Social Network Analysis with R
JungHwan Yun
[Author]
@ JungHwan Yun
@ Master Student in Data-Science
@ Seoul National University of Science & Technology(SeoulTech)
@ E-mail : junghwan.yun@seoultech.ac.kr
[Contents]
@ Topic : Social Network Analysis with R
@ Class : Social Network Analysis
@ Version : 2.0
@ Version date : 2017-05-10
@ Summary : Package “sna”의 활용법을 다룹니다.
1. 패키지 로딩 및 작업환경 설정
- sna 패키지 설치 및 로딩
- setwd()를 이용하여 작업환경 설정
# install.packages("sna")
# setwd("D:/Google Drive/1_MASTER_Class/3_1_Social_Network_Analysis/1_Lecture_Material/C6_R_SNA/Train_Data")
library(sna)2. 행렬 입력의 기본 형태
- sna패키지의 기본 파일 입력방식은 adjacency matrix(정방행렬)이다
- 정방행렬을 직접입력.
- 직접행렬을 입력하기 때문에 행렬 연산도 가능함.
A <-matrix(c(0,1,1,0,1,
0,0,1,0,0,
1,0,0,1,0,
0,0,0,0,0,
1,0,0,0,0),byrow=T,nrow=5)
rownames(A) <-c("M1","M2","M3","M4","M5")
colnames(A) <-c("M1","M2","M3","M4","M5")
print(A)## M1 M2 M3 M4 M5
## M1 0 1 1 0 1
## M2 0 0 1 0 0
## M3 1 0 0 1 0
## M4 0 0 0 0 0
## M5 1 0 0 0 0- Alternative Input
- Edge list형태로 정의하여 해당하는 좌표만을 입력하여 행렬로 변환시키는 것도 가능.
A.1 <-matrix(0,5,5)
edge.list<-matrix(c(1,2,
1,3,
1,5,
2,3,
3,1,
3,4,
5,1),byrow=T,nrow=7,ncol=2)
A.1[edge.list] <-1
rownames(A.1) <-c("M1","M2","M3","M4","M5")
colnames(A.1) <-c("M1","M2","M3","M4","M5")
print(A.1)## M1 M2 M3 M4 M5
## M1 0 1 1 0 1
## M2 0 0 1 0 0
## M3 1 0 0 1 0
## M4 0 0 0 0 0
## M5 1 0 0 0 03. 네트워크 기본 도식하기
- gplot()을 이용하여 네트워크를 그리는 것이 가능함.
gplot(A, displaylabels=T, boxed.labels=F, vertex.cex=1, arrowhead.cex=1)
- gplot에는 네트워크의 형태를 다르게 나타낼 수 있는 다양한 옵션들이 존재함. (자세한 옵션은 gplot()의 문서 참고)
- gplot() 옵션 주기
- vertex.cex: 크기
- vertex.col: 색깔
- vertex.sides: 노드다각형, default=50
- vertex.border: 테두리색
- displaylabels: T/F
- label: 노드레이블지정
- boxed.labels
- label.pos: 레이블의위치
gplot(A,displaylabels=T,boxed.labels=F, vertex.sides=12,vertex.col="black",arrowhead.cex=1)
gplot(A,displaylabels=T,boxed.labels=F, vertex.sides=12,vertex.col="red",edge.lwd=4,edge.col="grey",arrowhead.cex=1)
gplot(A,displaylabels=T,boxed.labels=F, vertex.sides=12,vertex.col="blue",edge.lwd=10,edge.col="grey",arrowhead.cex=2, mode = "fruchtermanreingold")
gplot(A,displaylabels=T,boxed.labels=F, vertex.sides=12,vertex.col="white",edge.lwd=4,edge.col="black",arrowhead.cex=2, mode = "mds")
gplot(A,displaylabels=T,boxed.labels=F,vertex.sides=12,vertex.col="white",edge.lwd=4,edge.col="grey",arrowhead.cex=3, mode = "circle")
4. 네트워크지표산출
- 네트워크 분석에서 활용되는 네트워크 지표들 역시 산출 계산 가능함.
- 연결 중앙성
- Undirected Network : degree()
- Directed Network : degree(, cmode= “indegree”, “outdegree”, “freeman”)
degree(A, cmode = "indegree")## [1] 2 1 2 1 1degree(A, cmode = "outdegree")## [1] 3 1 2 0 1- 사이 중앙성
- betweenness()
betweenness(A)## [1] 6 0 5 0 0- 인접 중앙성
- closeness()
closeness(A)## [1] 0.8000000 0.5000000 0.6666667 0.0000000 0.5000000- 위세중앙성
- evcent()
evcent(A)## [1] 0.7236068 0.2763932 0.4472136 0.0000000 0.4472136- 밀도
- gden()
gden(A)## [1] 0.35- 경로거리 산출
- geodist()
geodist(A)## $counts
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 1 1 1 1
## [2,] 1 1 1 1 1
## [3,] 1 1 1 1 1
## [4,] 0 0 0 1 0
## [5,] 1 1 1 1 1
##
## $gdist
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 1 1 2 1
## [2,] 2 0 1 2 3
## [3,] 1 2 0 1 2
## [4,] Inf Inf Inf 0 Inf
## [5,] 1 2 2 3 0D <-geodist(A)$gdist
(path1 <-apply(D,1,sum))## [1] 5 8 6 Inf 8(path2 <-apply(D,2,sum))## [1] Inf Inf Inf 8 Inf5. Random Network 생성하기
- 네트워크를 비교하기 위해서는 동일한 크기의 랜덤 네트워크를 생성하여 비교하는 방법이 쓰이기도 함.
- n을 증가 시키면서 가상의 Random network를 생성하여 평균 거리 측정
- rgraph() 함수를 사용하여 random network 생성 가능
- n+1 명인 사회
- 평균적으로 5명을 안다.
- n = 10인 경우
- 하나의 커다란 component가 생성되는 것을 확인 할 수 있음. (실행할때 마다 결과가 바뀜)
n <-10
mu <-5
world.n<-rgraph(n+1, tprob=mu/n)
gplot(world.n, displaylabels=T, boxed.labels=F, vertex.cex=2, arrowhead.cex=1)
gden(world.n)## [1] 0.4636364N <-n*(n+1)
D.n<-geodist(world.n)$gdist
diag(D.n) <-NA
median(D.n, na.rm=T)## [1] 2mean(D.n, na.rm=T)## [1] 1.581818addmargins(table(D.n),1)## D.n
## 1 2 3 Sum
## 51 54 5 110addmargins(round(table(D.n)/N*100,1))## D.n
## 1 2 3 Sum
## 46.4 49.1 4.5 100.0components(world.n)## Node 1, Reach 11, Total 11
## Node 2, Reach 11, Total 22
## Node 3, Reach 11, Total 33
## Node 4, Reach 11, Total 44
## Node 5, Reach 11, Total 55
## Node 6, Reach 11, Total 66
## Node 7, Reach 11, Total 77
## Node 8, Reach 11, Total 88
## Node 9, Reach 11, Total 99
## Node 10, Reach 11, Total 110
## Node 11, Reach 11, Total 121## [1] 1- n = 100명인 경우
n <-100
N <-n*(n+1)
mu <-5
world.n<-rgraph(n+1, tprob=mu/n)
gden(world.n)## [1] 0.0490099D.n<-geodist(world.n)$gdist
diag(D.n) <-NA
median(D.n, na.rm=T)## [1] 3mean(D.n, na.rm=T)## [1] Infaddmargins(table(D.n),1)## D.n
