Datacamp audition
Minoo Ashtiani
jafarilab.com, Pasteur Institute of Iran
January 23, 2018
Centrality Analysis
- What is centrality analysis?
- Which node is the most important and why?
- Which centrality measure can best fit on your complex network topology?
Centrality measures
- A function that assigns a numerical value to each vertex of a network is called centrality
- Let \(G = (V, E)\) be a directed or undirected graph. A function \(C: V\rightarrow R\) is called a centrality.
Centrality measure types
Generate a simple random graph:
library(igraph)# n = number of nodes, m = the number of edges
erdos.gr <- sample_gnm(n=100, m=200)
erdos.gr## IGRAPH f8c91a6 U--- 100 200 -- Erdos renyi (gnm) graph
## + attr: name (g/c), type (g/c), loops (g/l), m (g/n)
## + edges from f8c91a6:
## [1] 1-- 7 3--11 2--12 8--12 8--15 7--16 14--20 17--21 14--22 6--23
## [11] 8--23 4--24 5--24 3--26 23--28 8--29 11--30 18--30 3--31 18--31
## [21] 16--32 11--33 15--34 13--35 12--36 11--37 4--38 17--38 20--39 4--40
## [31] 14--40 24--40 36--40 5--41 28--41 4--42 21--42 32--42 1--43 29--45
## [41] 38--45 17--47 19--47 14--48 28--48 4--49 9--49 19--49 3--50 10--50
## [51] 12--50 15--51 18--51 19--51 6--52 28--52 8--53 27--53 40--53 31--54
## [61] 35--55 47--55 4--56 16--56 46--56 8--57 34--57 21--58 31--58 45--58
## [71] 23--59 34--59 17--60 34--60 5--61 26--61 30--61 37--62 54--62 55--62
## + ... omitted several edgesLocal centrality measures
- Degree centrality
degree.cent <- degree(erdos.gr, mode = "all")
degree.cent## [1] 2 1 4 7 6 4 4 8 3 4 5 7 3 5 5 5 4 7 3 4 3 2 5 7 0 5 2 6 4 4 6 4 2 5 4
## [36] 5 2 5 1 5 4 4 1 3 6 3 3 5 3 9 5 4 4 2 3 4 3 5 2 5 3 7 5 1 3 0 5 3 7 3
## [71] 5 5 4 0 3 1 1 2 3 8 7 4 8 3 3 6 4 1 5 2 6 3 3 7 3 5 2 4 4 5Global centrality measures
- Closeness centrality
closeness.cent <- closeness(erdos.gr, mode="all")
closeness.cent## [1] 0.0013888889 0.0014925373 0.0016420361 0.0017123288 0.0016638935
