas outside the 800 m threshold. Read together, the table and map show why citywide coverage must be interpreted spatially. A single aggregate percentage would obscure whether low coverage reflects scattered marginal gaps or a more structured geography of under-service.
The key result is therefore not simply that coverage increases as the distance threshold widens. It is that the main walking threshold captures a relatively small share of residents, while a substantial population remains outside even extended network-distance bands. This pattern supports the study’s central claim that evaluating library provision through branch presence or straight-line proximity alone would understate the population-level access gap. Network-based, population-weighted coverage reveals a public-service geography in which library access is present but unevenly distributed.
4.2 Accessibility Inequality and Threshold Sensitivity
The sensitivity results in Table 3 show that the interpretation of limited access is not an artifact of a single 800 m cutoff. A stricter 400 m threshold captures only a very small share of barangays and residents, while the 1,200 m and 1,600 m thresholds expand coverage but still leave substantial populations outside proximate access. The 2,400 m threshold captures most barangays, yet more than one-quarter of the city population remains beyond it. The pattern indicates that the accessibility problem is not confined to marginal cases just outside the main walking standard.
| Network-distance threshold (m) | Barangays covered | Barangays covered (%) | Population covered | Population covered (%) |
|---|---|---|---|---|
| 400 | 15 | 10.6 | 287,912 | 9.3 |
| 800 | 36 | 25.4 | 452,646 | 14.7 |
| 1,200 | 60 | 42.3 | 866,532 | 28.1 |
| 1,600 | 93 | 65.5 | 1,534,802 | 49.8 |
| 2,400 | 121 | 85.2 | 2,271,786 | 73.7 |
The Gini coefficient for barangay network distance is 0.327, indicating moderate inequality in the distribution of distance burden across barangays. The Spearman correlation between barangay population and network distance is 0.223, suggesting that population concentration is not strongly aligned with better pedestrian accessibility. In equity terms, this means that high-population barangays are not reliably positioned closer to QCPL branches.
Table 4 identifies the barangays with the largest combined burden of population and network distance. This demand-distance index shifts attention from distance alone to the number of residents exposed to that distance. Commonwealth and Batasan Hills are especially important under this diagnostic because their large populations make their accessibility burden much larger than their distance ranking alone would imply.
| Barangay | District | Network distance (m) | Population | Person-km burden |
|---|---|---|---|---|
| Commonwealth | District 2 | 2,857.3 | 215,035 | 614,419 |
| Batasan Hills | District 2 | 3,297.2 | 168,770 | 556,471 |
| Pasong Tamo | District 6 | 2,119.2 | 113,319 | 240,149 |
| Sauyo | District 6 | 2,771.7 | 77,274 | 214,183 |
| Pasong Putik Proper (Pasong Putik) | District 5 | 5,148.0 | 40,919 | 210,652 |
| Tandang Sora | District 6 | 2,372.6 | 86,005 | 204,053 |
| Bagong Silangan | District 2 | 1,672.6 | 113,572 | 189,955 |
| Fairview | District 5 | 2,690.5 | 63,913 | 171,959 |
| Payatas | District 2 | 1,209.6 | 141,998 | 171,758 |
| Kaligayahan | District 5 | 2,456.6 | 62,132 | 152,636 |
4.3 District-Level Disparities
District-level results show that limited network-based access is not evenly distributed across Quezon City. As shown in Table 5, population coverage within 800 m ranges from 2.6% in District 5 to 25.0% in District 4. District 3 has the highest barangay coverage within 800 m, with 14 of 37 barangays covered, but its population coverage remains only 24.3%. This gap between barangay counts and population coverage reinforces the need to evaluate district outcomes using both spatial-unit and population-weighted indicators.
| District | Barangays | Population | Barangays within 800 m | Population within 800 m (%) | Underserved barangays | Underserved population |
|---|---|---|---|---|---|---|
| District 1 | 37 | 416,906 | 8 | 22.0 | 29 | 325,248 |
| District 2 | 5 | 752,989 | 1 | 15.1 | 4 | 639,375 |
| District 3 | 37 | 339,527 | 14 | 24.3 | 23 | 256,903 |
| District 4 | 38 | 437,039 | 11 | 25.0 | 27 | 327,629 |
| District 5 | 14 | 610,202 | 1 | 2.6 | 13 | 594,106 |
| District 6 | 11 | 527,607 | 1 | 7.4 | 10 | 488,363 |
The most pronounced disparities are found in Districts 2, 5, and 6. District 5 has the lowest 800 m population coverage, with only 16,096 residents represented within the principal walking threshold and 594,106 residents in underserved barangays. District 6 shows a similar pattern: only one of 11 barangays is within 800 m, and 488,363 residents are represented in underserved barangays. District 2 is distinctive because it contains only five barangays but has the largest affected population in the district summary, with 639,375 residents in barangays beyond the 800 m threshold. These results show why district equity cannot be inferred from barangay counts alone.
