社交網絡分析是一種無監督的機器學習方法，有一些類似於機器學習中的KNN，識別出不同的網絡群體，可以應用在 FB推薦朋友、或是商品推薦、影片推薦、甚至是疾病傳播、反詐欺等等。 社交網絡通常使用圖來描述，圖可以非常直觀的描述事物之間的關係。在圖中，節點（node）表示一個人，或者一個事物，邊（edge）代表人或者事物之間的關係。
## package library(statnet) library(igraph) # detach(package:igraph)
social network
建構graph
g<-graph.empty(directed=F)
g<-add.vertices(g,3)
g<-add.edges(g,c(c(1,2,1,3,2,3,2,1,3,2,1,1)))
V(g)$label <- c("a","b","c")
V(g)$color <- c('red','blue','orange')
V(g)$size <- c(20,40,60)
V(g)$member <- c(1,2,1)
V(g)[which(V(g)$member==1)]
## + 2/3 vertices, from 48eba38: ## [1] 1 3
V(g)[degree(g)>1]
## + 3/3 vertices, from 48eba38: ## [1] 1 2 3
建構graph
g<-g-V(g)[degree(g)==0] edge.connectivity(g, 1,3)
## [1] 3
neighbors(g,v=which(V(g)$label=="a"))
## + 5/3 vertices, from 4900aec: ## [1] 1 1 2 2 3
# default mode是out，還有in,total
V(g)[neighbors(g,v=which(V(g)$label=="b"),
mode="total")]
## + 4/3 vertices, from 4900aec: ## [1] 1 1 3 3
建構graph
which_loop(g)
## [1] FALSE FALSE FALSE FALSE FALSE TRUE
which_multiple(g)
## [1] FALSE FALSE FALSE TRUE TRUE FALSE
E(g)$weight <- c(2,8,13,4,11,3) g<-set_vertex_attr(g,"name",value=V(g)$label) E(g)
## + 6/6 edges from 4900aec (vertex names): ## [1] a--b a--c b--c a--b b--c a--a
建構graph
E(g)[E(g)$weight>2]
## + 5/6 edges from 4900aec (vertex names): ## [1] a--c b--c a--b b--c a--a
g<-g-E(g)[E(g)$weight==1] count.multiple(g)
## [1] 2 1 2 2 2 1
E(g)
## + 6/6 edges from 491fa39 (vertex names): ## [1] a--b a--c b--c a--b b--c a--a
建構graph
# 簡化網絡
gsim <- simplify(g,
remove.multiple = TRUE,
remove.loops = TRUE,
edge.attr.comb = "mean")
E(gsim)$weight
## [1] 3 8 12
plot
plot(g,
layout=layout.fruchterman.reingold,
edge.arrow.size=0.4,
vertex.color=V(g)$color,
vertex.size=V(g)$size,
edge.width=E(g)$weight)
繪圖參數
| Method name | Short name | Algorithm description |
|---|---|---|
| layout_circle | circle, circular | Deterministic layout that places the vertices on a circle |
| layout_drl | drl | The Distributed Recursive Layout algorithm for large graphs |
| layout_fruchterman_reingold | fr | Fruchterman-Reingold force-directed algorithm |
| layout_fruchterman_reingold_3d | fr3d, fr_3d | Fruchterman-Reingold force-directed algorithm in three dimensions |
| layout_grid_fruchterman_reingold | grid_fr | Fruchterman-Reingold force-directed algorithm with grid heuristics for large graphs |
| layout_kamada_kawai_3d | kk3d, kk_3d | Kamada-Kawai force-directed algorithm in three dimensions |
| layout_lgl | large, lgl, large_graph | The Large Graph Layout algorithm for large graphs |
| layout_random_3d | random_3d | Places the vertices completely randomly in 3D |
| layout_reingold_tilford | rt, tree | Reingold-Tilford tree layout, useful for (almost) tree-like graphs |
繪圖參數
| Method name | description |
|---|---|
| vertex.color | Node color |
| vertex.frame.color | Node border color |
| vertex.shape | “none”, “circle”, “square”, “rectangle” |
| vertex.size | Size of the node (default is 15) |
| vertex.size2 | The second size of the node (e.g. for a rectangle) |
