Import Data

nodes=read.csv("nodes_airlines.csv")
edges=read.csv("edges_airlines.csv") 
library(igraph)
## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union
library(ggraph)
## Loading required package: ggplot2
library(tidygraph)
## 
## Attaching package: 'tidygraph'
## The following object is masked from 'package:igraph':
## 
##     groups
## The following object is masked from 'package:stats':
## 
##     filter
library(visNetwork)
library(maps)

Plotting Edges Network

g1=graph_from_data_frame(edges)
plot(g1)

network1=graph_from_data_frame(d=edges,vertices=nodes,directed=T)
plot(network1)

Mapping United States and adding Airport Nodes

map("world", regions=c("usa"), fill=T, col="white", bg="white", ylim=c(21.0,50.0), xlim=c(-130.0,-65.0))
points(nodes$longitude,nodes$latitude, pch=3, cex=0.1, col="red")

Interactive Graph

node_labels <- nodes$Code
vis_net <- toVisNetworkData(network1)
visNetwork(vis_net$nodes, vis_net$edges) %>%
  visEdges(arrows = "to") %>%
  visNodes(label = node_labels)%>%
  visLayout(randomSeed = 456)

Circular Layout

tidy_net <- as_tbl_graph(network1)
ggraph(tidy_net, layout = "circle") +
  geom_edge_link() +
  geom_node_point() +
  geom_node_text(aes(label = Code), vjust = 1.5) +
  theme_void()
## Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Centrality Measures