Figure 3 visualizes these district differences and supports the interpretation of Table 5. The figure makes clear that the geography of access is not simply a citywide shortage distributed evenly across districts. Instead, the 800 m threshold produces a district pattern in which some districts retain moderate barangay-level access while others have only minimal proximate coverage. The visual contrast is especially important because Districts 5 and 6 combine low 800 m coverage with large affected populations, making them central to any equity-oriented branch planning or outreach strategy.
The district results therefore refine the citywide coverage finding. Overall, only 14.7% of residents are within 800 m network distance of a branch, but the burden of limited access is concentrated unevenly. Districts with large underserved populations should not be interpreted merely as having lower numerical coverage; they represent areas where the spatial arrangement of branches and the distribution of residents combine to produce a larger public-service equity gap.
4.4 Statistical Diagnostics
The inferential diagnostics in Table 6 support the descriptive interpretation without extending the study into causal explanation. The population-distance association is positive and statistically significant: Spearman’s \(\rho\) is 0.223 (0.008). This means that larger barangays tend, on average, to have longer network distances to the nearest QCPL branch. The relationship is modest, but its direction is important for equity interpretation because population concentration is not being offset by systematically better branch proximity.
The paired distance tests provide stronger evidence for the methodological claim. Network distances are significantly greater than geodesic distances under both the paired \(t\) test and Wilcoxon signed-rank test. The mean network-to-geodesic ratio is 1.79, and the median ratio is 1.48, indicating that straight-line measures substantially understate pedestrian-network burden for the typical barangay.
The district-level Kruskal-Wallis test is also statistically significant, indicating that network-distance distributions differ across districts. This result supports the claim that accessibility burden is unevenly distributed across Quezon City’s district geography. It should not be interpreted as a formal spatial-clustering result, because the test compares district groups rather than adjacency-based spatial dependence.
| Hypothesis / diagnostic | Test | Statistic | p value |
|---|---|---|---|
| Population demand vs. network distance | Spearman rank correlation | rho = 0.223 | 0.008 |
| Population demand vs. network distance | Pearson correlation | r = 0.244 | 0.003 |
| Network distance > geodesic distance | Paired t test | t(141) = 14.03 | < .001 |
| Network distance > geodesic distance | Wilcoxon signed-rank test | V = 10,131 | < .001 |
| District differences in network distance | Kruskal-Wallis rank-sum test | chi-square(5) = 12.89 | 0.024 |
Table 7 reports the district-level distance distributions behind the Kruskal-Wallis result. District 5 has the highest mean network distance and the highest median network distance, while District 3 has the lowest median. District 2 has only five barangays, so its distance results should be interpreted alongside its unusually large affected population rather than as a stable distributional estimate.
| District | Barangays | Median network distance (m) | Mean network distance (m) |
|---|---|---|---|
| District 1 | 37 | 1,275.3 | 1,442.0 |
| District 2 | 5 | 1,672.6 | 1,863.7 |
| District 3 | 37 | 1,026.6 | 1,085.7 |
| District 4 | 38 | 1,258.8 | 1,455.5 |
| District 5 | 14 | 1,779.9 | 2,026.4 |
| District 6 | 11 | 1,421.9 | 1,648.9 |
4.5 Spatial Clustering of Accessibility Burden
The spatial clustering diagnostics strengthen the district and cartographic interpretation by testing whether accessibility burden is spatially structured across adjacent barangays. The queen-contiguity weights matrix links each barangay to boundary-touching neighbors and contains no isolated barangays; the mean number of neighbors is 5.6. As shown in Table 8, both nearest-branch network distance and the population-distance burden index show strong positive global spatial autocorrelation. The permutation results are consistent with the analytical Moran tests, indicating that high-burden and low-burden barangays are not randomly arranged across Quezon City.