## 1 2 3 4 5 6 Inf Sum
## 495 2080 4482 2545 371 27 100 10100addmargins(round(table(D.n)/N*100,1))## D.n
## 1 2 3 4 5 6 Inf Sum
## 4.9 20.6 44.4 25.2 3.7 0.3 1.0 100.1components(world.n)## Node 1, Reach 101, Total 101
## Node 2, Reach 101, Total 202
## Node 3, Reach 101, Total 303
## Node 4, Reach 101, Total 404
## Node 5, Reach 101, Total 505
## Node 6, Reach 101, Total 606
## Node 7, Reach 101, Total 707
## Node 8, Reach 101, Total 808
## Node 9, Reach 101, Total 909
## Node 10, Reach 101, Total 1010
## Node 11, Reach 101, Total 1111
## Node 12, Reach 1, Total 1112
## Node 13, Reach 101, Total 1213
## Node 14, Reach 101, Total 1314
## Node 15, Reach 101, Total 1415
## Node 16, Reach 101, Total 1516
## Node 17, Reach 101, Total 1617
## Node 18, Reach 101, Total 1718
## Node 19, Reach 101, Total 1819
## Node 20, Reach 101, Total 1920
## Node 21, Reach 101, Total 2021
## Node 22, Reach 101, Total 2122
## Node 23, Reach 101, Total 2223
## Node 24, Reach 101, Total 2324
## Node 25, Reach 101, Total 2425
## Node 26, Reach 101, Total 2526
## Node 27, Reach 101, Total 2627
## Node 28, Reach 101, Total 2728
## Node 29, Reach 101, Total 2829
## Node 30, Reach 101, Total 2930
## Node 31, Reach 101, Total 3031
## Node 32, Reach 101, Total 3132
## Node 33, Reach 101, Total 3233
## Node 34, Reach 101, Total 3334
## Node 35, Reach 101, Total 3435
## Node 36, Reach 101, Total 3536
## Node 37, Reach 101, Total 3637
## Node 38, Reach 101, Total 3738
## Node 39, Reach 101, Total 3839
## Node 40, Reach 101, Total 3940
## Node 41, Reach 101, Total 4041
## Node 42, Reach 101, Total 4142
## Node 43, Reach 101, Total 4243
## Node 44, Reach 101, Total 4344
## Node 45, Reach 101, Total 4445
## Node 46, Reach 101, Total 4546
## Node 47, Reach 101, Total 4647
## Node 48, Reach 101, Total 4748
## Node 49, Reach 101, Total 4849
## Node 50, Reach 101, Total 4950
## Node 51, Reach 101, Total 5051
## Node 52, Reach 101, Total 5152
## Node 53, Reach 101, Total 5253
## Node 54, Reach 101, Total 5354
## Node 55, Reach 101, Total 5455
## Node 56, Reach 101, Total 5556
## Node 57, Reach 101, Total 5657
## Node 58, Reach 101, Total 5758
## Node 59, Reach 101, Total 5859
## Node 60, Reach 101, Total 5960
## Node 61, Reach 101, Total 6061
## Node 62, Reach 101, Total 6162
## Node 63, Reach 101, Total 6263
## Node 64, Reach 101, Total 6364
## Node 65, Reach 101, Total 6465
## Node 66, Reach 101, Total 6566
## Node 67, Reach 101, Total 6667
## Node 68, Reach 101, Total 6768
## Node 69, Reach 101, Total 6869
## Node 70, Reach 101, Total 6970
## Node 71, Reach 101, Total 7071
## Node 72, Reach 101, Total 7172
## Node 73, Reach 101, Total 7273
## Node 74, Reach 101, Total 7374
## Node 75, Reach 101, Total 7475
## Node 76, Reach 101, Total 7576
## Node 77, Reach 101, Total 7677
## Node 78, Reach 101, Total 7778
## Node 79, Reach 101, Total 7879
## Node 80, Reach 101, Total 7980
## Node 81, Reach 101, Total 8081
## Node 82, Reach 101, Total 8182
## Node 83, Reach 101, Total 8283
## Node 84, Reach 101, Total 8384
## Node 85, Reach 101, Total 8485
## Node 86, Reach 101, Total 8586
## Node 87, Reach 101, Total 8687
## Node 88, Reach 101, Total 8788
## Node 89, Reach 101, Total 8889
## Node 90, Reach 101, Total 8990
## Node 91, Reach 101, Total 9091
## Node 92, Reach 101, Total 9192
## Node 93, Reach 101, Total 9293
## Node 94, Reach 101, Total 9394
## Node 95, Reach 101, Total 9495
## Node 96, Reach 101, Total 9596
## Node 97, Reach 101, Total 9697
## Node 98, Reach 101, Total 9798
## Node 99, Reach 101, Total 9899
## Node 100, Reach 101, Total 10000
## Node 101, Reach 101, Total 10101## [1] 2gplot(world.n, displaylabels=T, boxed.labels=F, vertex.cex=2, arrowhead.cex=1,displayisolates = T,mode = "kamadakawai")
6. Example 1: knoke-infor data
- Knoke데이터를 활용한 예제 풀이
- adjacency matrix입력 후 기본 네트워크 형태 확인
- 각종 네트워크 지표 확인
knoke.infor<-as.matrix(read.table("Train_Data/knoke-infor.txt",header=T))
rownames(knoke.infor) <-colnames(knoke.infor)
(knoke.infor)## COUN COMM EDUC INDU MAYR WRO NEWS UWAY WELF WEST
## COUN 0 1 0 0 1 0 1 0 1 0
## COMM 1 0 1 1 1 0 1 1 1 0
## EDUC 0 1 0 1 1 1 1 0 0 1
## INDU 1 1 0 0 1 0 1 0 0 0
## MAYR 1 1 1 1 0 0 1 1 1 1
## WRO 0 0 1 0 0 0 1 0 1 0
## NEWS 0 1 0 1 1 0 0 0 0 0
## UWAY 1 1 0 1 1 0 1 0 1 0
## WELF 0 1 0 0 1 0 1 0 0 0
## WEST 1 1 1 0 1 0 1 0 0 0gplot(knoke.infor, displaylabels=T,vertex.cex=1, vertex.col="green", edge.col="gray", boxed.labels=F, arrowhead.cex=1.25)
degree(knoke.infor)## [1] 9 15 10 9 16 4 12 8 8 7degree(knoke.infor,cmode = "indegree")## [1] 5 8 4 5 8 1 9 2 5 2betweenness(knoke.infor)## [1] 0.6666667 12.3333333 11.6944444 0.8055556 17.8333333 0.3333333
## [7] 2.7500000 0.0000000 1.2222222 0.3611111closeness(knoke.infor)## [1] 0.6000000 0.8181818 0.7500000 0.6000000 0.9000000 0.5294118 0.5625000
## [8] 0.6923077 0.5625000 0.6923077evcent(knoke.infor)## [1] 0.2540102 0.4119659 0.3573877 0.2619953 0.4657175 0.1532203 0.2207745
## [8] 0.3539690 0.2127894 0.3312272gden(knoke.infor)## [1] 0.54444447. 2-mode network
- 2-mode의 네트워크의 표현 방법
- 2-mode네트워크란 개인 : 개인의 관계가 아닌 개인 : 집단과 같은 분석단위가 다른 vertex사이의 관계라고 할 수 있음.
- CEO.txt는 26명의 CEO와 10개의 클럽사이의 affiliation network 임.
- Club:Club과 CEO:CEO의 네트워크를 도식하는 방법에 대하여 다룬다.