degree_centrality_net <- degree(network1, mode = "all", normalized = TRUE)
print(degree_centrality_net)
##           0           1           2           3           4           5 
## 0.042735043 0.021367521 0.042735043 0.008547009 0.034188034 0.012820513 
##           6           7           8           9          10          11 
## 0.008547009 0.012820513 0.025641026 0.076923077 0.072649573 0.076923077 
##          12          13          14          15          16          17 
## 0.017094017 0.021367521 0.025641026 0.004273504 0.004273504 0.008547009 
##          18          19          20          21          22          23 
## 0.055555556 0.047008547 0.051282051 0.034188034 0.055555556 0.008547009 
##          24          25          26          27          28          29 
## 0.055555556 0.055555556 0.012820513 0.042735043 0.025641026 0.004273504 
##          30          31          32          33          34          35 
## 0.047008547 0.025641026 0.012820513 0.008547009 0.034188034 0.076923077 
##          36          37          38          39          40          41 
## 0.038461538 0.094017094 0.012820513 0.008547009 0.008547009 0.324786325 
##          42          43          44          45          46          47 
## 0.004273504 0.025641026 0.089743590 0.094017094 0.008547009 0.004273504 
##          48          49          50          51          52          53 
## 0.085470085 0.081196581 0.534188034 0.012820513 0.004273504 0.055555556 
##          54          55          56          57          58          59 
## 0.008547009 0.025641026 0.012820513 0.008547009 0.004273504 0.064102564 
##          60          61          62          63          64          65 
## 0.008547009 0.051282051 0.008547009 0.025641026 0.008547009 0.055555556 
##          66          67          68          69          70          71 
## 0.012820513 0.004273504 0.038461538 0.094017094 0.346153846 0.021367521 
##          72          73          74          75          76          77 
## 0.029914530 0.004273504 0.025641026 0.055555556 0.008547009 0.064102564 
##          78          79          80          81          82          83 
## 0.025641026 0.029914530 0.478632479 0.008547009 0.068376068 0.025641026 
##          84          85          86          87          88          89 
## 0.260683761 0.012820513 0.051282051 0.158119658 0.025641026 0.004273504 
##          90          91          92          93          94          95 
## 0.029914530 0.012820513 0.025641026 0.042735043 0.004273504 0.034188034 
##          96          97          98          99         100         101 
## 0.055555556 0.055555556 0.047008547 0.012820513 0.004273504 0.029914530 
##         102         103         104         105         106         107 
## 0.059829060 0.042735043 0.042735043 0.102564103 0.111111111 0.004273504 
##         108         109         110         111         112         113 
## 0.004273504 0.102564103 0.017094017 0.085470085 0.017094017 0.008547009 
##         114         115         116         117         118         119 
## 0.017094017 0.072649573 0.004273504 0.008547009 0.128205128 0.055555556 
##         120         121         122         123         124         125 
## 0.076923077 0.004273504 0.025641026 0.034188034 0.008547009 0.038461538 
##         126         127         128         129         130         131 
## 0.004273504 0.081196581 0.081196581 0.004273504 0.384615385 0.034188034 
##         132         133         134         135         136         137 
## 0.064102564 0.021367521 0.068376068 0.042735043 0.555555556 0.017094017 
##         138         139         140         141         142         143 
## 0.021367521 0.004273504 0.008547009 0.017094017 0.004273504 0.004273504 
##         144         145         146         147         148         149 
## 0.004273504 0.025641026 0.021367521 0.008547009 0.012820513 0.021367521 
##         150         151         152         153         154         155 
## 0.012820513 0.008547009 0.085470085 0.004273504 0.316239316 0.004273504 
##         156         157         158         159         160         161 
## 0.008547009 0.047008547 0.004273504 0.042735043 0.021367521 0.008547009 
##         162         163         164         165         166         167 
## 0.021367521 0.072649573 0.042735043 0.034188034 0.004273504 0.004273504 
##         168         169         170         171         172         173 
## 0.094017094 0.051282051 0.008547009 0.076923077 0.098290598 0.153846154 
##         174         175         176         177         178         179 
## 0.008547009 0.034188034 0.076923077 0.012820513 0.008547009 0.025641026 
##         180         181         182         183         184         185 
## 0.034188034 0.029914530 0.029914530 0.025641026 0.004273504 0.059829060 
##         