| Outcome | Moran’s I | Expected I | Analytical p value | Permutation p value |
|---|---|---|---|---|
| Nearest-branch network distance | 0.527 | -0.007 | < .001 | 0.001 |
| Population-distance burden | 0.525 | -0.007 | < .001 | 0.001 |
Local Moran’s I identifies 12 high-high burden clusters and 3 spatial outliers at the nominal 0.05 level (Table 9). No low-low burden clusters are detected under this specification. The high-high cluster classification means that a barangay with high population-distance burden is surrounded by barangays that also have high burden. These clusters are concentrated in the northern part of the city, especially across Districts 2, 5, and 6, where large populations and long network distances coincide.
| Cluster type | Barangays | |
|---|---|---|
| 3 | Not significant | 127 |
| 1 | High-high burden cluster | 12 |
| 2 | Low-high spatial outlier | 3 |
Figure 4 shows that the Local Moran’s I result is not dispersed across the city as isolated significant barangays. Instead, the significant high-high classifications form a contiguous northern pattern, indicating that the highest population-distance burdens occur near other high-burden barangays. This is substantively important because it shifts the interpretation from individual barangay remoteness to a broader area of clustered service disadvantage. The low-high outliers shown adjacent to this cluster should also be read carefully: they do not negate the surrounding burden pattern, but indicate barangays whose own measured burden is lower than that of neighboring high-burden areas.
Table 10 lists the barangays driving the Local Moran’s I result. Payatas, Commonwealth, Batasan Hills, Bagong Silangan, Fairview, Pasong Putik Proper, Sauyo, Pasong Tamo, Tandang Sora, North Fairview, and nearby barangays form the most policy-relevant high-high cluster. Holy Spirit, Talipapa, and Greater Lagro appear as low-high spatial outliers because their own burden is lower than adjacent high-burden surroundings; this pattern is consistent with the presence of local access points or shorter nearest-branch network distances within a wider high-burden zone.
| Barangay | District | Network distance (m) | Population | Person-km burden | LISA class | Local I | p value | BH q value |
|---|---|---|---|---|---|---|---|---|
| Payatas | District 2 | 1,209.6 | 141,998 | 171,758 | High-high burden cluster | 7.215 | < .001 | < .001 |
| Holy Spirit | District 2 | 282.0 | 113,614 | 32,044 | Low-high spatial outlier | -0.275 | < .001 | < .001 |
| Commonwealth | District 2 | 2,857.3 | 215,035 | 614,419 | High-high burden cluster | 16.705 | < .001 | < .001 |
| Batasan Hills | District 2 | 3,297.2 | 168,770 | 556,471 | High-high burden cluster | 14.359 | < .001 | < .001 |
| Bagong Silangan | District 2 | 1,672.6 | 113,572 | 189,955 | High-high burden cluster | 6.351 | < .001 | < .001 |
| Fairview | District 5 | 2,690.5 | 63,913 | 171,959 | High-high burden cluster | 3.395 | < .001 | < .001 |
| Pasong Putik Proper (Pasong Putik) | District 5 | 5,148.0 | 40,919 | 210,652 | High-high burden cluster | 4.234 | < .001 | < .001 |
| Matandang Balara | District 3 | 1,327.3 | 69,667 | 92,469 | High-high burden cluster | 0.909 | < .001 | 0.004 |
| Sauyo | District 6 | 2,771.7 | 77,274 | 214,183 | High-high burden cluster | 2.433 | < .001 | 0.013 |
| Pasong Tamo | District 6 | 2,119.2 | 113,319 | 240,149 | High-high burden cluster | 2.602 | 0.003 | 0.049 |
| Talipapa | District 6 | 488.1 | 39,244 | 19,156 | Low-high spatial outlier | -0.268 | 0.010 | 0.127 |
| Greater Lagro | District 5 | 1,546.9 | 24,104 | 37,287 | Low-high spatial outlier | -0.012 | 0.021 | 0.244 |
| Tandang Sora | District 6 | 2,372.6 | 86,005 | 204,053 | High-high burden cluster | 1.939 | 0.027 | 0.298 |
| Santa Lucia | District 5 | 2,613.6 | 28,974 | 75,726 | High-high burden cluster | 0.442 | 0.030 | 0.309 |
| North Fairview | District 5 | 1,803.5 | 47,019 | 84,798 | High-high burden cluster | 0.520 | 0.040 | 0.378 |
Getis-Ord Gi* identifies 15 hot-spot barangays and no cold spots (Table 11). The Gi* result overlaps strongly with the high-high LISA pattern but answers a slightly different question: it identifies barangays embedded in locally high concentrations of accessibility burden rather than classifying high-low and low-high spatial outliers. This makes the Gi* output especially useful for planning communication because it isolates the contiguous hot-spot geography where high population-distance burden is concentrated.