(A <-as.matrix(read.table("Train_Data/CEO.txt")))## Club1 Club2 Club3 Club4 Club5 Club6 Club7 Club8 Club9 Club10 Club11
## CEO1 0 0 1 1 0 0 0 0 1 0 0
## CEO2 0 0 1 0 1 0 1 0 0 0 0
## CEO3 0 0 1 0 0 0 0 0 0 0 0
## CEO4 0 1 1 0 0 0 0 0 0 0 0
## CEO5 0 0 1 0 0 0 0 0 0 0 0
## CEO6 0 1 1 0 0 0 0 0 0 0 0
## CEO7 0 0 1 1 0 0 0 0 0 1 1
## CEO8 0 0 0 1 0 0 1 0 0 1 0
## CEO9 1 0 0 1 0 0 0 1 0 1 0
## CEO10 0 0 1 0 0 0 0 0 1 0 0
## CEO11 0 1 1 0 0 0 0 0 1 0 0
## CEO12 0 0 0 1 0 0 1 0 0 0 0
## CEO13 0 0 1 1 1 0 0 0 1 0 0
## CEO14 0 1 1 1 0 0 0 0 0 0 1
## CEO15 0 1 1 0 0 1 0 0 0 0 0
## CEO16 0 1 1 0 0 1 0 1 0 0 0
## CEO17 0 1 1 0 1 0 0 0 0 0 1
## CEO18 0 0 0 1 0 0 0 0 1 0 0
## CEO19 1 0 1 1 0 0 1 0 1 0 0
## CEO20 0 1 1 1 0 0 0 0 0 0 1
## CEO21 0 0 1 1 0 0 0 1 0 0 0
## CEO22 0 0 1 0 0 0 0 1 0 0 0
## CEO23 0 1 1 0 0 1 0 0 0 0 0
## CEO24 1 0 1 1 0 1 0 0 0 0 0
## CEO25 0 1 1 0 0 0 0 0 0 0 0
## CEO26 0 1 1 0 0 0 0 0 0 0 0
## Club12 Club13 Club14 Club15
## CEO1 0 0 0 0
## CEO2 0 0 0 0
## CEO3 1 0 0 0
## CEO4 0 0 0 1
## CEO5 0 1 1 0
## CEO6 0 0 1 0
## CEO7 0 0 0 0
## CEO8 0 0 0 0
## CEO9 0 0 0 0
## CEO10 0 0 0 0
## CEO11 0 0 0 0
## CEO12 0 0 0 0
## CEO13 0 0 0 0
## CEO14 1 1 0 1
## CEO15 0 1 0 1
## CEO16 0 0 1 0
## CEO17 1 0 0 1
## CEO18 1 1 0 1
## CEO19 0 0 0 0
## CEO20 0 0 0 1
## CEO21 0 0 0 0
## CEO22 0 0 0 1
## CEO23 0 0 0 1
## CEO24 0 0 0 1
## CEO25 0 1 0 0
## CEO26 1 0 0 0n <-nrow(A)
m <-ncol(A)- 행렬곱을 통해서 CEO-CEO관계와 CLUB-CLUB관계의 행렬을 생성
- R : CEO Matrix
- C : Club Matrix
R <-A%*%t(A) #CEO matrix
diag(R) <-0
print(R)## CEO1 CEO2 CEO3 CEO4 CEO5 CEO6 CEO7 CEO8 CEO9 CEO10 CEO11 CEO12 CEO13
## CEO1 0 1 1 1 1 1 2 1 1 2 2 1 3
## CEO2 1 0 1 1 1 1 1 1 0 1 1 1 2
## CEO3 1 1 0 1 1 1 1 0 0 1 1 0 1
## CEO4 1 1 1 0 1 2 1 0 0 1 2 0 1
## CEO5 1 1 1 1 0 2 1 0 0 1 1 0 1
## CEO6 1 1 1 2 2 0 1 0 0 1 2 0 1
## CEO7 2 1 1 1 1 1 0 2 2 1 1 1 2
## CEO8 1 1 0 0 0 0 2 0 2 0 0 2 1
## CEO9 1 0 0 0 0 0 2 2 0 0 0 1 1
## CEO10 2 1 1 1 1 1 1 0 0 0 2 0 2
## CEO11 2 1 1 2 1 2 1 0 0 2 0 0 2
## CEO12 1 1 0 0 0 0 1 2 1 0 0 0 1
## CEO13 3 2 1 1 1 1 2 1 1 2 2 1 0
## CEO14 2 1 2 3 2 2 3 1 1 1 2 1 2
## CEO15 1 1 1 3 2 2 1 0 0 1 2 0 1
## CEO16 1 1 1 2 2 3 1 0 1 1 2 0 1
## CEO17 1 2 2 3 1 2 2 0 0 1 2 0 2
## CEO18 2 0 1 1 1 0 1 1 1 1 1 1 2
## CEO19 3 2 1 1 1 1 2 2 2 2 2 2 3
## CEO20 2 1 1 3 1 2 3 1 1 1 2 1 2
## CEO21 2 1 1 1 1 1 2 1 2 1 1 1 2
## CEO22 1 1 1 2 1 1 1 0 1 1 1 0 1
## CEO23 1 1 1 3 1 2 1 0 0 1 2 0 1
## CEO24 2 1 1 2 1 1 2 1 2 1 1 1 2
## CEO25 1 1 1 2 2 2 1 0 0 1 2 0 1
## CEO26 1 1 2 2 1 2 1 0 0 1 2 0 1
## CEO14 CEO15 CEO16 CEO17 CEO18 CEO19 CEO20 CEO21 CEO22 CEO23 CEO24
## CEO1 2 1 1 1 2 3 2 2 1 1 2
## CEO2 1 1 1 2 0 2 1 1 1 1 1
## CEO3 2 1 1 2 1 1 1 1 1 1 1
## CEO4 3 3 2 3 1 1 3 1 2 3 2
## CEO5 2 2 2 1 1 1 1 1 1 1 1
## CEO6 2 2 3 2 0 1 2 1 1 2 1
## CEO7 3 1 1 2 1 2 3 2 1 1 2
## CEO8 1 0 0 0 1 2 1 1 0 0 1
## CEO9 1 0 1 0 1 2 1 2 1 0 2
## CEO10 1 1 1 1 1 2 1 1 1 1 1
## CEO11 2 2 2 2 1 2 2 1 1 2 1
## CEO12 1 0 0 0 1 2 1 1 0 0 1
## CEO13 2 1 1 2 2 3 2 2 1 1 2
## CEO14 0 4 2 5 4 2 5 2 2 3 3
## CEO15 4 0 3 3 2 1 3 1 2 4 3
## CEO16 2 3 0 2 0 1 2 2 2 3 2
## CEO17 5 3 2 0 2 1 4 1 2 3 2
## CEO18 4 2 0 2 0 2 2 1 1 1 2
## CEO19 2 1 1 1 2 0 2 2 1 1 3
## CEO20 5 3 2 4 2 2 0 2 2 3 3
## CEO21 2 1 2 1 1 2 2 0 2 1 2
## CEO22 2 2 2 2 1 1 2 2 0 2 2
## CEO23 3 4 3 3 1 1 3 1 2 0 3
## CEO24 3 3 2 2 2 3 3 2 2 3 0
## CEO25 3 3 2 2 1 1 2 1 1 2 1
## CEO26 3 2 2 3 1 1 2 1 1 2 1
## CEO25 CEO26
## CEO1 1 1
## CEO2 1 1
## CEO3 1 2
## CEO4 2 2
## CEO5 2 1
## CEO6 2 2
## CEO7 1 1
## CEO8 0 0
## CEO9 0 0
## CEO10 1 1
## CEO11 2 2
## CEO12 0 0
## CEO13 1 1
## CEO14 3 3
## CEO15 3 2
## CEO16 2 2
## CEO17 2 3
## CEO18 1 1
## CEO19 1 1
## CEO20 2 2
## CEO21 1 1
## CEO22 1 1
## CEO23 2 2
## CEO24 1 1
## CEO25 0 2
## CEO26 2 0degree(R,cmode="indegree",ignore.eval=F)## [1] 37 26 25 39 27 33 37 16 18 26 36 14 39 61 46 39 48 32 42 53 35 32 42
## [24] 45 35 35round(closeness(R, ignore.eval=F),2)## [1] 0.71 0.83 0.81 0.62 0.76 0.62 0.71 0.60 0.60 0.78 0.60 0.62 0.68 0.56
## [15] 0.60 0.60 0.56 0.69 0.64 0.58 0.71 0.69 0.62 0.62 0.64 0.64C <-t(A)%*%A #club matrix
diag(C) <-0
print(C)## Club1 Club2 Club3 Club4 Club5 Club6 Club7 Club8 Club9 Club10 Club11
## Club1 0 0 2 3 0 1 1 1 1 1 0
## Club2 0 0 11 2 1 3 0 1 1 0 3
## Club3 2 11 0 8 3 4 2 3 5 1 4
## Club4 3 2 8 0 1 1 3 2 4 3 3
## Club5 0 1 3 1 0 0 1 0 1 0 1
## Club6 1 3 4 1 0 0 0 1 0 0 0
## Club7 1 0 2 3 1 0 0 0 1 1 0
## Club8 1 1 3 2 0 1 0 0 0 1 0
## Club9 1 1 5 4 1 0 1 0 0 0 0
## Club10 1 0 1 3 0 0 1 1 0 0 1
## Club11 0 3 4 3 1 0 0 0 0 1 0
## Club12 0 3 4 2 1 0 0 0 1 0 2
## Club13 0 3 4 2 0 1 0 0 1 0 1
## Club14 0 2 3 0 0 1 0 1 0 0 0
## Club15 1 6 8 4 1 3 0 1 1 0 3
## Club12 Club13 Club14 Club15
## Club1 0 0 0 1
## Club2 3 3 2 6
## Club3 4 4 3 8
## Club4 2 2 0 4
## Club5 1 0 0 1
## Club6 0 1 1 3
## Club7 0 0 0 0
## Club8 0 0 1 1
## Club9 1 1 0 1
## Club10 0 0 0 0
## Club11 2 1 0 3
## Club12 0 2 0 3
## Club13 2 0 1 3
## Club14 0 1 0 0
## Club15 3 3 0 0degree(C,cmode="indegree",ignore.eval=F)## [1] 11 36 62 38 10 15 9 11 16 8 18 18 18 8 34round(closeness(C, ignore.eval=F),2)## [1] 0.64 0.54 0.37 0.48 0.61 0.56 0.56 0.61 0.64 0.56 0.56 0.44 0.56 0.48
## [15] 0.56- Network Dichotomized
- Cut-off를 설정하여 Cut-off값을 기준으로 0/1로 변환
- 네트워크의 단순화를 위함.