186         187         188         189         190         191 
## 0.017094017 0.008547009 0.012820513 0.106837607 0.029914530 0.042735043 
##         192         193         194         195         196         197 
## 0.213675214 0.047008547 0.064102564 0.076923077 0.004273504 0.021367521 
##         198         199         200         201         202         203 
## 0.034188034 0.012820513 0.235042735 0.008547009 0.012820513 0.076923077 
##         204         205         206         207         208         209 
## 0.034188034 0.059829060 0.029914530 0.042735043 0.017094017 0.004273504 
##         210         211         212         213         214         215 
## 0.038461538 0.038461538 0.029914530 0.059829060 0.008547009 0.021367521 
##         216         217         218         219         220         221 
## 0.012820513 0.025641026 0.029914530 0.051282051 0.004273504 0.021367521 
##         222         223         224         225         226         227 
## 0.004273504 0.059829060 0.017094017 0.008547009 0.021367521 0.008547009 
##         228         229         230         231         232         233 
## 0.012820513 0.051282051 0.008547009 0.004273504 0.004273504 0.008547009 
##         234 
## 0.008547009
closeness_centrality_net <- closeness(network1, mode = "all", normalized = TRUE)
print(closeness_centrality_net)
##         0         1         2         3         4         5         6         7 
## 0.4756098 0.4382022 0.4689379 0.4006849 0.4543689 0.4134276 0.4000000 0.3567073 
##         8         9        10        11        12        13        14        15 
## 0.4642857 0.4905660 0.4864865 0.4915966 0.4048443 0.3836066 0.4216216 0.3622291 
##        16        17        18        19        20        21        22        23 
## 0.4098074 0.3644860 0.4804928 0.4552529 0.4698795 0.4246824 0.4552529 0.3667712 
##        24        25        26        27        28        29        30        31 
## 0.4448669 0.4785276 0.4112478 0.4689379 0.4148936 0.3972835 0.4534884 0.4440228 
##        32        33        34        35        36        37        38        39 
## 0.4006849 0.4390244 0.4736842 0.4834711 0.4482759 0.4989339 0.4027539 0.4105263 
##        40        41        42        43        44        45        46        47 
## 0.4105263 0.5835411 0.3250000 0.4500000 0.4957627 0.4895397 0.3817292 0.3250000 
##        48        49        50        51        52        53        54        55 
## 0.5120350 0.4885177 0.6628895 0.4112478 0.3972835 0.4597250 0.4112478 0.4223827 
##        56        57        58        59        60        61        62        63 
## 0.4193548 0.4000000 0.3993174 0.4775510 0.3667712 0.4431818 0.4105263 0.4309392 
##        64        65        66        67        68        69        70        71 
## 0.4105263 0.4947146 0.3768116 0.3972835 0.4633663 0.5142857 0.5939086 0.4317343 
##        72        73        74        75        76        77        78        79 
## 0.4440228 0.3993174 0.4457143 0.4717742 0.3842365 0.4615385 0.4277879 0.4727273 
##        80        81        82        83        84        85        86        87 
## 0.6573034 0.3817292 0.4606299 0.4333333 0.5611511 0.4186047 0.4579256 0.5154185 
##        88        89        90        91        92        93        94        95 
## 0.4069565 0.3250000 0.4341373 0.3986371 0.4534884 0.4465649 0.3250000 0.4423440 
##        96        97        98        99       100       101       102       103 
## 0.4561404 0.4746450 0.4698795 0.4112478 0.3732057 0.4570312 0.4844720 0.4606299 
##       104       105       106       107       108       109       110       111 
## 0.4500000 0.4936709 0.4968153 0.3972835 0.3357245 0.5154185 0.4193548 0.4885177 
##       112       113       114       115       116       117       118       119 
## 0.4034483 0.3817292 0.4423440 0.4915966 0.3622291 0.3979592 0.5258427 0.4824742 
##       120       121       122       123       124       125       126       127 
## 0.4834711 0.3732057 0.4231465 0.4423440 0.4105263 0.4680000 0.3732057 0.5131579 
##       128       129       130       131       132       133       134       135 
## 0.4885177 0.3972835 0.6141732 0.4491363 0.4915966 0.4431818 0.4775510 0.4736842 
##       136       137       138       139       140       141       142       143 
## 0.6923077 0.4309392 0.4178571 0.3451327 0.4105263 0.4141593 0.3732057 0.3250000 
##       144       145       146       147       148       149       150       151 
## 0.3250000 0.4027539 0.4301471 0.4105263 0.3768116 0.4020619 0.4027539 0.4390244 
##       152       153       154       155       156       157       158       159 
## 0.4926316 0.4098074 0.5835411 0.3972835 0.3639191 0.4736842 0.3357245 0.4698795 
##       160       161       162       163       164       165       166       167 
## 0.4365672 0.4105263 0.4365672 0.4947146 