## [6] 0.0015503876 0.0015948963 0.0017543860 0.0015479876 0.0016339869
## [11] 0.0016103060 0.0017391304 0.0015698587 0.0016694491 0.0016806723
## [16] 0.0016835017 0.0016000000 0.0017361111 0.0015337423 0.0015576324
## [21] 0.0015455951 0.0015197568 0.0017064846 0.0017211704 0.0001010101
## [26] 0.0016891892 0.0014903130 0.0017094017 0.0016778523 0.0016501650
## [31] 0.0017211704 0.0016286645 0.0014771049 0.0016366612 0.0015649452
## [36] 0.0017123288 0.0014771049 0.0016694491 0.0013568521 0.0016977929
## [41] 0.0016233766 0.0016077170 0.0012269939 0.0015455951 0.0017152659
## [46] 0.0015772871 0.0014970060 0.0017543860 0.0015337423 0.0017543860
## [51] 0.0016977929 0.0015898251 0.0016286645 0.0015432099 0.0015360983
## [56] 0.0016420361 0.0015576324 0.0016611296 0.0015455951 0.0016977929
## [61] 0.0015873016 0.0016863406 0.0016891892 0.0014705882 0.0016077170
## [66] 0.0001010101 0.0016583748 0.0015576324 0.0017271157 0.0015923567
## [71] 0.0016447368 0.0016260163 0.0016051364 0.0001010101 0.0016077170
## [76] 0.0013568521 0.0015037594 0.0015243902 0.0015360983 0.0016835017
## [81] 0.0017094017 0.0015873016 0.0017699115 0.0016233766 0.0016286645
## [86] 0.0017605634 0.0016447368 0.0013513514 0.0016366612 0.0015600624
## [91] 0.0016750419 0.0016447368 0.0015847861 0.0017667845 0.0015600624
## [96] 0.0016129032 0.0015600624 0.0016420361 0.0016339869 0.0016666667Which centrality measure is appropriate?
- The CINNA (Central Informative Nodes in Network Analysis) is an R package for computing, analyzing and comparing centrality measures.
How does it work?
library(CINNA)data("zachary")
zachary## IGRAPH 455c916 U--- 34 78 --
## + attr: id (v/n)
## + edges from 455c916:
## [1] 1-- 2 1-- 3 2-- 3 1-- 4 2-- 4 3-- 4 1-- 5 1-- 6 1-- 7 5-- 7
## [11] 6-- 7 1-- 8 2-- 8 3-- 8 4-- 8 1-- 9 3-- 9 3--10 1--11 5--11
## [21] 6--11 1--12 1--13 4--13 1--14 2--14 3--14 4--14 6--17 7--17
## [31] 1--18 2--18 1--20 2--20 1--22 2--22 24--26 25--26 3--28 24--28
## [41] 25--28 3--29 24--30 27--30 2--31 9--31 1--32 25--32 26--32 29--32
## [51] 3--33 9--33 15--33 16--33 19--33 21--33 23--33 24--33 30--33 31--33
## [61] 32--33 9--34 10--34 14--34 15--34 16--34 19--34 20--34 21--34 23--34
## [71] 24--34 27--34 28--34 29--34 30--34 31--34 32--34 33--34Proper centrality measures
pr_cent<-proper_centralities(zachary)## [1] "subgraph centrality scores"
## [2] "Topological Coefficient"
## [3] "Average Distance"
## [4] "Barycenter Centrality"
## [5] "BottleNeck Centrality"
## [6] "Centroid value"
## [7] "Closeness Centrality (Freeman)"
## [8] "ClusterRank"
## [9] "Decay Centrality"
## [10] "Degree Centrality"
## [11] "Diffusion Degree"
## [12] "DMNC - Density of Maximum Neighborhood Component"
## [13] "Eccentricity Centrality"
## [14] "eigenvector centralities"
## [15] "K-core Decomposition"
## [16] "Geodesic K-Path Centrality"
## [17] "Katz Centrality (Katz Status Index)"
## [18] "Kleinberg's authority centrality scores"
## [19] "Kleinberg's hub centrality scores"
## [20] "clustering coefficient"
## [21] "Lin Centrality"
## [22] "Lobby Index (Centrality)"
## [23] "Markov Centrality"
## [24] "Radiality Centrality"
## [25] "Shortest-Paths Betweenness Centrality"
## [26] "Current-Flow Closeness Centrality"
## [27] "Closeness centrality (Latora)"
## [28] "Communicability Betweenness Centrality"
## [29] "Community Centrality"
## [30] "Cross-Clique Connectivity"
## [31] "Entropy Centrality"
## [32] "EPC - Edge Percolated Component"
## [33] "Laplacian Centrality"
## [34] "Leverage Centrality"
## [35] "MNC - Maximum Neighborhood Component"
## [36] "Hubbell Index"
## [37] "Semi Local Centrality"
## [38] "Closeness Vitality"
## [39] "Residual Closeness Centrality"
## [40] "Stress Centrality"
## [41] "Load Centrality"
## [42] "Flow Betweenness Centrality"
## [43] "Information Centrality"Centrality calculation & recognition of most informative centrality measures
calculate_centralities(zachary, include = pr_cent[1:5])%>%
pca_centralities(scale.unit = TRUE)
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