| Cluster type | Barangays | |
|---|---|---|
| 2 | Not significant | 127 |
| 1 | Hot spot | 15 |
| Barangay | District | Network distance (m) | Population | Person-km burden | Gi* class | Gi* z score | p value | BH q value |
|---|---|---|---|---|---|---|---|---|
| Payatas | District 2 | 1,209.6 | 141,998 | 171,758 | Hot spot | 8.93 | < .001 | < .001 |
| Holy Spirit | District 2 | 282.0 | 113,614 | 32,044 | Hot spot | 8.28 | < .001 | < .001 |
| Commonwealth | District 2 | 2,857.3 | 215,035 | 614,419 | Hot spot | 6.77 | < .001 | < .001 |
| Batasan Hills | District 2 | 3,297.2 | 168,770 | 556,471 | Hot spot | 6.15 | < .001 | < .001 |
| Bagong Silangan | District 2 | 1,672.6 | 113,572 | 189,955 | Hot spot | 5.99 | < .001 | < .001 |
| Fairview | District 5 | 2,690.5 | 63,913 | 171,959 | Hot spot | 5.63 | < .001 | < .001 |
| Pasong Putik Proper (Pasong Putik) | District 5 | 5,148.0 | 40,919 | 210,652 | Hot spot | 5.49 | < .001 | < .001 |
| Matandang Balara | District 3 | 1,327.3 | 69,667 | 92,469 | Hot spot | 3.67 | < .001 | 0.004 |
| Sauyo | District 6 | 2,771.7 | 77,274 | 214,183 | Hot spot | 3.34 | < .001 | 0.013 |
| Pasong Tamo | District 6 | 2,119.2 | 113,319 | 240,149 | Hot spot | 2.93 | 0.003 | 0.049 |
| Talipapa | District 6 | 488.1 | 39,244 | 19,156 | Hot spot | 2.58 | 0.010 | 0.127 |
| Greater Lagro | District 5 | 1,546.9 | 24,104 | 37,287 | Hot spot | 2.31 | 0.021 | 0.244 |
| Tandang Sora | District 6 | 2,372.6 | 86,005 | 204,053 | Hot spot | 2.21 | 0.027 | 0.298 |
| Santa Lucia | District 5 | 2,613.6 | 28,974 | 75,726 | Hot spot | 2.16 | 0.030 | 0.309 |
| North Fairview | District 5 | 1,803.5 | 47,019 | 84,798 | Hot spot | 2.05 | 0.040 | 0.378 |
The spatial clustering results elevate the study beyond descriptive coverage mapping. The burden pattern is not only uneven by district and population; it is spatially autocorrelated and locally concentrated. This matters for public-library planning because clustered burden is less likely to be resolved by isolated small adjustments. A northern hot-spot pattern suggests that branch expansion, mobile-library deployment, and pedestrian-network improvements should be evaluated as area-based interventions rather than only as responses to individually distant barangays.
4.6 Underserved Barangays and Priority Areas
The barangay-level results identify 106 barangays beyond the 800 m network-distance threshold, representing 2,631,624 residents. This group should not be treated as homogeneous. Some barangays are just outside the main walking threshold, while others are several kilometers away from their nearest QCPL branch by network distance. The priority question is therefore not only which barangays are underserved, but which combine severe distance burdens with substantial resident populations.
Table 13 lists the ten barangays with the longest network distance to the nearest QCPL branch. Pasong Putik Proper has the largest measured network distance, at 5,148.0 m from the nearest branch. Several other priority barangays exceed 3,000 m, including Horseshoe, Batasan Hills, Paang Bundok, Valencia, and N.S. Amoranto. These distances are far beyond the principal 800 m threshold and remain outside even the 2,400 m extended band used in the coverage analysis.