0.4689379 0.4457143 0.3622291 0.3357245 
##       168       169       170       171       172       173       174       175 
## 0.4947146 0.4814815 0.4105263 0.4875000 0.4957627 0.5043103 0.3639191 0.4597250 
##       176       177       178       179       180       181       182       183 
## 0.5043103 0.3567073 0.4027539 0.3972835 0.4309392 0.4526112 0.4406780 0.4398496 
##       184       185       186       187       188       189       190       191 
## 0.3250000 0.4795082 0.4341373 0.3667712 0.3714286 0.5200000 0.4317343 0.4936709 
##       192       193       194       195       196       197       198       199 
## 0.5518868 0.4968153 0.4885177 0.5053996 0.3451327 0.4357542 0.4775510 0.4398496 
##       200       201       202       203       204       205       206       207 
## 0.5665860 0.3817292 0.4112478 0.5098039 0.4661355 0.4936709 0.4333333 0.4689379 
##       208       209       210       211       212       213       214       215 
## 0.4055459 0.3622291 0.4680000 0.4270073 0.4262295 0.4834711 0.4055459 0.4020619 
##       216       217       218       219       220       221       222       223 
## 0.3762058 0.4293578 0.4543689 0.4814815 0.3993174 0.4083770 0.3622291 0.4864865 
##       224       225       226       227       228       229       230       231 
## 0.4134276 0.4105263 0.4440228 0.4006849 0.4223827 0.4814815 0.4027539 0.3972835 
##       232       233       234 
## 0.3622291 0.4119718 0.4000000
betweenness_centrality_net <- betweenness(network1, directed = TRUE, normalized = TRUE)
print(betweenness_centrality_net)
##            0            1            2            3            4            5 
## 2.372518e-03 7.636180e-04 1.584588e-03 4.929799e-04 9.375953e-04 2.541930e-03 
##            6            7            8            9           10           11 
## 0.000000e+00 4.464886e-03 1.706959e-03 5.647612e-03 6.506187e-03 9.056403e-03 
##           12           13           14           15           16           17 
## 1.494465e-02 3.788040e-03 3.415714e-03 0.000000e+00 0.000000e+00 0.000000e+00 
##           18           19           20           21           22           23 
## 2.510214e-02 4.486087e-03 2.772675e-03 2.686726e-03 1.420158e-02 0.000000e+00 
##           24           25           26           27           28           29 
## 1.399180e-02 8.925483e-04 0.000000e+00 1.216150e-02 1.014753e-03 0.000000e+00 
##           30           31           32           33           34           35 
## 5.358465e-03 1.058450e-03 0.000000e+00 0.000000e+00 8.145941e-04 4.608668e-03 
##           36           37           38           39           40           41 
## 3.266723e-03 1.559798e-02 7.747927e-04 0.000000e+00 0.000000e+00 4.405968e-02 
##           42           43           44           45           46           47 
## 0.000000e+00 1.821386e-03 1.230221e-02 1.993564e-02 0.000000e+00 0.000000e+00 
##           48           49           50           51           52           53 
## 5.352091e-03 1.564625e-02 1.122768e-01 3.668244e-05 0.000000e+00 5.885745e-03 
##           54           55           56           57           58           59 
## 0.000000e+00 1.911561e-04 2.248733e-03 0.000000e+00 0.000000e+00 5.740056e-03 
##           60           61           62           63           64           65 
## 0.000000e+00 7.392187e-03 0.000000e+00 3.616889e-03 0.000000e+00 5.608091e-03 
##           66           67           68           69           70           71 
## 0.000000e+00 0.000000e+00 3.033808e-03 1.388372e-02 5.370723e-02 5.706186e-04 
##           72           73           74           75           76           77 
## 1.580691e-04 0.000000e+00 1.865079e-03 2.801463e-03 0.000000e+00 5.557765e-03 
##           78           79           80           81           82           83 
## 7.527634e-04 1.437509e-04 1.062795e-01 0.000000e+00 5.113746e-03 5.180160e-04 
##           84           85           86           87           88           89 
## 4.773755e-02 1.867389e-04 9.915413e-04 1.669120e-02 1.436729e-04 0.000000e+00 
##           90           91           92           93           94           95 
## 1.319484e-04 0.000000e+00 6.624054e-04 1.693794e-03 0.000000e+00 7.521704e-05 
##           96           97           98           99          100          101 
## 5.208285e-03 1.982989e-03 2.010302e-03 9.170610e-06 0.000000e+00 9.318198e-04 
##          102          103          104          105          106          107 
## 2.428867e-03 4.784379e-04 6.809222e-03 9.209185e-03 1.164343e-02 0.000000e+00 
##          108          109          110          111          112          113 
## 0.000000e+00 1.936824e-02 0.000000e+00 9.269581e-03 2.997757e-03 0.000000e+00 
##          114          115          116          117          118          119 
## 9.523229e-05 1.522196e-02 0.000000e+00 0.000000e+00 