# Describe the congressmen's retweet network with R chengjun wang @ Tencent
# 2014/04/16
library(igraph)
# detach('package:igraph', unload=TRUE) detach('package:statnet',
# unload=TRUE)
setwd("E:/Github/ergm") # change here to your work directory
att = read.table("./party_info.txt", sep = ",", header = T, stringsAsFactors = F)
mat = as.matrix(read.table("./retweet_network.txt", header = TRUE, sep = ",",
row.names = 1, stringsAsFactors = F, as.is = TRUE))
table(att$party) # democracy, independent, and republic.
##
## D I R
## 251 2 274
g = graph.adjacency(mat, mode = c("directed"), weighted = TRUE, diag = FALSE)
g
## IGRAPH DNW- 527 426 --
## + attr: name (v/c), weight (e/n)
V(g)$name = colnames(mat)
# edgelist = data.frame( get.edgelist(g, names = T) , stringsAsFactors =
# FALSE)
set.seed(2010)
lay = layout.fruchterman.reingold(g)
V(g)$party = att$party[match(V(g)$name, att$id)]
V(g)$color[V(g)$party == "D"] = "red"
V(g)$color[V(g)$party == "R"] = "green"
V(g)$color[V(g)$party == "I"] = "yellow"
V(g)$size = (degree(g) + 1)
plot(g, layout = lay, vertex.size = V(g)$size, edge.arrow.size = 0.2, vertex.label = NA,
vertex.size = 3)
################# Graph Statistics No of nodes
length(V(g))
## [1] 527
# No of edges
length(E(g))
## [1] 426
# Density (No of edges / possible edges)
graph.density(g)
## [1] 0.001537
# Number of islands
clusters(g)$no
## [1] 262
# Global cluster coefficient: (close triplets/all triplets)
transitivity(g, type = "global")
## [1] 0.0624
# Reciprocity of the graph
reciprocity(g)
## [1] 0.1268
# Connected Component algorithms is to find the island of nodes that are
# interconnected with each other, in other words, one can traverse from one
# node to another one via a path.
# Notice that connectivity is symmetric in undirected graph.Therefore in
# directed graph, there is a concept of 'strong' connectivity which means
# both nodes are considered connected only when it is reachable in both
# direction.
# A 'weak' connectivity means nodes are connected
# Nodes reachable from node4
subcomponent(g, 4, mode = "out")
## [1] 4 9 10 22 31 48 64 73 79 92 18 87 397 36 57 100 54
## [18] 142 342 434 473 514 45 77 66 89 30 121 151 184 224 307 377 410
## [35] 428 495 25 85 75 465 209 452 11 3 68 390 146 375 319 162 281
## [52] 301 426 469 480 501 239 275 418 513 76 166 392 449 462 337 356 58
## [69] 233 385 355 329 23 26 217 2 53 27 33 50 81 99 37
# Nodes who can reach node4
subcomponent(g, 4, mode = "in")
## [1] 4 48 60 469 2 65 495 7 23 26 63 213 290 142 249 281 326
## [18] 374 375 428 452 511 516 53 76 199 241 449 296 359 191 96 114 204
## [35] 297 299 377 381 392 397 465 481 501 254 334 506 153 378 410 319 356
## [52] 488 513 514 71 146 352 261 482 370 239 470 64 434 162 244 382 390
## [69] 475 106 171 292 324 337 466 166 209 167 309 303 75 224 240
clusters(g, mode = "weak")
## $membership
## [1] 1 1 1 1 2 3 1 1 1 1 1 4 1 1 1 5 6
## [18] 1 7 1 8 1 1 9 1 1 1 10 11 1 1 12 1 13
## [35] 14 1 1 15 16 1 17 18 19 20 1 21 22 1 23 1 24
## [52] 1 1 1 1 19 1 1 25 1 1 1 1 1 1 1 1 1
## [69] 26 1 1 27 1 28 1 1 1 29 1 30 1 1 31 32 1
## [86] 33 1 34 1 35 36 1 37 38 39 1 1 40 1 1 41 42
## [103] 43 44 1 1 1 45 46 1 39 47 48 1 49 50 51 1 52
## [120] 53 1 1 54 55 1 1 56 57 58 59 1 60 61 62 1 63
## [137] 64 65 66 67 68 1 69 70 71 1 72 73 1 74 1 75 1
## [154] 1 76 1 77 78 79 80 81 1 82 1 83 1 1 84 85 86
## [171] 1 1 87 1 88 1 89 1 1 1 90 91 92 1 93 94 1
## [188] 95 96 97 1 1 98 1 1 9 99 100 1 101 102 1 1 1
## [205] 103 57 104 105 1 106 1 1 1 107 108 