- Dichotomize전후를 비교
- CEO Network의 Dichotomize 전후 비교 : cut-off = 2
- 네트워크의 형태가 다소 축약된 것을 알 수 있음.
- 그렇지만 Dichotomize는 정보의 손실을 의미하기 때문에 Cut-off 설정에 유의해야함.
R_dic <- R
R_dic[which(R_dic < 2)] <-0
R_dic[which(R_dic >= 2)] <-1
round(betweenness(R),2)## [1] 7.69 5.21 0.30 0.30 0.30 0.00 7.69 0.26 0.86 0.30 0.30 0.26 7.69 7.69
## [15] 0.30 2.18 0.30 6.18 7.69 7.69 7.69 2.49 0.30 7.69 0.30 0.30gplot(R, displaylabels=T, vertex.cex=1, vertex.col="green", edge.col="black", boxed.labels=F, arrowhead.cex=1)
gplot(R_dic, displaylabels=T, vertex.cex=1, vertex.col="green", edge.col="black", boxed.labels=F, arrowhead.cex=1)
- CLUB Network의 Dichotomize 전후 비교 : cut-off = 3
- 네트워크의 형태가 다소 축약된 것을 알 수 있음.
- 그렇지만 Dichotomize는 정보의 손실을 의미하기 때문에 Cut-off 설정에 유의해야함.
C_dic <- C
C_dic[which(C_dic < 3)] <- 0
C_dic[which(C_dic >= 3)] <-1
round(betweenness(C),2)## [1] 3.70 8.14 21.40 13.94 2.19 2.53 1.40 4.20 3.99 1.90 3.02
## [12] 0.57 4.22 0.33 6.47gplot(C, displaylabels=T, vertex.cex=1, vertex.col="red", edge.col="black", boxed.labels=F, arrowhead.cex=1)
gplot(C_dic, displaylabels=T, vertex.cex=1, vertex.col="red", edge.col="black", boxed.labels=F, arrowhead.cex=1)
8. symmetrization of the network
- 약한 연결과 강한 연결을 구분함.
- rule = “weak” : 약한 연결
- rule = “strong” : 강한 연결
A <-matrix(c(0,1,1,0,1,
0,0,1,0,0,
1,0,0,1,0,
0,0,0,0,0,
1,0,0,0,0),byrow=T,nrow=5)
rownames(A) <-c("M1","M2","M3","M4","M5")
colnames(A) <-c("M1","M2","M3","M4","M5")
print(A)## M1 M2 M3 M4 M5
## M1 0 1 1 0 1
## M2 0 0 1 0 0
## M3 1 0 0 1 0
## M4 0 0 0 0 0
## M5 1 0 0 0 0- 약한 연결 : A -> B OR A <- B
B <-symmetrize(A,rule="weak")
rownames(B) <-c("M1","M2","M3","M4","M5")
colnames(B) <-c("M1","M2","M3","M4","M5")
print(B)## M1 M2 M3 M4 M5
## M1 0 1 1 0 1
## M2 1 0 1 0 0
## M3 1 1 0 1 0
## M4 0 0 1 0 0
## M5 1 0 0 0 0- 강한 연결 : A <-> B
C <-symmetrize(A,rule="strong")
rownames(C) <-c("M1","M2","M3","M4","M5")
colnames(C) <-c("M1","M2","M3","M4","M5")
print(C)## M1 M2 M3 M4 M5
## M1 0 0 1 0 1
## M2 0 0 0 0 0
## M3 1 0 0 0 0
## M4 0 0 0 0 0
## M5 1 0 0 0 09. Network Cluster
- sedist() : 노드 사이의 거리를 거리행렬 산출
- equiv.clust() : 덴드로그램 형태로 표현 가능
##Generate random graphs
G1 <-rgraph(10, tprob= 0.5)
G2 <-rgraph(10, tprob= 0.5)
G<-G1*G2
G## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 0 0 0 0 0 0 1 1 0
## [2,] 0 0 1 0 1 0 0 0 0 0
## [3,] 0 0 0 1 0 1 0 0 0 0
## [4,] 0 0 0 0 0 0 0 0 1 1
## [5,] 0 0 0 0 0 0 0 0 0 1
## [6,] 1 0 0 1 0 0 0 0 1 0
## [7,] 0 0 0 0 0 0 0 0 0 0
## [8,] 1 1 0 0 0 0 0 0 1 0
## [9,] 1 1 0 0 0 0 0 1 0 0
## [10,] 0 1 1 0 1 0 0 0 1 0# sedist: Find a Matrix of Distances Between Positions (structural equivalence)
#Based on Structural Equivalence
sedist(G,method="hamming")## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 0 6 9 5 8 5 5 2 3 9
## [2,] 6 0 5 9 4 9 5 6 7 5
## [3,] 9 5 0 6 3 4 4 9 10 8
## [4,] 5 9 6 0 5 2 4 7 8 6
## [5,] 8 4 3 5 0 7 3 8 9 5
## [6,] 5 9 4 2 7 0 4 5 8 8
## [7,] 5 5 4 4 3 4 0 5 8 6
## [8,] 2 6 9 7 8 5 5 0 3 7
## [9,] 3 7 10 8 9 8 8 3 0 8
## [10,] 9 5 8 6 5 8 6 7 8 0#cluster based on structural equivalence
cluster <-equiv.clust(G, method="hamming", cluster.method = "complete")
plot(cluster)