| vertex.label | Character vector used to label the nodes |
| vertex.label.family | Font family of the label (e.g.“Times”, “Helvetica”) |
| vertex.label.font | Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol |
| vertex.label.cex | Font size (multiplication factor, device-dependent) |
| vertex.label.dist | Distance between the label and the vertex |
繪圖參數
| Method name | description |
|---|---|
| edge.color | Edge color |
| edge.width | Edge width, defaults to 1 |
| edge.arrow.size | Arrow size, defaults to 1 |
| edge.arrow.width | Arrow width, defaults to 1 |
| edge.lty | Line type, could be 0 or “blank”, 1 or “solid”, 2 or “dashed”,3 or “dotted”, 4 or “dotdash”, 5 or “longdash”, 6 or “twodash” |
| edge.label | Character vector used to label edges |
| edge.label.family | Font family of the label (e.g.“Times”, “Helvetica”) |
| edge.label.font | Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol |
| edge.label.cex | Font size for edge labels |
| edge.curved | Edge curvature, range 0-1 (FALSE sets it to 0, TRUE to 0.5) |
data.frame轉成graph
g <- graph.data.frame(data.frame(
id1=c('Bob','Mark','Red','Mat',
'White','White','Bob'),
di2=c('Red','White','Mat','Blue',
'Bob','Mark','Mat')))
# 等同於
# g <- graph(edges=c('Bob','Red','Mark',
# 'White','Red','Mat','Mat',
# 'Blue','White','Bob','White',
# 'Mark','Bob','Mat'),directed = TRUE)
g[]
## 6 x 6 sparse Matrix of class "dgCMatrix" ## Bob Mark Red Mat White Blue ## Bob . . 1 1 . . ## Mark . . . . 1 . ## Red . . . 1 . . ## Mat . . . . . 1 ## White 1 1 . . . . ## Blue . . . . . .
data.frame轉成graph
plot(g,
layout=layout.fruchterman.reingold,
edge.arrow.size=0.4,
vertex.color='lightblue',
vertex.size=25)
matrix轉成graph
adjm <- matrix(sample(0:1, 100, replace=TRUE, prob=c(0.9,0.1)), nc=10) g1 <- graph_from_adjacency_matrix(adjm, weighted=TRUE, mode="undirected") # mode有directed, undirected, upper, lower, max, min, plus g1
## IGRAPH 49d1f1f U-W- 10 9 -- ## + attr: weight (e/n) ## + edges from 49d1f1f: ## [1] 1--4 2--4 2--6 2--8 3--4 3--7 4--6 5--6 7--9
matrix轉成graph
plot(g1,
layout=layout.fruchterman.reingold,
edge.arrow.size=0.4,
vertex.color='white',
vertex.size=25)
matrix轉成graph
rownames(adjm) <- sample(letters, nrow(adjm))
colnames(adjm) <- seq(ncol(adjm))
# add.rownames以及add.colnames定義名稱
g10 <- graph_from_adjacency_matrix(adjm, weighted=TRUE,
add.rownames="row",
add.colnames="col")
g10
## IGRAPH 49fa821 D-W- 10 10 -- ## + attr: col (v/c), row (v/c), weight (e/n) ## + edges from 49fa821: ## [1] 1->4 2->4 2->8 4->2 4->3 4->6 5->6 6->2 7->3 7->9
matrix轉成graph
plot(g10,
layout=layout.fruchterman.reingold,
edge.arrow.size=0.4,
vertex.color='white',
vertex.size=25)
graphs 結合
g1 <- graph.full(4) plot(g1)
graphs 結合
g2 <- graph.ring(3) plot(g2)
graphs 結合
g <- g1 %du% g2 plot(g)
graphs 結合
# Find different graph.difference(g1, g2, directed=F)
## IGRAPH 4a867f8 U--- 4 3 -- Full graph ## + attr: name (g/c), loops (g/l) ## + edges from 4a867f8: ## [1] 1--4 2--4 3--4
內建圖形函數