1 1 109 110 1 111
## [222] 112 1 1 113 114 115 1 1 1 116 117 1 118 1 119 120 121
## [239] 1 1 1 122 123 1 124 125 126 127 1 128 1 129 130 1 131
## [256] 132 1 1 1 1 1 133 134 135 136 137 1 1 1 138 1 1
## [273] 139 140 1 141 142 143 144 145 1 146 147 148 149 1 150 1 1
## [290] 1 151 1 1 1 152 1 1 153 1 154 1 1 1 1 1 155
## [307] 1 156 1 157 158 1 1 1 159 160 161 1 1 1 162 163 164
## [324] 1 1 1 1 165 1 166 1 167 1 1 168 1 1 169 1 1
## [341] 170 1 171 172 173 174 1 175 1 176 177 1 178 179 1 1 1
## [358] 1 1 1 180 181 1 182 183 1 184 1 1 1 1 185 186 1
## [375] 1 1 1 1 187 188 1 1 1 189 1 190 1 1 191 1 192
## [392] 1 193 194 195 1 1 1 196 197 1 198 199 200 201 202 1 1
## [409] 203 1 1 1 1 204 205 1 1 1 1 206 207 208 209 1 210
## [426] 1 92 1 211 212 213 214 215 1 216 217 218 1 1 219 220 221
## [443] 1 222 223 1 1 224 1 1 225 1 1 226 227 228 229 1 1
## [460] 1 1 1 1 230 1 1 231 232 1 1 233 1 1 234 1 235
## [477] 236 1 237 1 1 1 238 1 239 240 1 1 1 1 241 242 243
## [494] 244 1 245 246 10 247 1 1 248 249 250 251 1 252 1 253 254
## [511] 1 255 1 1 57 1 256 257 258 259 260 261 1 1 1 262 1
##
## $csize
## [1] 259 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1
## [18] 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [35] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
## [52] 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1
## [69] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [86] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [103] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [120] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [137] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [154] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [171] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [188] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [205] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [239] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [256] 1 1 1 1 1 1 1
##
## $no
## [1] 262
clusters(g, mode = "strong")
## $membership
## [1] 480 436 471 436 435 434 433 432 479 477 474 431 430 428 399 398 397
## [18] 438 396 393 392 476 436 390 454 436 461 388 387 470 475 386 460 385
## [35] 384 465 478 383 382 381 380 379 378 377 473 376 375 436 374 459 373
## [52] 429 436 469 372 371 472 449 370 369 367 366 365 436 364 466 363 468
## [69] 362 426 361 360 465 359 436 436 466 358 481 357 458 416 356 355 453
## [86] 354 437 353 467 352 351 439 350 349 347 346 368 345 457 466 344 343
## [103] 342 341 425 339 338 337 336 335 348 334 333 331 330 329 328 325 324
## [120] 323 464 319 318 317 427 322 316 315 314 313 312 311 310 309 308 307
## [137] 306 305 304 303 302 436 301 300 299 436 298 297 295 294 463 293 287
## [154] 286 285 284 283 282 281 280 279 436 278 277 276 436 270 269 268 267
## [171] 265 321 264 263 262 259 258 257 256 255 254 253 251 462 250 249 248
## [188] 247 246 245 242 417 241 415 327 391 240 239 238 237 236 235 422 292
## [205] 234 233 232 231 436 230 275 408 274 229 228 412 445 227 226 225 224
## [222] 223 222 436 221 220 219 218 414 217 216 215 448 214 213 212 211 210
## [239] 436 209 208 207 206 205 204 203 202 201 200 199 407 198 197 193 192
## [256] 191 190 189 188 187 272 186 185 184 183 182 181 180 179 178 424 177
## [273] 176 175 443 174 173 172 171 170 436 169 168 167 166 165 164 163 326
## [290] 243 162 196 290 261 161 160 159 158 157 156 456 404 194 155 413 154
## [307] 440 153 148 147 146 271 145 418 144 143 142 141 436 399 140 139 138
## [324] 137 260 289 