| Barangay | District | Nearest QCPL branch | Network distance (m) | Population |
|---|---|---|---|---|
| Pasong Putik Proper (Pasong Putik) | District 5 | Payatas Lupang Pangako Branch | 5,148.0 | 40,919 |
| Horseshoe | District 4 | Roxas Branch | 3,499.8 | 3,095 |
| Batasan Hills | District 2 | Holy Spirit Branch | 3,297.2 | 168,770 |
| Paang Bundok | District 1 | Masambong Branch | 3,217.7 | 4,900 |
| Valencia | District 4 | Roxas Branch | 3,102.1 | 14,525 |
| N.S. Amoranto (Gintong Silahis) | District 1 | Masambong Branch | 3,038.5 | 6,061 |
| Salvacion | District 1 | San Isidro Galas Branch | 2,965.4 | 6,861 |
| Pinagkaisahan | District 4 | Quezon City Public Library | 2,895.1 | 5,903 |
| Commonwealth | District 2 | Holy Spirit Branch | 2,857.3 | 215,035 |
| Immaculate Concepcion | District 4 | Tagumpay Branch | 2,843.1 | 8,633 |
The table also shows why prioritization should combine distance and population. Horseshoe has the second-longest network distance but a comparatively small population, while Commonwealth and Batasan Hills combine very large populations with network distances greater than 2,800 m. From an equity-planning perspective, the latter cases carry especially high service implications because they represent large numbers of residents located far beyond the main pedestrian catchment. Similarly, Pasong Putik Proper combines the most severe distance burden with more than 40,000 residents, making it a strong candidate for branch expansion analysis, mobile-library deployment, or targeted outreach.
Figure 6 spatializes the barangay-level underserved pattern. The map reinforces the point that priority areas are not simply the residual spaces between existing branches. Instead, the network-distance classification reveals clusters and outlying barangays where pedestrian access is structurally weak. Read together with Table 13, the figure supports a two-part planning interpretation: some interventions should address the most distant barangays, while others should focus on high-population underserved barangays where even moderate improvements could affect many residents.
The priority-area results sharpen the district-level findings. Districts 2, 5, and 6 contain large underserved populations, but the barangay-level results show where within and across districts the most severe distance burdens occur. This matters because district-level remedies may be too coarse. An equity-oriented response would need to distinguish between high-population barangays requiring expanded service capacity and lower-population but highly distant barangays requiring targeted access interventions.
4.7 Geodesic Overestimation of Pedestrian Access
The geodesic-network comparison shows that straight-line distance substantially understates pedestrian distance to QCPL branches. As summarized in Table 14, the mean geodesic distance across barangays is 918.2 m, while the mean network distance is 1,441.3 m. The mean difference is therefore 523.1 m, with a median difference of 411.4 m. In practical terms, a barangay that appears relatively near a branch in straight-line space may require a substantially longer route through the pedestrian network.
| Metric | Value |
|---|---|
| Mean geodesic distance (m) | 918.2 |
| Mean network distance (m) | 1,441.3 |
| Mean difference (m) | 523.1 |
| Median difference (m) | 411.4 |
| Maximum difference (m) | 2,653.5 |
| Minimum difference (m) | -171.7 |
| Barangays where network distance is >25% longer | 124 |
| Share of barangays where network distance is >25% longer (%) | 87.3 |
| Barangays where network distance is >50% longer | 65 |
| Share of barangays where network distance is >50% longer (%) | 45.8 |
| Barangays where network distance is >100% longer | 27 |
| Share of barangays where network distance is >100% longer (%) | 19.0 |
The scale of overestimation is widespread rather than exceptional. Network distance is more than 25% longer than geodesic distance in 124 barangays, or 87.3% of the city total. In 65 barangays, equivalent to 45.8%, network distance exceeds geodesic distance by more than 50%. In 27 barangays, or 19.0%, the network route is more than double the geodesic distance. The paired tests in Table 6 confirm that this difference is statistically significant rather than a small descriptive artifact. Straight-line distance is therefore not merely a slightly optimistic approximation; for many barangays, it would materially overstate the ease of pedestrian access.
Figure 7 visualizes the spatial pattern of this measurement gap. The figure shows that overestimation varies across barangays, reinforcing the methodological point that geodesic bias is spatially uneven. This unevenness matters for equity analysis because the areas most affected by network detours may also be the areas most likely to be misclassified as adequately served by circular buffers. Read alongside Table 14, the figure demonstrates that the choice of distance metric changes not only the magnitude of measured access but also the spatial interpretation of where access is weak.