10. Example2 : erg modeling of fmh network, Goodreau et al.(2008)
# install.packages("ergm")
library(ergm)##
## ergm: version 3.6.1, created on 2017-01-04
## Copyright (c) 2017, Mark S. Handcock, University of California -- Los Angeles
## David R. Hunter, Penn State University
## Carter T. Butts, University of California -- Irvine
## Steven M. Goodreau, University of Washington
## Pavel N. Krivitsky, University of Wollongong
## Martina Morris, University of Washington
## with contributions from
## Li Wang
## Kirk Li, University of Washington
## Skye Bender-deMoll, University of Washington
## Based on "statnet" project software (statnet.org).
## For license and citation information see statnet.org/attribution
## or type citation("ergm").## NOTE: Versions before 3.6.1 had a bug in the implementation of the
## bd() constriant which distorted the sampled distribution somewhat.
## In addition, Sampson's Monks datasets had mislabeled verteces. See
## the NEWS and the documentation for more details.data(faux.magnolia.high)
fmh<-faux.magnolia.high
fmh2 <-as.sociomatrix(faux.magnolia.high)
gplot(fmh2, vertex.cex= 1, arrowhead.cex= 0.5)
- observe 661 components
- sort size of component by size
fmh.comp<-component.dist(fmh2)## Node 1, Reach 2, Total 2
## Node 2, Reach 439, Total 441
## Node 3, Reach 439, Total 880
## Node 4, Reach 439, Total 1319
## Node 5, Reach 439, Total 1758
## Node 6, Reach 1, Total 1759
## Node 7, Reach 439, Total 2198
## Node 8, Reach 19, Total 2217
## Node 9, Reach 1, Total 2218
## Node 10, Reach 1, Total 2219
## Node 11, Reach 2, Total 2221
## Node 12, Reach 7, Total 2228
## Node 13, Reach 1, Total 2229
## Node 14, Reach 439, Total 2668
## Node 15, Reach 2, Total 2670
## Node 16, Reach 439, Total 3109
## Node 17, Reach 23, Total 3132
## Node 18, Reach 1, Total 3133
## Node 19, Reach 23, Total 3156
## Node 20, Reach 1, Total 3157
## Node 21, Reach 439, Total 3596
## Node 22, Reach 7, Total 3603
## Node 23, Reach 3, Total 3606
## Node 24, Reach 1, Total 3607
## Node 25, Reach 439, Total 4046
## Node 26, Reach 5, Total 4051
## Node 27, Reach 1, Total 4052
## Node 28, Reach 1, Total 4053
## Node 29, Reach 1, Total 4054
## Node 30, Reach 1, Total 4055
## Node 31, Reach 5, Total 4060
## Node 32, Reach 1, Total 4061
## Node 33, Reach 8, Total 4069
## Node 34, Reach 1, Total 4070
## Node 35, Reach 2, Total 4072
## Node 36, Reach 6, Total 4078
## Node 37, Reach 439, Total 4517
## Node 38, Reach 439, Total 4956
## Node 39, Reach 1, Total 4957
## Node 40, Reach 3, Total 4960
## Node 41, Reach 439, Total 5399
## Node 42, Reach 3, Total 5402
## Node 43, Reach 2, Total 5404
## Node 44, Reach 2, Total 5406
## Node 45, Reach 4, Total 5410
## Node 46, Reach 3, Total 5413
## Node 47, Reach 439, Total 5852
## Node 48, Reach 1, Total 5853
## Node 49, Reach 1, Total 5854
## Node 50, Reach 439, Total 6293
## Node 51, Reach 1, Total 6294
## Node 52, Reach 5, Total 6299
## Node 53, Reach 439, Total 6738
## Node 54, Reach 1, Total 6739
## Node 55, Reach 2, Total 6741
## Node 56, Reach 1, Total 6742
## Node 57, Reach 4, Total 6746
## Node 58, Reach 1, Total 6747
## Node 59, Reach 3, Total 6750
## Node 60, Reach 2, Total 6752
## Node 61, Reach 439, Total 7191
## Node 62, Reach 11, Total 7202
## Node 63, Reach 439, Total 7641
## Node 64, Reach 12, Total 7653
## Node 65, Reach 439, Total 8092
## Node 66, Reach 2, Total 8094
## Node 67, Reach 1, Total 8095
## Node 68, Reach 23, Total 8118
## Node 69, Reach 439, Total 8557
## Node 70, Reach 5, Total 8562
## Node 71, Reach 7, Total 8569
## Node 72, Reach 439, Total 9008
## Node 73, Reach 439, Total 9447
## Node 74, Reach 7, Total 9454
## Node 75, Reach 5, Total 9459
## Node 76, Reach 1, Total 9460
## Node 77, Reach 1, Total 9461
## Node 78, Reach 23, Total 9484
## Node 79, Reach 1, Total 9485
## Node 80, Reach 3, Total 9488
## Node 81, Reach 1, Total 9489
## Node 82, Reach 23, Total 9512
## Node 83, Reach 439, Total 9951
## Node 84, Reach 3, Total 9954
## Node 85, Reach 1, Total 9955
## Node 86, Reach 439, Total 10394
## Node 87, Reach 2, Total 10396
## Node 88, Reach 1, Total 10397
## Node 89, Reach 5, Total 10402
## Node 90, Reach 23, Total 10425
## Node 91, Reach 1, Total 10426
## Node 92, Reach 439, Total 10865
## Node 93, Reach 8, Total 10873
## Node 94, Reach 3, Total 10876
## Node 95, Reach 1, Total 10877
## Node 96, Reach 1, Total 10878
## Node 97, Reach 5, Total 10883
## Node 98, Reach 1, Total 10884
## Node 99, Reach 1, Total 10885
## Node 100, Reach 8, Total 10893
## Node 101, Reach 1, Total 10894
## Node 102, Reach 439, Total 11333
## Node 103, Reach 1, Total 11334
## Node 104, Reach 1, Total 11335
## Node 105, Reach 1, Total 11336
## Node 106, Reach 6, Total 11342
## Node 107, Reach 3, Total 11345
## Node 108, Reach 3, Total 11348
## Node 109, Reach 3, Total 11351
## Node 110, Reach 1, Total 11352
## Node 111, Reach 1, Total 11353
## Node 112, Reach 1, Total 11354
## Node 113, Reach 1, Total 11355
## Node 114, Reach 439, Total 11794
## Node 115, Reach 439, Total 12233
## Node 116, Reach 1, Total 12234
## Node 117, Reach 1, Total 12235
## Node 118, Reach 2, Total 12237
## Node 119, Reach 439, Total 12676
## Node 120, Reach 7, Total 12683
## Node 121, Reach 439, Total 13122
## Node 122, Reach 439, Total 13561
## Node 123, Reach 439, Total 14000
## Node 124, Reach 1, Total 14001
## Node 125, Reach 439, Total 14440
## Node 126, Reach 1, Total 14441
## Node 127, Reach 1, Total 14442
## Node 128, Reach 439, Total 14881
## Node 129, Reach 3, Total 14884
## Node 130, Reach 439, Total 15323
## Node 131, Reach 11, Total 15334
## Node 132, Reach 2, Total 15336
## Node 133, Reach 439, Total 15775
## Node 134, Reach 7, Total 15782
## Node 135, Reach 4, Total 15786
## Node 136, Reach 1, Total 15787
## Node 137, Reach 439, Total 16226
## Node 138, Reach 7, Total 16233
## Node 139, Reach 1, Total 16234
## Node 140, Reach 439, Total 16673
## Node 141, Reach 439, Total 17112
## Node 142, Reach 12, Total 17124
## Node 143, Reach 1, Total 17125
## Node 144, Reach 7, Total 17132
## Node 145, Reach 1, Total 17133
## Node 146, Reach 1, Total 17134
## Node 147, Reach 1, Total 17135
## Node 148, Reach 439, Total 17574
## Node 149, Reach 3, Total 17577
## Node 150, Reach 439, Total 18016
## Node 151, Reach 1, Total 18017
## Node 152, Reach 1, Total 18018
## Node 153, Reach 1, Total 18019
## Node 154, Reach 2, Total 18021
## Node 155, Reach 1, Total 18022
## Node 156, Reach 1, Total 18023
## Node 157, Reach 439, Total 18462
## Node 158, Reach 439, Total 18901
## Node 159, Reach 1, Total 18902
## Node 160, Reach 1, Total 18903
## Node 161, Reach 3, Total 18906
## Node 162, Reach 1, Total 18907
## Node 163, Reach 439, Total 19346
## Node 164, Reach 1, Total 19347
## Node 165, Reach 8, Total 19355
## Node 166, Reach 439, Total 19794
## Node 167, Reach 1, Total 19795
## Node 168, Reach 1, Total 19796
## Node 169, Reach 1, Total 19797
## Node 170, Reach 439, Total 20236
## Node 171, Reach 1, Total 20237
## Node 172, Reach 439, Total 20676
## Node 173, Reach 1, Total 20677
## Node 174, Reach 1, Total 20678
## Node 175, Reach 5, Total 20683
## Node 176, Reach 2, Total 20685
## Node 177, Reach 2, Total 20687
## Node 178, Reach 1, Total 20688
## Node 179, Reach 1, Total 20689
## Node 180, Reach 439, Total 21128
## Node 