empty
eg <- make_empty_graph(40) plot(eg, vertex.size=10, vertex.label=NA)
full
fg <- make_full_graph(40) plot(fg, vertex.size=10, vertex.label=NA)
star
st <- make_star(40) plot(st, vertex.size=10, vertex.label=NA)
tree
tr <- make_tree(40, children = 3, mode = "undirected") plot(tr, vertex.size=10, vertex.label=NA)
ring
rn <- make_ring(40) plot(rn, vertex.size=10, vertex.label=NA)
Watts-Strogatz
sw <- sample_smallworld(dim=2, size=10, nei=1, p=0.1) plot(sw, vertex.size=6, vertex.label=NA, layout=layout_in_circle)
Erdos-Renyi Model
# Generate Random Graphs According To The Erdos-Renyi Model
g <- erdos.renyi.game(20, 0.3)
plot(g, layout=layout.fruchterman.reingold,
vertex.label=NA, vertex.size=5)
Erdos-Renyi Model:gnm
# Generate random graph, fixed number of arcs
g <- erdos.renyi.game(20, 15, type='gnm') # sample_gnm
plot(g, layout=layout.fruchterman.reingold,
vertex.label=NA, vertex.size=5)
Erdos-Renyi Model:gnp
# Generate Random Graphs According To The G(N,P) Erdos-Renyi Model g <- sample_gnp(100, 1/100) comps <- components(g)$membership colbar <- rainbow(max(comps)+1) V(g)$color <- colbar[comps+1] plot(g, layout=layout_with_fr, vertex.size=5, vertex.label=NA)
Barabasi-Albert Model
# Generate Scale-Free Graphs According To The Barabasi-Albert Model
g <- barabasi.game(60, power=1, zero.appeal=1.3)
plot(g, layout=layout.fruchterman.reingold,
vertex.label=NA, vertex.size=5, edge.arrow.size=0.2)
lattice
lt = graph.lattice(c(3,4,2)) plot(lt, layout=layout.fruchterman.reingold)
communities
g <- make_full_graph(5) %du% make_full_graph(5) %du% make_full_graph(5) g <- add_edges(g, c(1,6, 1,11, 6,11)) com <- cluster_spinglass(g, spins=5) V(g)$color <- com$membership+1 g <- set_graph_attr(g, "layout", layout_with_kk(g)) plot(g, vertex.label.dist=1.5)
layout
g <- graph(c(2,1,3,1,4,1,5,1,6,1,7,1),directed = F) par(mfrow=c(1,3)) plot(g,vertex.size=40,layout=layout_on_grid,main="簡單的網格布局") plot(g,vertex.size=40,layout=layout.auto,main="自動布局") plot(g,vertex.size=40,layout=layout_as_star,main="星形布局")
layout
par(mfrow=c(1,3)) plot(g,vertex.size=40,layout=layout.circle,main="環形布局") plot(g,vertex.size=40,layout=layout_randomly,main="隨機布局") plot(g,vertex.size=40,layout=layout_as_tree(g),main="樹狀布局")
# {-}
分群
g <- tr <- make_tree(40, children = 3, mode = "undirected") plot(g)
分群
ceb <- cluster_edge_betweenness(g) # 建構模型 dendPlot(ceb)
分群
plot(ceb,g)
分群
# 其他分群方法 # cluster_label_prop # cluster_fast_greedy # spinglass.community
其他package
networkD3
library(networkD3)
data(MisLinks)
data(MisNodes)
forceNetwork(Links = MisLinks, Nodes = MisNodes, Source = "source",
Target = "target", Value = "value", NodeID = "name",
Group = "group", opacity = 0.4, zoom = TRUE)
networkD3
MyNodes = data.frame(name = c("Google", "Apple", "Amazon",
"Youtube", "Paypal"),
group = c("A", "B", "C", "A", "C"),
size = c(100, 25, 9, 1, 4))
# 描述圈圈間的聯結，source必定大於target
MyLinks = data.frame(source = c(1, 2, 2, 3),
target = c(0, 0, 1, 0),