2.479915e-02 2.751874e-03 
##          120          121          122          123          124          125 
## 6.982198e-03 0.000000e+00 3.313075e-03 3.409336e-03 0.000000e+00 8.885425e-04 
##          126          127          128          129          130          131 
## 0.000000e+00 2.291268e-03 6.338585e-03 0.000000e+00 1.048652e-01 3.975896e-03 
##          132          133          134          135          136          137 
## 7.954682e-03 2.020435e-03 8.381849e-03 2.255385e-04 1.468414e-01 2.215415e-04 
##          138          139          140          141          142          143 
## 4.728212e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##          144          145          146          147          148          149 
## 0.000000e+00 1.575904e-03 1.491980e-03 0.000000e+00 0.000000e+00 1.146157e-03 
##          150          151          152          153          154          155 
## 0.000000e+00 0.000000e+00 9.414358e-03 0.000000e+00 3.141194e-02 0.000000e+00 
##          156          157          158          159          160          161 
## 0.000000e+00 3.221191e-03 0.000000e+00 1.387858e-03 0.000000e+00 0.000000e+00 
##          162          163          164          165          166          167 
## 0.000000e+00 0.000000e+00 8.961235e-03 0.000000e+00 0.000000e+00 0.000000e+00 
##          168          169          170          171          172          173 
## 1.295569e-02 2.826099e-03 0.000000e+00 3.212118e-03 1.971671e-02 2.850949e-02 
##          174          175          176          177          178          179 
## 0.000000e+00 1.587206e-03 1.020936e-02 1.094553e-04 0.000000e+00 8.428648e-03 
##          180          181          182          183          184          185 
## 5.223013e-03 3.135598e-03 2.090438e-03 0.000000e+00 0.000000e+00 4.755451e-03 
##          186          187          188          189          190          191 
## 2.311918e-05 0.000000e+00 0.000000e+00 4.793957e-03 1.075538e-03 5.089891e-03 
##          192          193          194          195          196          197 
## 3.215780e-02 3.067820e-03 2.259175e-03 1.469593e-03 0.000000e+00 3.068035e-04 
##          198          199          200          201          202          203 
## 2.804434e-03 0.000000e+00 5.659473e-02 0.000000e+00 0.000000e+00 2.212609e-02 
##          204          205          206          207          208          209 
## 1.465119e-02 6.458850e-03 2.748767e-03 8.839685e-04 4.590094e-04 0.000000e+00 
##          210          211          212          213          214          215 
## 1.848105e-03 1.528875e-03 3.994359e-04 2.975317e-03 3.402056e-05 1.146169e-04 
##          216          217          218          219          220          221 
## 0.000000e+00 4.127253e-03 0.000000e+00 3.862067e-03 0.000000e+00 4.507494e-05 
##          222          223          224          225          226          227 
## 0.000000e+00 8.786504e-03 6.581045e-04 0.000000e+00 1.664846e-03 0.000000e+00 
##          228          229          230          231          232          233 
## 0.000000e+00 4.820933e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 
##          234 
## 0.000000e+00
pagerank_centrality_net <- page_rank(network1)$vector
print(pagerank_centrality_net)
##            0            1            2            3            4            5 
## 0.0061074752 0.0036528199 0.0071523919 0.0023392159 0.0048561105 0.0017803882 
##            6            7            8            9           10           11 
## 0.0033333827 0.0014295547 0.0042401911 0.0109927363 0.0067398683 0.0165033089 
##           12           13           14           15           16           17 
## 0.0030190672 0.0033734551 0.0023441386 0.0008823592 0.0009974990 0.0019787700 
##           18           19           20           21           22           23 
## 0.0077618008 0.0082233631 0.0060649941 0.0044354834 0.0090825680 0.0011104706 
##           24           25           26           27           28           29 
## 0.0094237466 0.0091605461 0.0032603403 0.0054438086 0.0049631026 0.0013980807 
##           30           31           32           33           34           35 
## 0.0059465589 0.0047391165 0.0027574212 0.0025484760 0.0042404735 0.0129657687 
##           36           37           38           39           40           41 
## 0.0066610017 0.0115507476 0.0023392159 0.0013325006 0.0018453732 0.0348829939 
##           42           43           44           45           46           47 
## 0.0007882390 0.0044260434 0.0139672023 0.0127824277 0.0024805930 0.0007882390 
##           48           49           50           51           52           53 
## 0.0104230697 0.0088220073 0.0547403617 0.0013296656 0.0013980807 0.0058232389 
##           54           55           56           57           58           59 
## 0.0014847577 0.0021355628 0.0026646314 