181, Reach 1, Total 21129
## Node 182, Reach 439, Total 21568
## Node 183, Reach 439, Total 22007
## Node 184, Reach 2, Total 22009
## Node 185, Reach 1, Total 22010
## Node 186, Reach 1, Total 22011
## Node 187, Reach 439, Total 22450
## Node 188, Reach 1, Total 22451
## Node 189, Reach 1, Total 22452
## Node 190, Reach 1, Total 22453
## Node 191, Reach 1, Total 22454
## Node 192, Reach 1, Total 22455
## Node 193, Reach 1, Total 22456
## Node 194, Reach 439, Total 22895
## Node 195, Reach 439, Total 23334
## Node 196, Reach 2, Total 23336
## Node 197, Reach 1, Total 23337
## Node 198, Reach 2, Total 23339
## Node 199, Reach 1, Total 23340
## Node 200, Reach 439, Total 23779
## Node 201, Reach 7, Total 23786
## Node 202, Reach 1, Total 23787
## Node 203, Reach 439, Total 24226
## Node 204, Reach 439, Total 24665
## Node 205, Reach 1, Total 24666
## Node 206, Reach 439, Total 25105
## Node 207, Reach 439, Total 25544
## Node 208, Reach 1, Total 25545
## Node 209, Reach 439, Total 25984
## Node 210, Reach 1, Total 25985
## Node 211, Reach 1, Total 25986
## Node 212, Reach 2, Total 25988
## Node 213, Reach 439, Total 26427
## Node 214, Reach 439, Total 26866
## Node 215, Reach 3, Total 26869
## Node 216, Reach 439, Total 27308
## Node 217, Reach 439, Total 27747
## Node 218, Reach 4, Total 27751
## Node 219, Reach 3, Total 27754
## Node 220, Reach 1, Total 27755
## Node 221, Reach 2, Total 27757
## Node 222, Reach 3, Total 27760
## Node 223, Reach 1, Total 27761
## Node 224, Reach 439, Total 28200
## Node 225, Reach 439, Total 28639
## Node 226, Reach 5, Total 28644
## Node 227, Reach 439, Total 29083
## Node 228, Reach 5, Total 29088
## Node 229, Reach 1, Total 29089
## Node 230, Reach 1, Total 29090
## Node 231, Reach 439, Total 29529
## Node 232, Reach 439, Total 29968
## Node 233, Reach 1, Total 29969
## Node 234, Reach 1, Total 29970
## Node 235, Reach 1, Total 29971
## Node 236, Reach 3, Total 29974
## Node 237, Reach 7, Total 29981
## Node 238, Reach 2, Total 29983
## Node 239, Reach 1, Total 29984
## Node 240, Reach 8, Total 29992
## Node 241, Reach 1, Total 29993
## Node 242, Reach 2, Total 29995
## Node 243, Reach 2, Total 29997
## Node 244, Reach 1, Total 29998
## Node 245, Reach 1, Total 29999
## Node 246, Reach 2, Total 30001
## Node 247, Reach 1, Total 30002
## Node 248, Reach 8, Total 30010
## Node 249, Reach 1, Total 30011
## Node 250, Reach 1, Total 30012
## Node 251, Reach 439, Total 30451
## Node 252, Reach 1, Total 30452
## Node 253, Reach 7, Total 30459
## Node 254, Reach 439, Total 30898
## Node 255, Reach 439, Total 31337
## Node 256, Reach 1, Total 31338
## Node 257, Reach 1, Total 31339
## Node 258, Reach 2, Total 31341
## Node 259, Reach 439, Total 31780
## Node 260, Reach 1, Total 31781
## Node 261, Reach 1, Total 31782
## Node 262, Reach 439, Total 32221
## Node 263, Reach 19, Total 32240
## Node 264, Reach 439, Total 32679
## Node 265, Reach 3, Total 32682
## Node 266, Reach 1, Total 32683
## Node 267, Reach 1, Total 32684
## Node 268, Reach 1, Total 32685
## Node 269, Reach 1, Total 32686
## Node 270, Reach 439, Total 33125
## Node 271, Reach 1, Total 33126
## Node 272, Reach 1, Total 33127
## Node 273, Reach 19, Total 33146
## Node 274, Reach 439, Total 33585
## Node 275, Reach 12, Total 33597
## Node 276, Reach 1, Total 33598
## Node 277, Reach 7, Total 33605
## Node 278, Reach 439, Total 34044
## Node 279, Reach 439, Total 34483
## Node 280, Reach 3, Total 34486
## Node 281, Reach 1, Total 34487
## Node 282, Reach 7, Total 34494
## Node 283, Reach 23, Total 34517
## Node 284, Reach 439, Total 34956
## Node 285, Reach 439, Total 35395
## Node 286, Reach 1, Total 35396
## Node 287, Reach 439, Total 35835
## Node 288, Reach 1, Total 35836
## Node 289, Reach 439, Total 36275
## Node 290, Reach 439, Total 36714
## Node 291, Reach 439, Total 37153
## Node 292, Reach 439, Total 37592
## Node 293, Reach 1, Total 37593
## Node 294, Reach 439, Total 38032
## Node 295, Reach 1, Total 38033
## Node 296, Reach 439, Total 38472
## Node 297, Reach 1, Total 38473
## Node 298, Reach 439, Total 38912
## Node 299, Reach 439, Total 39351
## Node 300, Reach 1, Total 39352
## Node 301, Reach 439, Total 39791
## Node 302, Reach 3, Total 39794
## Node 303, Reach 3, Total 39797
## Node 304, Reach 2, Total 39799
## Node 305, Reach 19, Total 39818
## Node 306, Reach 1, Total 39819
## Node 307, Reach 1, Total 39820
## Node 308, Reach 439, Total 40259
## Node 309, Reach 1, Total 40260
## Node 310, Reach 439, Total 40699
## Node 311, Reach 439, Total 41138
## Node 312, Reach 1, Total 41139
## Node 313, Reach 5, Total 41144
## Node 314, Reach 1, Total 41145
## Node 315, Reach 3, Total 41148
## Node 316, Reach 1, Total 41149
## Node 317, Reach 439, Total 41588
## Node 318, Reach 2, Total 41590
## Node 319, Reach 8, Total 41598
## Node 320, Reach 3, Total 41601
## Node 321, Reach 1, Total 41602
## Node 322, Reach 1, Total 41603
## Node 323, Reach 439, Total 42042
## Node 324, Reach 1, Total 42043
## Node 325, Reach 439, Total 42482
## Node 326, Reach 5, Total 42487
## Node 327, Reach 439, Total 42926
## Node 328, Reach 1, Total 42927
## Node 329, Reach 1, Total 42928
## Node 330, Reach 3, Total 42931
## Node 331, Reach 1, Total 42932
## Node 332, Reach 4, Total 42936
## Node 333, Reach 1, Total 42937
## Node 334, Reach 439, Total 43376
## Node 335, Reach 439, Total 43815
## Node 336, Reach 3, Total 43818
## Node 337, Reach 3, Total 43821
## Node 338, Reach 1, Total 43822
## Node 339, Reach 1, Total 43823
## Node 340, Reach 1, Total 43824
## Node 341, Reach 3, Total 43827
## Node 342, Reach 8, Total 43835
## Node 343, Reach 2, Total 43837
## Node 344, Reach 439, Total 44276
## Node 345, Reach 3, Total 44279
## Node 346, Reach 3, Total 44282
## Node 347, Reach 439, Total 44721
## Node 348, Reach 6, Total 44727
## Node 349, Reach 5, Total 44732
## Node 350, Reach 1, Total 44733
## Node 351, Reach 2, Total 44735
## Node 352, Reach 8, Total 44743
## Node 353, Reach 6, Total 44749
## Node 354, Reach 1, Total 44750
## Node 355, Reach 439, Total 45189
## Node 356, Reach 439, Total 45628
## Node 357, Reach 1, Total 45629
## Node 358, Reach 439, Total 46068
## Node 359, Reach 6, Total 46074
## Node 360, Reach 1, Total 46075
## Node 361, Reach 1, Total 46076
## Node 362, Reach 3, Total 46079
## Node 363, Reach 5, Total 46084
## Node 364, Reach 3, Total 46087
## Node 365, Reach 1, Total 46088
## Node 366, Reach 2, Total 46090
## Node 367, Reach 439, Total 46529
## Node 368, Reach 2, Total 46531
## Node 369, Reach 6, Total 46537
## Node 370, Reach 3, Total 46540
## Node 371, Reach 2, Total 46542
## Node 372, Reach 11, Total 46553
## Node 373, Reach 1, Total 46554
## Node 374, Reach 439, Total 46993
## Node 375, Reach 23, Total 47016
## Node 376, Reach 1, Total 47017
## Node 377, Reach 5, Total 47022
## Node 378, Reach 1, Total 47023
## Node 379, Reach 1, Total 47024
## Node 380, Reach 439, Total 47463
## Node 381, Reach 1, Total 47464
## Node 382, Reach 439, Total 47903
## Node 383, Reach 3, Total 47906
## Node 384, Reach 1, Total 47907
## Node 385, Reach 23, Total 47930
## Node 386, Reach 2, Total 47932
## Node 387, Reach 5, Total 47937
## Node 388, Reach 23, Total 47960
## Node 389, Reach 439, Total 48399
## Node 390, Reach 1, Total 48400
## Node 391, Reach 