value = c(1, 2, 5, 10)) # value代表線的粗細
networkD3
forceNetwork(Links = MyLinks, Nodes = MyNodes, Source = "source",
Target = "target", Value = "value", NodeID = "name",
Group = "group", opacity = 1, zoom = TRUE)
qplot with matrix
library(qgraph)
adj=matrix(sample(0:1,10^2,TRUE,prob=c(0.8,0.2)),nrow=10,ncol=10)
qgraph(adj)
title("Unweighted and directed graphs",line=2.5)
# Save plot to nonsquare pdf file: # qgraph(adj,filetype='pdf',height=5,width=10)
big5
library("psych")
data(big5)
data(big5groups)
big5
# Correlations:
big5Graph <- qgraph(cor(big5),minimum=0.25,groups=big5groups,
legend=TRUE,borders=FALSE, title = "Big 5 correlations")
big5
# Same graph with spring layout: qgraph(big5Graph,layout="spring")
# different color scheme: # qgraph(big5Graph,posCol="blue",negCol="purple")
big5
Exploratory factor analysis (have problems)
big5efa <- factanal(big5,factors=5,rotation="promax",
scores="regression")
qgraph(big5efa,groups=big5groups,layout="circle",
minimum=0.2,cut=0.4,vsize=c(1.5,10),borders=FALSE,
vTrans=200,title="Big 5 EFA")
qgraph.efa(big5, 5, groups = big5groups, rotation = "promax",
minimum = 0.2, cut = 0.4, vsize = c(1, 15),
borders = FALSE,asize = 0.07, esize = 4, vTrans = 200)
## Principal component analysis:
big5pca <- principal(cor(big5),5,rotate="promax")
qgraph(big5pca,groups=big5groups,layout="circle",
rotation="promax",minimum=0.2,cut=0.4,vsize=c(1.5,10),
borders=FALSE,vTrans=200,title="Big 5 PCA")
bfi
data(bfi) # Compute correlations: CorMat <- cor_auto(bfi[,1:25])
## Variables detected as ordinal: A1; A2; A3; A4; A5; C1; C2; C3; C4; C5; E1; E2; E3; E4; E5; N1; N2; N3; N4; N5; O1; O2; O3; O4; O5
bfi
# Compute graph with tuning = 0 (BIC):
BICgraph <- qgraph(CorMat, graph = "glasso", sampleSize = nrow(bfi),
tuning = 0, layout = "spring", title = "BIC", details = TRUE)
bfi
# Compute graph with tuning = 0.5 (EBIC)
EBICgraph <- qgraph(CorMat, graph = "glasso", sampleSize = nrow(bfi),
tuning = 0.5, layout = "spring", title = "BIC", details = TRUE)
bfi
centrality and clustering
centralityPlot(list(BIC = BICgraph, EBIC = EBICgraph))
## Note: z-scores are shown on x-axis rather than raw centrality indices.
bfi
clusteringPlot(list(BIC = BICgraph, EBIC = EBICgraph))
## Note: z-scores are shown on x-axis rather than raw centrality indices.
bfi
centrality_auto(BICgraph)
## $node.centrality ## Betweenness Closeness Strength ExpectedInfluence ## A1 1 0.002716442 1.1992733 0.07940007 ## A2 21 0.003053247 1.3587499 0.58200348 ## A3 21 0.003090016 1.1067197 0.80763344 ## A4 11 0.003001281 1.0386258 0.47713479 ## A5 15 0.003169514 1.0816605 0.80328286 ## C1 1 0.002780521 1.0664627 0.45471027 ## C2 24 0.003270458 1.4859096 0.93158317 ## C3 1 0.002764676 0.9766622 0.34190351 ## C4 20 0.003140338 1.6280943 0.46617377 ## C5 18 0.003199705 1.2710371 0.19734805 ## E1 2 0.002993497 1.3240260 0.01502171 ## E2 15 0.003322839 1.4523625 0.21331154 ## E3 11 0.003086533 1.2399614 0.91152675 ## E4 27 0.003389793 1.4695271 0.29832607 ## E5 18 0.003377435 1.4622480 0.42041191 ## N1 17 0.002604386 1.3456596 1.07989574 ## N2 0 0.002444764 1.3195712 0.92947534 ## N3 10 0.002758247 1.0946576 1.05587436 ## N4 21 0.003085156 1.2692686 0.84728277 ## N5 13 0.003115974 1.3093307 0.81756520 ## O1 5 0.002925719 1.1055701 0.56271655 ## O2 2 0.002856739 1.0634642 0.48765814 ## O3 14 0.003088008 1.4193970 0.36307920 ## O4 10 0.003330758 1.2380913 0.75518514 ## O5 4 0.003066329 1.2971293 0.25049673 ## ## $edge.betweenness.centrality ## from to edgebetweenness ## 194 N3 N4 23 ## 300 A5 E4 23 ## 245 A3 A5 22 ## 168 A2 A3 21 ## 74 C4 C5 18 ## 271 A4 C2 16 ## 100 C5 N4 15 ## 164 E5 N1 15 ## 175 N1 N2 15 ## 1 A1 A2 14 ## 15 C1 C2 14 ## 149 E3 O3 14 ## 126 E2 E4 13 ## 170 E5 O1 12 ## 254 A3 E3 12 ## 37 C2 C4 11 ## 49 C2 N5 11 ## 127 E2 E5 11 ## 232 A2 E5 11 ## 244 A3 A4 11 ## 163 E4 O5 10 ## 176 N1 N3 10 ## 206 N4 O4 10 ## 110 E1 E4 9 ## 137 E2 O4 9 ## 215 O1 O3 9 ## 52 C2 O3 8 ## 56 C3 C5 8 ## 156 E4 N4 8 ## 178 N1 N5 8 ## 87 C4 O2 7 ## 91 C4 O5 7 ## 108 E1 E2 7 ## 132 E2 N5 7 ## 209 N5 O2 7 ## 224 A2 C3 7 ## 278 A4 E4 7 ## 279 A1 C4 7 ## 17 C1 C4 6 ## 36 C2 C3 6 ## 179 A2 A4 6 ## 195 N3 N5 6 ## 4 A5 N1 5 ## 88 C4 O3 5 ## 93 C5 E2 5 ## 117 E1 N4 5 ## 140 E3 E5 5 ## 147 E3 O1 5 ## 185 N2 N3 5 ## 216 O1 O4 5 ## 218 O2 O3 5 ## 221 O3 O4 5 ## 222 O3 O5 5 ## 238 A2 N5 5 ## 274 A4 C5 5 ## 33 C1 O4 4 ## 39 C2 E1 4 ## 106 C5 O4 4 ## 139 E3 E4 4 ## 160 E4 O2 4 ## 202 N4 N5 4 ## 225 O4 O5 4 ## 299 A5 E3 4 ## 55 C3 C4 3 ## 57 A1 N1 3 ## 98 C5 N2 3 ## 220 O2 O5 3 ## 43 C2 E5 2 ## 92 C5 E1 2 ## 125 E2 E3 2 ## 184 N1 O5 2 ## 214 O1 O2 2 ## 242 A2 O4 2 ## 16 C1 C3 1 ## 23 C1 E5 1 ## 62 C3 E5 1 ## 121 E1 O3 1 ## 146 A1 O4 1 ## 157 A1 O5 1 ## 167 E5 N4 1 ## 169 E5 N5 1 ## 208 N5 O1 1 ## 282 A4 N2 1 ## 2 A1 E1 0 ## 3 A5 E5 0 ## 5 A5 N2 0 ## 6 A5 N3 0 ## 7 A5 N4 0 ## 8 A5 N5 0 ## 9 A5 O1 0 ## 10 A5 O2 0 ## 11 A5 O3 0 ## 12 A5 O4 0 ## 13 A1 E2 0 ## 14 A5 O5 0 ## 18 C1 C5 0 ## 19 C1 E1 0 ## 20 C1 E2 0 ## 21 C1 E3 0 ## 22 C1 E4 0 ## 24 A1 E3 0 ## 25 C1 N1 0 ## 26 C1 N2 0 ## 27 C1 N3 0 ## 28 C1 N4 0 ## 29 C1 N5 0 ## 30 C1 O1 0 ## 31 C1 O2 0 ## 32 C1 O3 0 ## 34 C1 O5 0 ## 35 A1 E4 0 ## 38 C2 C5 0 ## 40 C2 E2 0 ## 41 C2 E3 0 ## 42 C2 E4 0 ## 44 C2 N1 0 ## 45 C2 N2 0 ## 46 A1 E5 0 ## 47 C2 N3 0 ## 48 C2 N4 0 ## 50 C2 O1 0 ## 51 C2 O2 0 ## 53 C2 O4 0 ## 54 C2 O5 0 ## 58 C3 E1 0 ## 59 C3 E2 0 ## 60 C3 E3 0 ## 61 C3 E4 0 ## 63 C3 N1 0 ## 64 C3 N2 0 ## 65 C3 N3 0 ## 66 C3 N4 0 ## 67 C3 N5 0 ## 68 A1 N2 0 ## 69 C3 O1 0 ## 70 C3 O2 0 ## 71 C3 O3 0 ## 72 C3 O4 0 ## 73 C3 O5 0 ## 75 C4 E1 0 ## 76 C4 E2 0 ## 77 C4 E3 0 ## 78 C4 E4 0 ## 79 A1 N3 0 ## 80 C4 E5 0 ## 81 C4 N1 0 ## 82 C4 N2 0 ## 83 C4 N3 0 ## 84 C4 N4 0 ## 85 C4 N5 0 ## 86 C4 O1 0 ## 89 C4 O4 0 ## 90 A1 N4 0 ## 94 C5 E3 0 ## 95 C5 E4 0 ## 96 C5 E5 0 ## 97 C5 N1 0 ## 99 C5 N3 0 ## 101 A1 N5 0 ## 102 C5 N5 0 ## 103 C5 O1 0 ## 104 C5 O2 0 ## 105 C5 O3 0 ## 107 C5 O5 0 ## 109 E1 E3 0 ## 111 E1 E5 0 ## 112 A1 A3 0 ## 113 A1 O1 