The comparison supports the study’s methodological argument. If geodesic distance were used as the primary measure, QCPL branch accessibility would appear substantially stronger than the network-distance results indicate. The difference is not a technical detail confined to measurement; it affects the identification of underserved barangays, the estimation of population coverage, and the prioritization of districts and barangays for service improvement. For pedestrian-oriented public-library planning, network distance therefore provides a more defensible basis for evaluating spatial equity than straight-line proximity alone.
4.8 Research Question and Hypothesis Synthesis
Taken together, the results answer the five research questions and address the four hypotheses. Table 15 summarizes the link between each question, the corresponding hypothesis where applicable, the evidence used, and the resulting interpretation.
| Item | Empirical focus | Key evidence | Conclusion |
|---|---|---|---|
| RQ1 | Distribution of pedestrian network accessibility across barangays | 36 of 142 barangays and 14.7% of residents are within 800 m; barangays remain beyond 2,400 m. | Answered: network accessibility is limited and uneven across barangays. |
| RQ2 / \(H_2\) | Degree to which geodesic distance underestimates pedestrian-network burden | Mean network distance is 1,441.3 m versus 918.2 m geodesic; paired t test p = < .001. | \(H_2\) supported: geodesic distance systematically understates pedestrian-network travel burden. |
| RQ3 / \(H_1\) | Association between network accessibility, population concentration, and district location | Spearman rho between population and network distance is 0.223, p = 0.008; district network-distance distributions differ significantly, Kruskal-Wallis p = 0.024. | \(H_1\) supported: population demand is not aligned with lower burden; district location is also associated with burden. |
| RQ4 / \(H_3\) | Global and local spatial clustering of accessibility burden | Moran’s I for burden = 0.525, permutation p = 0.001; 12 high-high LISA clusters, 3 spatial outliers, and 15 Gi* hot spots are detected. | \(H_3\) supported: accessibility burden is positively spatially autocorrelated and locally clustered. |
| RQ5 / \(H_4\) | Barangays with the greatest population-weighted accessibility burden | The ten highest-burden barangays account for 50.4% of citywide person-kilometer burden; leading cases include Commonwealth, Batasan Hills, and Pasong Putik Proper. | \(H_4\) supported: population-weighted prioritization identifies concentrated high-demand burdens that distance-only rankings would understate. |
This synthesis closes the analytical loop between the study design and the empirical results. The evidence supports all four hypotheses within the study’s operational definition of spatial equity as the unequal distribution of population-weighted accessibility burden. The strongest claims concern pedestrian-network accessibility, demand-location mismatch, geodesic measurement bias, spatial clustering, and concentrated population-distance burden; broader claims about socioeconomic deprivation, realized library use, causal mechanisms, or optimal branch siting remain outside the tested design.
5 Discussion
The findings support the study’s central mechanism: public-library accessibility burden emerges from the misalignment among branch supply, population demand, and network impedance. QCPL branches may be present as civic infrastructure, but their public value is unevenly exposed to residents when the pedestrian network places large populations outside reasonable walking catchments. This is why the difference between barangay coverage and population coverage matters. At 800 m, the branch network covers 25.4% of barangays but only 14.7% of residents, indicating that proximate access is not aligned with where people are concentrated. The positive population-distance correlation reinforces this interpretation: higher population is associated with longer, not shorter, network distance to the nearest branch.
The demand-distance burden results sharpen this interpretation. A distance-only ranking identifies the most remote barangays, while a population-distance ranking identifies where long routes affect the largest number of residents. These are different equity problems. Pasong Putik Proper represents severe distance exclusion; Commonwealth and Batasan Hills represent high-population exposure to long network distance. Treating both conditions as simply “underserved” would flatten the planning problem. Equity-oriented planning needs to distinguish extensive spatial gaps from high-demand service exposure.
The district pattern also suggests that accessibility disadvantage is spatially structured rather than randomly distributed. Districts 2, 5, and 6 contain particularly large underserved populations, while District 5 has the lowest 800 m population coverage and the highest median network-distance burden. The Kruskal-Wallis result strengthens the district comparison by showing that network-distance distributions differ significantly across districts. The spatial autocorrelation results go further: Moran’s I shows that accessibility burden is globally clustered, and Local Moran’s I and Gi* identify a northern high-burden cluster that cuts across district boundaries. This indicates that the accessibility problem is not only a district-level administrative disparity but also a contiguous spatial concentration of population-distance burden.