439, Total 48839
## Node 392, Reach 2, Total 48841
## Node 393, Reach 1, Total 48842
## Node 394, Reach 2, Total 48844
## Node 395, Reach 439, Total 49283
## Node 396, Reach 439, Total 49722
## Node 397, Reach 1, Total 49723
## Node 398, Reach 439, Total 50162
## Node 399, Reach 2, Total 50164
## Node 400, Reach 1, Total 50165
## Node 401, Reach 1, Total 50166
## Node 402, Reach 439, Total 50605
## Node 403, Reach 2, Total 50607
## Node 404, Reach 4, Total 50611
## Node 405, Reach 1, Total 50612
## Node 406, Reach 1, Total 50613
## Node 407, Reach 7, Total 50620
## Node 408, Reach 439, Total 51059
## Node 409, Reach 439, Total 51498
## Node 410, Reach 439, Total 51937
## Node 411, Reach 3, Total 51940
## Node 412, Reach 1, Total 51941
## Node 413, Reach 1, Total 51942
## Node 414, Reach 439, Total 52381
## Node 415, Reach 3, Total 52384
## Node 416, Reach 439, Total 52823
## Node 417, Reach 2, Total 52825
## Node 418, Reach 1, Total 52826
## Node 419, Reach 23, Total 52849
## Node 420, Reach 1, Total 52850
## Node 421, Reach 1, Total 52851
## Node 422, Reach 5, Total 52856
## Node 423, Reach 1, Total 52857
## Node 424, Reach 4, Total 52861
## Node 425, Reach 439, Total 53300
## Node 426, Reach 439, Total 53739
## Node 427, Reach 23, Total 53762
## Node 428, Reach 1, Total 53763
## Node 429, Reach 2, Total 53765
## Node 430, Reach 3, Total 53768
## Node 431, Reach 1, Total 53769
## Node 432, Reach 1, Total 53770
## Node 433, Reach 2, Total 53772
## Node 434, Reach 1, Total 53773
## Node 435, Reach 7, Total 53780
## Node 436, Reach 1, Total 53781
## Node 437, Reach 439, Total 54220
## Node 438, Reach 3, Total 54223
## Node 439, Reach 439, Total 54662
## Node 440, Reach 5, Total 54667
## Node 441, Reach 1, Total 54668
## Node 442, Reach 1, Total 54669
## Node 443, Reach 1, Total 54670
## Node 444, Reach 439, Total 55109
## Node 445, Reach 4, Total 55113
## Node 446, Reach 7, Total 55120
## Node 447, Reach 439, Total 55559
## Node 448, Reach 12, Total 55571
## Node 449, Reach 439, Total 56010
## Node 450, Reach 7, Total 56017
## Node 451, Reach 7, Total 56024
## Node 452, Reach 439, Total 56463
## Node 453, Reach 1, Total 56464
## Node 454, Reach 1, Total 56465
## Node 455, Reach 2, Total 56467
## Node 456, Reach 439, Total 56906
## Node 457, Reach 439, Total 57345
## Node 458, Reach 23, Total 57368
## Node 459, Reach 2, Total 57370
## Node 460, Reach 1, Total 57371
## Node 461, Reach 1, Total 57372
## Node 462, Reach 439, Total 57811
## Node 463, Reach 1, Total 57812
## Node 464, Reach 1, Total 57813
## Node 465, Reach 439, Total 58252
## Node 466, Reach 5, Total 58257
## Node 467, Reach 1, Total 58258
## Node 468, Reach 1, Total 58259
## Node 469, Reach 439, Total 58698
## Node 470, Reach 439, Total 59137
## Node 471, Reach 439, Total 59576
## Node 472, Reach 439, Total 60015
## Node 473, Reach 439, Total 60454
## Node 474, Reach 7, Total 60461
## Node 475, Reach 439, Total 60900
## Node 476, Reach 8, Total 60908
## Node 477, Reach 3, Total 60911
## Node 478, Reach 5, Total 60916
## Node 479, Reach 439, Total 61355
## Node 480, Reach 439, Total 61794
## Node 481, Reach 439, Total 62233
## Node 482, Reach 1, Total 62234
## Node 483, Reach 439, Total 62673
## Node 484, Reach 1, Total 62674
## Node 485, Reach 1, Total 62675
## Node 486, Reach 4, Total 62679
## Node 487, Reach 439, Total 63118
## Node 488, Reach 439, Total 63557
## Node 489, Reach 1, Total 63558
## Node 490, Reach 439, Total 63997
## Node 491, Reach 1, Total 63998
## Node 492, Reach 439, Total 64437
## Node 493, Reach 439, Total 64876
## Node 494, Reach 5, Total 64881
## Node 495, Reach 1, Total 64882
## Node 496, Reach 9, Total 64891
## Node 497, Reach 439, Total 65330
## Node 498, Reach 1, Total 65331
## Node 499, Reach 439, Total 65770
## Node 500, Reach 2, Total 65772
## Node 501, Reach 439, Total 66211
## Node 502, Reach 439, Total 66650
## Node 503, Reach 1, Total 66651
## Node 504, Reach 2, Total 66653
## Node 505, Reach 4, Total 66657
## Node 506, Reach 1, Total 66658
## Node 507, Reach 439, Total 67097
## Node 508, Reach 9, Total 67106
## Node 509, Reach 439, Total 67545
## Node 510, Reach 439, Total 67984
## Node 511, Reach 1, Total 67985
## Node 512, Reach 439, Total 68424
## Node 513, Reach 2, Total 68426
## Node 514, Reach 2, Total 68428
## Node 515, Reach 1, Total 68429
## Node 516, Reach 5, Total 68434
## Node 517, Reach 439, Total 68873
## Node 518, Reach 439, Total 69312
## Node 519, Reach 2, Total 69314
## Node 520, Reach 2, Total 69316
## Node 521, Reach 439, Total 69755
## Node 522, Reach 439, Total 70194
## Node 523, Reach 1, Total 70195
## Node 524, Reach 439, Total 70634
## Node 525, Reach 439, Total 71073
## Node 526, Reach 439, Total 71512
## Node 527, Reach 1, Total 71513
## Node 528, Reach 439, Total 71952
## Node 529, Reach 2, Total 71954
## Node 530, Reach 439, Total 72393
## Node 531, Reach 4, Total 72397
## Node 532, Reach 8, Total 72405
## Node 533, Reach 1, Total 72406
## Node 534, Reach 3, Total 72409
## Node 535, Reach 439, Total 72848
## Node 536, Reach 439, Total 73287
## Node 537, Reach 2, Total 73289
## Node 538, Reach 439, Total 73728
## Node 539, Reach 1, Total 73729
## Node 540, Reach 1, Total 73730
## Node 541, Reach 7, Total 73737
## Node 542, Reach 1, Total 73738
## Node 543, Reach 1, Total 73739
## Node 544, Reach 439, Total 74178
## Node 545, Reach 1, Total 74179
## Node 546, Reach 2, Total 74181
## Node 547, Reach 1, Total 74182
## Node 548, Reach 439, Total 74621
## Node 549, Reach 439, Total 75060
## Node 550, Reach 439, Total 75499
## Node 551, Reach 2, Total 75501
## Node 552, Reach 439, Total 75940
## Node 553, Reach 7, Total 75947
## Node 554, Reach 1, Total 75948
## Node 555, Reach 2, Total 75950
## Node 556, Reach 2, Total 75952
## Node 557, Reach 439, Total 76391
## Node 558, Reach 439, Total 76830
## Node 559, Reach 439, Total 77269
## Node 560, Reach 1, Total 77270
## Node 561, Reach 2, Total 77272
## Node 562, Reach 439, Total 77711
## Node 563, Reach 1, Total 77712
## Node 564, Reach 7, Total 77719
## Node 565, Reach 1, Total 77720
## Node 566, Reach 1, Total 77721
## Node 567, Reach 1, Total 77722
## Node 568, Reach 439, Total 78161
## Node 569, Reach 1, Total 78162
## Node 570, Reach 439, Total 78601
## Node 571, Reach 8, Total 78609
## Node 572, Reach 1, Total 78610
## Node 573, Reach 7, Total 78617
## Node 574, Reach 8, Total 78625
## Node 575, Reach 1, Total 78626
## Node 576, Reach 2, Total 78628
## Node 577, Reach 439, Total 79067
## Node 578, Reach 1, Total 79068
## Node 579, Reach 2, Total 79070
## Node 580, Reach 2, Total 79072
## Node 581, Reach 4, Total 79076
## Node 582, Reach 1, Total 79077
## Node 583, Reach 5, Total 79082
## Node 584, Reach 439, Total 79521
## Node 585, Reach 8, Total 79529
## Node 586, Reach 1, Total 79530
## Node 587, Reach 2, Total 79532
## Node 588, Reach 8, Total 79540
## Node 589, Reach 439, Total 79979
## Node 590, Reach 439, Total 80418
## Node 591, Reach 2, Total 80420
## Node 592, Reach 1, Total 80421
## Node 593, Reach 5, Total 80426
## Node 594, Reach 1, Total 80427
## Node 595, Reach 6, Total 80433
## Node 596, Reach 1, Total 80434
## Node 597, Reach 23, Total 80457
## Node 598, Reach 439, Total 80896
## Node 599, Reach 23, Total 80919
## Node 600, Reach 439, Total 