0 ## 114 E1 N1 0 ## 115 E1 N2 0 ## 116 E1 N3 0 ## 118 E1 N5 0 ## 119 E1 O1 0 ## 120 E1 O2 0 ## 122 E1 O4 0 ## 123 E1 O5 0 ## 124 A1 O2 0 ## 128 E2 N1 0 ## 129 E2 N2 0 ## 130 E2 N3 0 ## 131 E2 N4 0 ## 133 E2 O1 0 ## 134 E2 O2 0 ## 135 A1 O3 0 ## 136 E2 O3 0 ## 138 E2 O5 0 ## 141 E3 N1 0 ## 142 E3 N2 0 ## 143 E3 N3 0 ## 144 E3 N4 0 ## 145 E3 N5 0 ## 148 E3 O2 0 ## 150 E3 O4 0 ## 151 E3 O5 0 ## 152 E4 E5 0 ## 153 E4 N1 0 ## 154 E4 N2 0 ## 155 E4 N3 0 ## 158 E4 N5 0 ## 159 E4 O1 0 ## 161 E4 O3 0 ## 162 E4 O4 0 ## 165 E5 N2 0 ## 166 E5 N3 0 ## 171 E5 O2 0 ## 172 E5 O3 0 ## 173 E5 O4 0 ## 174 E5 O5 0 ## 177 N1 N4 0 ## 180 N1 O1 0 ## 181 N1 O2 0 ## 182 N1 O3 0 ## 183 N1 O4 0 ## 186 N2 N4 0 ## 187 N2 N5 0 ## 188 N2 O1 0 ## 189 N2 O2 0 ## 190 A2 A5 0 ## 191 N2 O3 0 ## 192 N2 O4 0 ## 193 N2 O5 0 ## 196 N3 O1 0 ## 197 N3 O2 0 ## 198 N3 O3 0 ## 199 N3 O4 0 ## 200 N3 O5 0 ## 201 A2 C1 0 ## 203 N4 O1 0 ## 204 N4 O2 0 ## 205 N4 O3 0 ## 207 N4 O5 0 ## 210 N5 O3 0 ## 211 N5 O4 0 ## 212 A2 C2 0 ## 213 N5 O5 0 ## 217 O1 O5 0 ## 219 O2 O4 0 ## 223 A1 A4 0 ## 226 A2 C4 0 ## 227 A2 C5 0 ## 228 A2 E1 0 ## 229 A2 E2 0 ## 230 A2 E3 0 ## 231 A2 E4 0 ## 233 A2 N1 0 ## 234 A2 N2 0 ## 235 A1 A5 0 ## 236 A2 N3 0 ## 237 A2 N4 0 ## 239 A2 O1 0 ## 240 A2 O2 0 ## 241 A2 O3 0 ## 243 A2 O5 0 ## 246 A1 C1 0 ## 247 A3 C1 0 ## 248 A3 C2 0 ## 249 A3 C3 0 ## 250 A3 C4 0 ## 251 A3 C5 0 ## 252 A3 E1 0 ## 253 A3 E2 0 ## 255 A3 E4 0 ## 256 A3 E5 0 ## 257 A1 C2 0 ## 258 A3 N1 0 ## 259 A3 N2 0 ## 260 A3 N3 0 ## 261 A3 N4 0 ## 262 A3 N5 0 ## 263 A3 O1 0 ## 264 A3 O2 0 ## 265 A3 O3 0 ## 266 A3 O4 0 ## 267 A3 O5 0 ## 268 A1 C3 0 ## 269 A4 A5 0 ## 270 A4 C1 0 ## 272 A4 C3 0 ## 273 A4 C4 0 ## 275 A4 E1 0 ## 276 A4 E2 0 ## 277 A4 E3 0 ## 280 A4 E5 0 ## 281 A4 N1 0 ## 283 A4 N3 0 ## 284 A4 N4 0 ## 285 A4 N5 0 ## 286 A4 O1 0 ## 287 A4 O2 0 ## 288 A4 O3 0 ## 289 A4 O4 0 ## 290 A1 C5 0 ## 291 A4 O5 0 ## 292 A5 C1 0 ## 293 A5 C2 0 ## 294 A5 C3 0 ## 295 A5 C4 0 ## 296 A5 C5 0 ## 297 A5 E1 0 ## 298 A5 E2 0 ## ## $ShortestPathLengths ## A1 A2 A3 A4 A5 C1 C2 ## A1 0.000000 3.570297 7.254209 10.067359 10.905572 17.280307 15.571420 ## A2 3.570297 0.000000 3.683913 6.497062 7.335275 16.626393 13.109531 ## A3 7.254209 3.683913 0.000000 6.637428 3.651362 16.766759 13.249897 ## A4 10.067359 6.497062 6.637428 0.000000 10.288790 10.129331 6.612469 ## A5 10.905572 7.335275 3.651362 10.288790 0.000000 20.418121 16.901259 ## C1 17.280307 16.626393 16.766759 10.129331 20.418121 0.000000 3.516862 ## C2 15.571420 13.109531 13.249897 6.612469 16.901259 3.516862 0.000000 ## C3 12.859478 9.289181 12.973094 12.862595 16.624456 8.465580 6.250126 ## C4 10.955133 14.525430 17.866184 11.228756 20.098983 6.325174 4.616288 ## C5 14.321551 14.930147 15.415330 8.777902 19.066692 9.691592 7.982705 ## E1 19.924278 16.353981 12.670069 13.130301 9.018707 16.996005 13.479143 ## E2 17.636086 14.065790 11.492810 11.953042 7.841447 16.681291 17.218082 ## E3 13.684147 10.113850 6.429937 13.067365 6.139703 