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--- centrality [2015/11/24 09:15] – created hkimscil
+++ centrality [2024/11/18 10:44] (current) – [Eigenvector] hkimscil
@@ Line 4: / Line 4: @@
 ===== Closeness =====
+<code>setwd("D:/Users/Hyo/Cs-Kant/CS/Classes/sna_examples/sna_in_r")</code>
 <code># Social Network Analysis: Closeness Centrality
 library(sna)
@@ Line 19: / Line 20: @@
 </code>
-<code>gplot(L, displaylabels = T, vertex.cex = 1, label.cex = 2, edge.col="red",
+<code>gplot(L, displaylabels = T, vertex.cex = 1, label.cex = 2, edge.col="blue",
-             boxed.labels = F, arrowhead.cex = 1, mode = "kamadakawai")
+boxed.labels = F, arrowhead.cex = 1, mode = "kamadakawai")
 </code>
 {{centrality_suzuki.png}}
@@ Line 53: / Line 54: @@
 </code>
 {{knoke_info.png}}
+  - COUN: county government
+  - COMM: chamber of commerce
+  - EDUC: board of education
+  - INDU: Industry development agency
+  - MAYR: Mayor
+  - WRO: Women Right Organization group
+  - NEWS: Newspaper
+  - WAY: United Way (private organization)
+  - WELF: Welfare
+  - WEST: West group (private organization)
-COUN: county government
+for out link (information out)
-COMM: chamber of commerce
-EDUC: board of education
-INDU: Industry development agency
-MAYR: Mayor
-WRO: Women Right Organization group
-NEWS: Newspaper
-WAY: United Way (private organization)
-WELF: Welfare
-WEST: West group (private organization)
 <code>round(closeness(knoke.infor,cmode="suminvdir"),2)
  [1] 0.70 0.89 0.83 0.70 0.94 0.63 0.65 0.81 0.65 0.78
 </code>
+for in link (information in)
 <code>round(closeness(t(knoke.infor),cmode="suminvdir"),2)
  [1] 0.76 0.94 0.72 0.78 0.94 0.46 1.00 0.59 0.78 0.61
@@ Line 76: / Line 76: @@
 ===== Betweenness =====
+노드 k에 대해서 노드 i 과 j 의 최단 경로 사이에 끼이게 되는 경우의 총합
+<code># Social Network Analysis: Betweenness Centrality
+library(sna)
+# The nearly linear network
+L <- matrix(c(0,0,0,1,0,0,0,0,0,
+,0,0,1,0,0,0,0,0,
+,0,0,1,0,0,0,0,0,
+,1,1,0,1,0,0,0,0,
+,0,0,1,0,1,0,0,0,
+,0,0,0,1,0,1,0,0,
+,0,0,0,0,1,0,1,0,
+,0,0,0,0,0,1,0,1,
+,0,0,0,0,0,0,1,0),byrow=T,nrow=9)
+gplot(L, displaylabels=T, vertex.cex=1, label.cex=1,
+      edge.col="red", boxed.labels=F, arrowhead.cex=1,
+      mode="kamadakawai")
+</code>
+<code>betweenness(L)
+</code>
+<code>[1]  0  0  0 36 32 30 24 14  0
+</code>
+<code># The star network
+S <- matrix(c(0,1,1,1,1,1,1,1,1,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0,
+,0,0,0,0,0,0,0,0),byrow=T,nrow=9)
+gplot(S, displaylabels=T, vertex.cex=1, label.cex=1,
+      edge.col="red", boxed.labels=F, arrowhead.cex=1,
+      mode="kamadakawai")
+</code>
+{{star_between.png}}
+<code>betweenness(S)
+</code>
+<code>[1] 56  0  0  0  0  0  0  0  0
+</code>
+<code># Two stars network
+twostars <- matrix(0,13,13)
+edges <- matrix(c(1,2,1,3,1,4,1,5,1,6,
+,7,7,8,8,13,9,13,10,13,11,13,12,13),
+                  byrow=T,ncol=2)
+twostars[edges] <- 1
+twostars <- twostars + t(twostars) - twostars * t(twostars)
+gplot(twostars, displaylabels=T, vertex.cex=1, label.cex=1,
+      edge.col="red", boxed.labels=F, arrowhead.cex=1, mode="kamadakawai")
+betweenness(twostars)
+closeness(twostars)
+</code>
+{{two_star_network.png}}
+<code>>> betweenness(twostars)
+ [1] 76  0  0  0  0 70 72 70  0  0  0  0 76
+> round(closeness(twostars),2)
+ [1] 0.35 0.27 0.27 0.27 0.27 0.39 0.40 0.39 0.27 0.27 0.27 0.27 0.35
+</code>
+===== Eigenvector =====
+__Eigenvector Centrality__
+  * 중요한 노드에 연결된 노드가 중요하다는 관점
+  * That is, the centrality of each node i is proportional to the sum of the centrality of its neighbors.
+<code>rownames(knoke.infor)
+</code>
+<code>> rownames(knoke.infor)
+ [1] "COUN" "COMM" "EDUC" "INDU" "MAYR" "WRO"  "NEWS" "UWAY" "WELF" "WEST"
+</code>
+<code>round(evcent(knoke.infor),2)
+</code>
+<code>> round(evcent(knoke.infor),2)
+ [1] 0.25 0.41 0.36 0.26 0.47 0.15 0.22 0.35 0.21 0.33
+</code>
+<code>round(evcent(t(knoke.infor)),2)
+</code>
+<code>> round(evcent(t(knoke.infor)),2)
+ [1] 0.30 0.45 0.21 0.34 0.45 0.04 0.46 0.18 0.28 0.13
+</code>