The geodesic-network comparison strengthens the methodological contribution. Straight-line distance does not merely add harmless measurement noise; it systematically makes pedestrian access appear stronger than the network-distance evidence supports. Mean network distance is more than 500 m longer than mean geodesic distance, and 87.3% of barangays have network distances more than 25% longer than their geodesic equivalents. In planning terms, circular buffers may misclassify areas as adequately served precisely where route structure creates practical barriers.
The results should therefore be read as a strong diagnostic rather than as a final accessibility model. A full service-equity model would include branch capacity, distance decay, competition among barangays for the same branches, multimodal travel, socioeconomic vulnerability, and candidate-site optimization (Delamater, 2013; Luo and Wang, 2003; Tao et al., 2020; Zhu et al., 2018). The present evidence is still policy-relevant because it identifies where those more expensive planning analyses should begin: high-population underserved barangays, districts with large affected populations, spatial hot spots of accessibility burden, and places where geodesic proximity most strongly overstates network access.
5.1 Policy and Planning Implications
The analysis supports a staged decision process rather than a single generic recommendation. Priority setting should distinguish four types of accessibility problems because each implies a different planning response.
| Priority type | Empirical signal | Example from the results | Planning response |
|---|---|---|---|
| Severe distance burden | Very long network distance to nearest branch | Pasong Putik Proper | New branch feasibility review, mobile-library stop, or partner service point |
| High population burden | Large population combined with long network distance | Commonwealth and Batasan Hills | Capacity-sensitive expansion, larger service point, or high-frequency outreach |
| District-level undercoverage | Low coverage and large underserved population | Districts 2, 5, and 6 | District service review and coordinated branch/mobile-library planning |
| High geodesic-network gap | Straight-line proximity strongly understates walking burden | Fragmented-route barangays | Pedestrian links, safer crossings, or route-directness improvements |
First, QCPL and related city agencies should use network-distance diagnostics as the baseline for public-library planning. Circular buffers may remain useful for communication, but they should not be used as the primary evidence for walkable service coverage.
Second, investment screening should combine distance severity and population exposure. Barangays with extreme network distances are candidates for new service points, mobile-library stops, or partnerships with schools and barangay facilities. High-population underserved barangays, especially Commonwealth and Batasan Hills, require a different response: any new or expanded service there would need capacity planning because improved access could generate demand from many residents.
Third, district-level planning should prioritize areas where low coverage, large affected populations, and statistically significant hot spots coincide. Districts 2, 5, and 6 should be treated as priority geographies for feasibility assessment, but district labels should not substitute for barangay-level targeting. The demand-distance burden index and spatial clustering diagnostics provide a more decision-oriented starting point because they identify where marginal improvements could affect the largest exposed populations and where high burden is locally concentrated.
Fourth, pedestrian-network improvement should be evaluated alongside branch expansion. Some areas may be far from branches because of route fragmentation rather than absolute geographic separation. In those cases, safer crossings, more direct pedestrian links, or improved access paths may reduce network impedance without requiring a new branch. The geodesic-network gap helps identify where such route-focused interventions may matter most (Chen and Chen, 2021; Gutierrez Puebla and Garcia Palomares, 2008).
Finally, a second-stage planning model should estimate candidate interventions explicitly. A defensible optimization exercise would require branch capacity, operating cost, land availability, candidate sites, and a complete barangay-to-branch distance matrix. With those inputs, QCPL could compare scenarios such as one new branch, several mobile-library stops, extended hours at existing branches, or pedestrian-network improvements, ranking each by marginal gain in population-weighted accessibility.
5.2 Limitations and Future Research
This study has several limitations. First, the analysis measures potential pedestrian accessibility rather than realized library use. It does not measure actual visits, route choices, user preferences, program participation, or residents’ willingness to walk. The results describe the spatial opportunity structure within which use may occur, not observed library demand.
Second, the analysis is conducted at the barangay scale. Barangay-level origins are appropriate for citywide planning, but they simplify internal variation and may introduce centroid-related positional bias. This is a MAUP and ecological-inference limitation, especially for large or high-population barangays (Buzzelli, 2020; Openshaw, 1984). Future work should use smaller spatial units, population-weighted centroids, building-level population estimates, or multi-node sampling within barangays.