19.097089 15.580227 ## E4 15.147202 11.576905 7.892993 8.353225 4.241631 18.482556 14.965694 ## E5 11.107030 7.536734 11.220646 14.033796 13.338028 14.307232 11.466751 ## N1 16.666997 17.203811 18.417355 23.700874 14.765993 22.060544 18.543682 ## N2 18.405226 18.942041 20.155585 22.100224 16.504222 23.798774 20.281911 ## N3 21.429441 20.816606 22.308272 19.142400 18.656910 19.078857 15.561994 ## N4 21.451558 21.150074 19.073781 15.907909 15.422419 16.821600 15.112713 ## N5 18.571815 15.001518 18.685431 16.359375 16.147241 13.263768 9.746906 ## O1 17.753935 14.183638 12.708491 19.345919 12.418256 16.933389 15.435779 ## O2 19.581942 21.210571 17.526658 19.855566 16.242537 14.951984 13.243097 ## O3 19.007276 15.436979 11.753066 16.869566 11.462832 13.773960 10.257098 ## O4 14.862676 14.046767 17.730679 18.437107 14.325513 10.197226 13.714088 ## O5 17.866041 19.778939 16.095026 16.555258 12.443664 13.980493 12.271606 ## C3 C4 C5 E1 E2 E3 E4 ## A1 12.859478 10.955133 14.321551 19.924278 17.636086 13.684147 15.147202 ## A2 9.289181 14.525430 14.930147 16.353981 14.065790 10.113850 11.576905 ## A3 12.973094 17.866184 15.415330 12.670069 11.492810 6.429937 7.892993 ## A4 12.862595 11.228756 8.777902 13.130301 11.953042 13.067365 8.353225 ## A5 16.624456 20.098983 19.066692 9.018707 7.841447 6.139703 4.241631 ## C1 8.465580 6.325174 9.691592 16.996005 16.681291 19.097089 18.482556 ## C2 6.250126 4.616288 7.982705 13.479143 17.218082 15.580227 14.965694 ## C3 0.000000 8.050522 5.640965 19.729269 18.412432 19.403031 20.866087 ## C4 8.050522 0.000000 3.366418 18.067297 16.137885 17.562143 15.857352 ## C5 5.640965 3.366418 0.000000 14.700879 12.771467 20.928561 16.371284 ## E1 19.729269 18.067297 14.700879 0.000000 3.738939 13.066853 4.777076 ## E2 18.412432 16.137885 12.771467 3.738939 0.000000 10.844424 3.599817 ## E3 19.403031 17.562143 20.928561 13.066853 10.844424 0.000000 8.289777 ## E4 20.866087 15.857352 16.371284 4.777076 3.599817 8.289777 0.000000 ## E5 15.606836 16.083038 19.300523 10.267995 6.529056 7.198326 10.128873 ## N1 20.767908 18.493360 15.126942 18.539517 16.196134 16.865404 19.007623 ## N2 20.945606 18.671059 15.304641 18.740612 17.934363 18.603633 19.378818 ## N3 16.005463 13.730916 10.364498 13.777073 14.120882 21.627848 14.415279 ## N4 12.770973 10.496425 7.130008 10.542582 14.281521 19.470566 11.180789 ## N5 15.997033 14.363194 13.278563 12.044732 8.305794 19.150218 11.905610 ## O1 21.685906 17.417695 17.174215 16.914899 13.175960 6.278554 14.568331 ## O2 16.677332 8.626810 11.993228 16.777982 15.600723 11.096721 12.000906 ## O3 16.507224 12.239014 15.605432 16.555443 13.580246 5.323129 13.334892 ## O4 16.079017 13.804470 10.438052 10.223004 6.484065 12.419309 10.083882 ## O5 15.705841 7.655319 11.021737 12.979110 11.801850 10.455987 8.202033 ## E5 N1 N2 N3 N4 N5 O1 ## A1 11.107030 16.666997 18.405226 21.429441 21.451558 18.571815 17.753935 ## A2 7.536734 17.203811 18.942041 20.816606 