0.0011955646 0.0007882390 0.0057080253 
##           60           61           62           63           64           65 
## 0.0011104706 0.0059648119 0.0009974990 0.0057445377 0.0018453732 0.0056853809 
##           66           67           68           69           70           71 
## 0.0016667258 0.0013980807 0.0051595804 0.0161040726 0.0312912537 0.0036090945 
##           72           73           74           75           76           77 
## 0.0015631367 0.0007882390 0.0031056063 0.0035559265 0.0011705465 0.0105957631 
##           78           79           80           81           82           83 
## 0.0065146082 0.0039430334 0.0315682747 0.0011705465 0.0061003820 0.0033037585 
##           84           85           86           87           88           89 
## 0.0225620268 0.0017012614 0.0033030079 0.0111023321 0.0011955646 0.0007882390 
##           90           91           92           93           94           95 
## 0.0018244815 0.0023062404 0.0031587769 0.0033117030 0.0007882390 0.0023055196 
##           96           97           98           99          100          101 
## 0.0027109882 0.0034420005 0.0026738070 0.0013325006 0.0007882390 0.0026070734 
##          102          103          104          105          106          107 
## 0.0025488139 0.0050263976 0.0056007428 0.0079325412 0.0162828314 0.0007882390 
##          108          109          110          111          112          113 
## 0.0010163504 0.0092361336 0.0011705465 0.0083015072 0.0042831683 0.0015055481 
##          114          115          116          117          118          119 
## 0.0012956525 0.0051592091 0.0008823592 0.0007882390 0.0075448908 0.0045298842 
##          120          121          122          123          124          125 
## 0.0075333840 0.0007882390 0.0027202299 0.0054347776 0.0009974990 0.0056351887 
##          126          127          128          129          130          131 
## 0.0007882390 0.0028759418 0.0066323583 0.0007882390 0.0233882220 0.0047953922 
##          132          133          134          135          136          137 
## 0.0063283015 0.0030824624 0.0060442153 0.0023684403 0.0199412508 0.0010254101 
##          138          139          140          141          142          143 
## 0.0025481456 0.0007882390 0.0007882390 0.0007882390 0.0007882390 0.0007882390 
##          144          145          146          147          148          149 
## 0.0007882390 0.0030927856 0.0019358365 0.0010115734 0.0010254101 0.0013682440 
##          150          151          152          153          154          155 
## 0.0019804385 0.0007882390 0.0107634243 0.0007882390 0.0142578840 0.0007882390 
##          156          157          158          159          160          161 
## 0.0008823592 0.0048189974 0.0010163504 0.0019843854 0.0012535215 0.0007882390 
##          162          163          164          165          166          167 
## 0.0012535215 0.0007882390 0.0030532863 0.0007882390 0.0008823592 0.0010163504 
##          168          169          170          171          172          173 
## 0.0083342141 0.0028779725 0.0011232406 0.0032512617 0.0062677886 0.0056356934 
##          174          175          176          177          178          179 
## 0.0008823592 0.0025271617 0.0039789989 0.0013957998 0.0007882390 0.0044227847 
##          180          181          182          183          184          185 
## 0.0037923738 0.0033574568 0.0030587121 0.0010254101 0.0007882390 0.0035076882 
##          186          187          188          189          190          191 
## 0.0011955646 0.0008823592 0.0008823592 0.0021928386 0.0015553479 0.0050863663 
##          192          193          194          195          196          197 
## 0.0062269209 0.0029364878 0.0017128919 0.0014667005 0.0007882390 0.0020155059 
##          198          199          200          201          202          203 
## 0.0020547897 0.0007882390 0.0049828332 0.0007882390 0.0007882390 0.0045630888 
##          204          205          206          207          208          209 
## 0.0033544461 0.0037439020 0.0019963824 0.0017071641 0.0011434137 0.0007882390 
##          210          211          212          213          214          215 
## 0.0013851682 0.0026048471 0.0016762039 0.0040180647 0.0022001697 0.0015003198 
##          216          217          218          219          220          221 
## 0.0007882390 0.0032414107 0.0007882390 0.0035937791 0.0007882390 0.0010115734 
##          222          223          224          225          226          227 
## 0.0007882390 0.0039707086 0.0016613679 0.0007882390 0.0028188888 0.0007882390 
##          228          229          230          231          232          233 
## 0.0007882390 0.0034829413 0.0013780504 0.0007882390 0.0007882390 0.0007882390 
##          234 
## 0.0007882390