136 135 446 134 151 133 132 131 130 244 436 129 128 127
## [341] 126 452 125 124 123 122 405 121 320 120 119 118 117 116 444 436 115
## [358] 340 273 399 114 113 406 112 111 403 110 109 151 108 107 106 105 104
## [375] 436 103 436 102 101 100 99 98 400 97 447 96 95 409 94 436 93
## [392] 436 92 91 90 402 436 195 89 88 87 86 85 84 83 82 410 152
## [409] 81 436 80 325 79 78 77 332 409 442 288 76 75 74 73 72 71
## [426] 451 252 436 70 69 68 67 66 436 65 64 63 401 296 62 61 60
## [443] 59 58 57 419 423 56 436 421 55 436 136 54 53 52 51 420 50
## [460] 49 150 455 266 48 436 47 46 45 436 44 43 291 441 42 41 40
## [477] 39 38 37 450 35 149 34 33 32 31 30 29 409 411 28 27 26
## [494] 25 436 24 23 389 22 395 436 21 20 19 18 17 16 394 15 14
## [511] 13 12 436 436 11 10 9 8 7 6 5 4 36 3 399 2 1
##
## $csize
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [24] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [47] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [70] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [93] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [116] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## [139] 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [162] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [208] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [231] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [254] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [277] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [300] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [323] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [346] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [392] 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
## [415] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 36 1
## [438] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [461] 1 1 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##
## $no
## [1] 481
# 1. Connectivity between two nodes measure the distinct paths with no
# shared edges between two nodes. (ie: how much edges need to be removed to
# disconnect them)
edge.connectivity(g)
## [1] 0
# Compute the connectivity for two nodes
edge.connectivity(g, 7, 2)
## [1] 1
# Same as edge.connectivity
graph.adhesion(g)
## [1] 0
# The adhesion of a graph is the minimum number of edges needed to remove to
# obtain a graph which is not strongly connected. This is the same as the
# edge connectivity of the graph. Edge connectivity, 0 since graph is
# disconnected
# 2. Shortest path between two nodes
shortest.paths(g, 1, 2)
## V2
## V1 4
# Compute the shortest path matrix
matrix_of_shortest_path = shortest.paths(g)
# 3. the diameter of the graph Diameter of the graph the length of the
# longest geodesic. the geodesic distance is the number of relations in the
# shortest possible walk from one actor to another
diameter(g)
## [1] 15
get.diameter(g)
## [1] 167 261 359 213 65 48 4 64 397 142 410 375 449 26 2 37
# 4. degree distribution
d = degree(g)
dd = degree.distribution(g)
########################################## plot and fit the power law distribution power law distribution
plot(degree.distribution(g), type = "b", xlab = "node degree", ylab = "Probability")
plot(degree.distribution(g), log = "xy", type = "b", xlab = "node degree", ylab = "probability")
## Warning: 8 y values <= 0 omitted from logarithmic plot
# rank-order distribution
d = degree(graph, mode = "all")
## Error: Not a graph object
d = d[d != 0]
p = d/sum(as.numeric(d))