21.150074 15.001518 14.183638 ## A3 11.220646 18.417355 20.155585 22.308272 19.073781 18.685431 12.708491 ## A4 14.033796 23.700874 22.100224 19.142400 15.907909 16.359375 19.345919 ## A5 13.338028 14.765993 16.504222 18.656910 15.422419 16.147241 12.418256 ## C1 14.307232 22.060544 23.798774 19.078857 16.821600 13.263768 16.933389 ## C2 11.466751 18.543682 20.281911 15.561994 15.112713 9.746906 15.435779 ## C3 15.606836 20.767908 20.945606 16.005463 12.770973 15.997033 21.685906 ## C4 16.083038 18.493360 18.671059 13.730916 10.496425 14.363194 17.417695 ## C5 19.300523 15.126942 15.304641 10.364498 7.130008 13.278563 17.174215 ## E1 10.267995 18.539517 18.740612 13.777073 10.542582 12.044732 16.914899 ## E2 6.529056 16.196134 17.934363 14.120882 14.281521 8.305794 13.175960 ## E3 7.198326 16.865404 18.603633 21.627848 19.470566 19.150218 6.278554 ## E4 10.128873 19.007623 19.378818 14.415279 11.180789 11.905610 14.568331 ## E5 0.000000 9.667078 11.405308 14.429522 13.803300 12.985795 6.646904 ## N1 9.667078 0.000000 1.738230 4.762444 7.996935 8.796775 16.313982 ## N2 11.405308 1.738230 0.000000 4.963539 8.198029 10.535005 18.052212 ## N3 14.429522 4.762444 4.963539 0.000000 3.234490 5.815088 18.841527 ## N4 13.803300 7.996935 8.198029 3.234490 0.000000 6.148556 15.607036 ## N5 12.985795 8.796775 10.535005 5.815088 6.148556 0.000000 16.969613 ## O1 6.646904 16.313982 18.052212 18.841527 15.607036 16.969613 0.000000 ## O2 17.079195 18.942574 20.680804 15.960887 16.294355 10.145799 10.432291 ## O3 11.825586 21.492664 23.230893 19.201544 15.967054 15.919391 5.178682 ## O4 13.013121 16.867808 17.068903 12.105364 8.870873 14.789859 6.736163 ## O5 16.958444 19.818976 21.557206 19.478038 16.243548 15.059860 10.311540 ## O2 O3 O4 O5 ## A1 19.581942 19.007276 14.862676 17.866041 ## A2 21.210571 15.436979 14.046767 19.778939 ## A3 17.526658 11.753066 17.730679 16.095026 ## A4 19.855566 16.869566 18.437107 16.555258 ## A5 16.242537 11.462832 14.325513 12.443664 ## C1 14.951984 13.773960 10.197226 13.980493 ## C2 13.243097 10.257098 13.714088 12.271606 ## C3 16.677332 16.507224 16.079017 15.705841 ## C4 8.626810 12.239014 13.804470 7.655319 ## C5 11.993228 15.605432 10.438052 11.021737 ## E1 16.777982 16.555443 10.223004 12.979110 ## E2 15.600723 13.580246 6.484065 11.801850 ## E3 11.096721 5.323129 12.419309 10.455987 ## E4 12.000906 13.334892 10.083882 8.202033 ## E5 17.079195 11.825586 13.013121 16.958444 ## N1 18.942574 21.492664 16.867808 19.818976 ## N2 20.680804 23.230893 17.068903 21.557206 ## N3 15.960887 19.201544 12.105364 19.478038 ## N4 16.294355 15.967054 8.870873 16.243548 ## N5 10.145799 15.919391 14.789859 15.059860 ## O1 10.432291 5.178682 6.736163 10.311540 ## O2 0.000000 5.773592 12.286735 4.914061 ## O3 5.773592 0.000000 7.096180 5.132858 ## O4 12.286735 7.096180 0.000000 7.372674 ## O5 4.914061 5.132858 7.372674 0.000000 ## ## attr(,"class") ## [1] "list" "centrality_auto"
bfi
clustcoef_auto(BICgraph)