Third, network distance captures route length but not all dimensions of pedestrian accessibility. The available data do not measure sidewalk quality, crossing safety, slope, shade, flooding exposure, traffic stress, perceived security, disability access, or library entrance connectivity. A stronger pedestrian model would weight links by walkability and safety, not only route length.
Fourth, the nearest-facility assumption simplifies library behavior. Residents may bypass the closest branch because of branch size, collections, opening hours, school or work trips, transit access, or familiarity. The nearest-branch model should therefore be interpreted as a first-order accessibility approximation, not as a revealed-choice model of library use.
Fifth, the threshold scheme is transparent but still partly normative. The 800 m threshold is useful as a walkable planning benchmark, and the sensitivity analysis tests alternative cutoffs, but the study does not observe actual walking tolerance among QCPL users. Future work should calibrate thresholds using travel surveys, observed route data, or locally validated walking-time assumptions.
Sixth, the study does not evaluate branch capacity, operating hours, staffing, collections, digital services, or program availability. This prevents estimation of E2SFCA, gravity, or capacity-competition models (Delamater, 2013; Luo and Wang, 2003; Tao et al., 2020). Future research should compile comparable branch-capacity indicators and a complete barangay-to-branch distance matrix so that service pressure and distance decay can be modeled directly.
Seventh, the spatial clustering results depend on the selected spatial weights matrix. This study uses queen contiguity because barangays are polygonal administrative units and shared boundaries are substantively meaningful for neighborhood-scale planning. Alternative specifications, such as rook contiguity, distance bands, or k-nearest-neighbor weights, may alter some local classifications. Future research should test the sensitivity of Moran’s I, Local Moran’s I, and Gi* results to alternative weight definitions.
Finally, the policy implications are directional rather than prescriptive. The analysis identifies underserved districts and barangays, but it does not determine where a new branch should be built or how resources should be allocated. Siting and investment decisions require additional evidence on land availability, costs, institutional capacity, community preferences, multimodal access, socioeconomic vulnerability, and expected service demand.
6 Conclusion
This study has evaluated network-based spatial accessibility to Quezon City Public Library branches as a problem of public-service equity under network constraints. The results show that proximate pedestrian access is limited: only 36 of 142 barangays, representing 452,646 residents or 14.7% of the population, fall within the 800 m network-distance threshold. Although coverage increases at wider thresholds, 21 barangays and 812,484 residents remain beyond 2,400 m.
The analysis also shows that the access gap is structured by demand-supply mismatch. Districts 2, 5, and 6 carry especially large underserved populations, while the demand-distance burden results distinguish severe distance exclusion from high-population exposure to long network routes. This distinction is central to equitable planning because the most distant barangays are not always the barangays where access improvements would affect the largest number of residents.
Methodologically, the study demonstrates that geodesic distance substantially overestimates pedestrian accessibility. Mean network distance is 1,441.3 m compared with a mean geodesic distance of 918.2 m, and 87.3% of barangays have network distances more than 25% longer than their geodesic equivalents. The paired statistical tests confirm that this is a systematic measurement difference. The district test and population-distance correlation further show that accessibility burden is unevenly distributed and modestly misaligned with population demand.
The spatial clustering diagnostics show that accessibility burden is not merely uneven; it is spatially concentrated. Moran’s I confirms positive spatial autocorrelation, while Local Moran’s I and Getis-Ord Gi* identify a northern high-burden cluster involving high-population and network-distant barangays. This clustering result strengthens the planning implication because it points to an area-based accessibility problem rather than a set of isolated barangay anomalies.
The research questions are therefore answered through a linked sequence of descriptive, comparative, relational, spatial-statistical, and prioritization results. The hypotheses are also addressed: \(H_1\) is supported by the positive population-distance association, \(H_2\) by the paired geodesic-network tests, \(H_3\) by the Moran’s I, LISA, and Gi* diagnostics, and \(H_4\) by the concentration of population-distance burden among the highest-burden barangays. The district-level Kruskal-Wallis test provides additional relational evidence for RQ3 by showing that accessibility burden differs across district location.
The study’s broader contribution is to move public-library planning from simple coverage mapping toward a network-constrained, population-weighted, and spatially explicit equity diagnostic for a Global South urban context. The analysis remains short of a full capacity-sensitive, vulnerability-sensitive, or optimization-based model, but it establishes where such planning should begin: high-burden barangays, districts with concentrated underserved populations, spatial hot spots of accessibility burden, and areas where straight-line proximity most strongly misrepresents pedestrian access.
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