Rank = rank(-d, ties.method = c("first"))
plot(d ~ Rank, log = "xy", xlab = "Rank (log)", ylab = "Degree (log)", main = "Rank-Order Distribution")
fit_power_law = function(graph) {
# calculate degree
d = degree(graph, mode = "all")
dd = degree.distribution(graph, mode = "all", cumulative = FALSE)
degree = 1:max(d)
probability = dd[-1]
# delete blank values
nonzero.position = which(probability != 0)
probability = probability[nonzero.position]
degree = degree[nonzero.position]
reg = lm(log(probability) ~ log(degree))
cozf = coef(reg)
power.law.fit = function(x) exp(cozf[[1]] + cozf[[2]] * log(x))
alpha = -cozf[[2]]
R.square = summary(reg)$r.squared
print(paste("Alpha =", round(alpha, 3)))
print(paste("R square =", round(R.square, 3)))
# plot
plot(probability ~ degree, log = "xy", xlab = "Degree (log)", ylab = "Probability (log)",
col = 1, main = "Degree Distribution")
curve(power.law.fit, col = "red", add = T, n = length(d))
}
fit_power_law(g)
## [1] "Alpha = 1.694"
## [1] "R square = 0.897"
################# Centrality Measures
# 1. Degree centrality gives a higher score to a node that has a high
# in/out-degree 2. Closeness centrality gives a higher score to a node that
# has short path distance to every other nodes 3. Betweenness centrality
# gives a higher score to a node that sits on many shortest path of other
# node pairs 4. Eigenvector centrality gives a higher score to a node if it
# connects to many high score nodes 5. Local cluster coefficient measures
# how my neighbors are inter-connected with each other, which means the node
# becomes less important.
# g1 = barabasi.game(100, directed=F) g2 = barabasi.game(100, directed=F) g
# = g1 %u% g2
# Degree
deg = degree(g)
deg_in = degree(g, mode = "in")
deg_out = degree(g, mode = "out")
plot(data.frame(deg, deg_in, deg_out))
# Closeness (inverse of average dist)
clo = closeness(g)
# Betweenness
bet = betweenness(g)
# Local cluster coefficient
tra = transitivity(g, type = "local")
# Eigenvector centrality
eig = evcent(g)$vector
net.cen = data.frame(degree = deg, closeness = clo, betweenness = bet, eigenvector = eig,
transtivity = tra)
plot(net.cen)
# Plot the eigevector and betweenness centrality par(mfrow=c(1, 2))
plot(evcent(g)$vector, betweenness(g))
text(evcent(g)$vector, betweenness(g), cex = 0.6, pos = 4)
# plot the network
V(g)$labels = NA
# V(g)$labels[which(degree(g) > 15)] = which(degree(g) > 15)
V(g)[4]$labels = 4
V(g)[495]$labels = 495
V(g)$shape = "circle"
E(g)$color = "grey"
# V(g)[4]$shape = 'square' V(g)[495]$shape = 'rectangle'
plot(g, layout = lay, vertex.size = V(g)$size, edge.arrow.size = 0.2, vertex.label = V(g)$labels,
vertex.shape = V(g)$shape, vertex.size = 3)
################## Shortest path 'Shortest Path algorithm aims to find the shortest path from
################## node A to node B.
# shortest path
pa = get.shortest.paths(g, 77, 495)[[1]]
## Warning: At structural_properties.c:4482 :Couldn't reach some vertices
pa = get.shortest.paths(g, 495, 77)[[1]]
pa = unlist(pa)
E(g)$color = "grey"
E(g, path = pa)$color = "red"
E(g, path = pa)$width = 3
plot(g, layout = lay, vertex.size = V(g)$size, edge.arrow.size = 0.2, vertex.label = V(g)$labels,
vertex.shape = V(g)$shape, vertex.size = 3)
####################### network diameter
d = get.diameter(g)
E(g)$color = "grey"
E(g, path = d)$color = "blue"
E(g, path = d)$width = 3
plot(g, layout = lay, vertex.size = V(g)$size, edge.arrow.size = 0.2, vertex.label = V(g)$labels,
vertex.shape = V(g)$shape, vertex.size = 3)