81358
## Node 601, Reach 6, Total 81364
## Node 602, Reach 2, Total 81366
## Node 603, Reach 439, Total 81805
## Node 604, Reach 1, Total 81806
## Node 605, Reach 1, Total 81807
## Node 606, Reach 19, Total 81826
## Node 607, Reach 1, Total 81827
## Node 608, Reach 3, Total 81830
## Node 609, Reach 23, Total 81853
## Node 610, Reach 439, Total 82292
## Node 611, Reach 439, Total 82731
## Node 612, Reach 1, Total 82732
## Node 613, Reach 3, Total 82735
## Node 614, Reach 4, Total 82739
## Node 615, Reach 19, Total 82758
## Node 616, Reach 2, Total 82760
## Node 617, Reach 3, Total 82763
## Node 618, Reach 19, Total 82782
## Node 619, Reach 1, Total 82783
## Node 620, Reach 439, Total 83222
## Node 621, Reach 439, Total 83661
## Node 622, Reach 439, Total 84100
## Node 623, Reach 1, Total 84101
## Node 624, Reach 439, Total 84540
## Node 625, Reach 1, Total 84541
## Node 626, Reach 3, Total 84544
## Node 627, Reach 5, Total 84549
## Node 628, Reach 4, Total 84553
## Node 629, Reach 1, Total 84554
## Node 630, Reach 439, Total 84993
## Node 631, Reach 1, Total 84994
## Node 632, Reach 439, Total 85433
## Node 633, Reach 9, Total 85442
## Node 634, Reach 1, Total 85443
## Node 635, Reach 1, Total 85444
## Node 636, Reach 5, Total 85449
## Node 637, Reach 4, Total 85453
## Node 638, Reach 7, Total 85460
## Node 639, Reach 7, Total 85467
## Node 640, Reach 1, Total 85468
## Node 641, Reach 1, Total 85469
## Node 642, Reach 439, Total 85908
## Node 643, Reach 2, Total 85910
## Node 644, Reach 2, Total 85912
## Node 645, Reach 1, Total 85913
## Node 646, Reach 439, Total 86352
## Node 647, Reach 1, Total 86353
## Node 648, Reach 1, Total 86354
## Node 649, Reach 439, Total 86793
## Node 650, Reach 439, Total 87232
## Node 651, Reach 439, Total 87671
## Node 652, Reach 9, Total 87680
## Node 653, Reach 3, Total 87683
## Node 654, Reach 2, Total 87685
## Node 655, Reach 439, Total 88124
## Node 656, Reach 1, Total 88125
## Node 657, Reach 439, Total 88564
## Node 658, Reach 1, Total 88565
## Node 659, Reach 1, Total 88566
## Node 660, Reach 1, Total 88567
## Node 661, Reach 5, Total 88572
## Node 662, Reach 1, Total 88573
## Node 663, Reach 1, Total 88574
## Node 664, Reach 4, Total 88578
## Node 665, Reach 5, Total 88583
## Node 666, Reach 5, Total 88588
## Node 667, Reach 439, Total 89027
## Node 668, Reach 1, Total 89028
## Node 669, Reach 2, Total 89030
## Node 670, Reach 1, Total 89031
## Node 671, Reach 3, Total 89034
## Node 672, Reach 6, Total 89040
## Node 673, Reach 5, Total 89045
## Node 674, Reach 23, Total 89068
## Node 675, Reach 1, Total 89069
## Node 676, Reach 1, Total 89070
## Node 677, Reach 439, Total 89509
## Node 678, Reach 7, Total 89516
## Node 679, Reach 4, Total 89520
## Node 680, Reach 19, Total 89539
## Node 681, Reach 439, Total 89978
## Node 682, Reach 1, Total 89979
## Node 683, Reach 439, Total 90418
## Node 684, Reach 1, Total 90419
## Node 685, Reach 439, Total 90858
## Node 686, Reach 12, Total 90870
## Node 687, Reach 439, Total 91309
## Node 688, Reach 439, Total 91748
## Node 689, Reach 439, Total 92187
## Node 690, Reach 439, Total 92626
## Node 691, Reach 7, Total 92633
## Node 692, Reach 439, Total 93072
## Node 693, Reach 1, Total 93073
## Node 694, Reach 439, Total 93512
## Node 695, Reach 2, Total 93514
## Node 696, Reach 1, Total 93515
## Node 697, Reach 1, Total 93516
## Node 698, Reach 439, Total 93955
## Node 699, Reach 1, Total 93956
## Node 700, Reach 1, Total 93957
## Node 701, Reach 1, Total 93958
## Node 702, Reach 439, Total 94397
## Node 703, Reach 439, Total 94836
## Node 704, Reach 1, Total 94837
## Node 705, Reach 1, Total 94838
## Node 706, Reach 439, Total 95277
## Node 707, Reach 439, Total 95716
## Node 708, Reach 439, Total 96155
## Node 709, Reach 1, Total 96156
## Node 710, Reach 2, Total 96158
## Node 711, Reach 3, Total 96161
## Node 712, Reach 439, Total 96600
## Node 713, Reach 2, Total 96602
## Node 714, Reach 1, Total 96603
## Node 715, Reach 1, Total 96604
## Node 716, Reach 23, Total 96627
## Node 717, Reach 1, Total 96628
## Node 718, Reach 439, Total 97067
## Node 719, Reach 439, Total 97506
## Node 720, Reach 439, Total 97945
## Node 721, Reach 12, Total 97957
## Node 722, Reach 439, Total 98396
## Node 723, Reach 439, Total 98835
## Node 724, Reach 439, Total 99274
## Node 725, Reach 439, Total 99713
## Node 726, Reach 8, Total 99721
## Node 727, Reach 439, Total 100160
## Node 728, Reach 1, Total 100161
## Node 729, Reach 439, Total 100600
## Node 730, Reach 8, Total 100608
## Node 731, Reach 439, Total 101047
## Node 732, Reach 1, Total 101048
## Node 733, Reach 439, Total 101487
## Node 734, Reach 1, Total 101488
## Node 735, Reach 1, Total 101489
## Node 736, Reach 1, Total 101490
## Node 737, Reach 2, Total 101492
## Node 738, Reach 1, Total 101493
## Node 739, Reach 439, Total 101932
## Node 740, Reach 1, Total 101933
## Node 741, Reach 439, Total 102372
## Node 742, Reach 1, Total 102373
## Node 743, Reach 439, Total 102812
## Node 744, Reach 439, Total 103251
## Node 745, Reach 439, Total 103690
## Node 746, Reach 1, Total 103691
## Node 747, Reach 439, Total 104130
## Node 748, Reach 2, Total 104132
## Node 749, Reach 439, Total 104571
## Node 750, Reach 1, Total 104572
## Node 751, Reach 439, Total 105011
## Node 752, Reach 439, Total 105450
## Node 753, Reach 439, Total 105889
## Node 754, Reach 1, Total 105890
## Node 755, Reach 1, Total 105891
## Node 756, Reach 439, Total 106330
## Node 757, Reach 1, Total 106331
## Node 758, Reach 1, Total 106332
## Node 759, Reach 2, Total 106334
## Node 760, Reach 439, Total 106773
## Node 761, Reach 439, Total 107212
## Node 762, Reach 1, Total 107213
## Node 763, Reach 1, Total 107214
## Node 764, Reach 439, Total 107653
## Node 765, Reach 439, Total 108092
## Node 766, Reach 439, Total 108531
## Node 767, Reach 8, Total 108539
## Node 768, Reach 5, Total 108544
## Node 769, Reach 439, Total 108983
## Node 770, Reach 2, Total 108985
## Node 771, Reach 439, Total 109424
## Node 772, Reach 2, Total 109426
## Node 773, Reach 2, Total 109428
## Node 774, Reach 439, Total 109867
## Node 775, Reach 1, Total 109868
## Node 776, Reach 2, Total 109870
## Node 777, Reach 11, Total 109881
## Node 778, Reach 439, Total 110320
## Node 779, Reach 439, Total 110759
## Node 780, Reach 439, Total 111198
## Node 781, Reach 1, Total 111199
## Node 782, Reach 1, Total 111200
## Node 783, Reach 439, Total 111639
## Node 784, Reach 439, Total 112078
## Node 785, Reach 3, Total 112081
## Node 786, Reach 439, Total 112520
## Node 787, Reach 1, Total 112521
## Node 788, Reach 439, Total 112960
## Node 789, Reach 1, Total 112961
## Node 790, Reach 439, Total 113400
## Node 791, Reach 1, Total 113401
## Node 792, Reach 1, Total 113402
## Node 793, Reach 439, Total 113841
## Node 794, Reach 439, Total 114280
## Node 795, Reach 439, Total 114719
## Node 796, Reach 3, Total 114722
## Node 797, Reach 12, Total 114734
## Node 798, Reach 1, Total 114735
## Node 799, Reach 1, Total 114736
## Node 800, Reach 1, Total 114737
## Node 801, Reach 439, Total 115176
## Node 802, Reach 3, Total 115179
## Node 803, Reach 1, Total 115180
## Node 804, Reach 12, Total 115192
## Node 805, Reach 2, Total 115194
## Node 806, Reach 1, Total 115195
## Node 807, Reach 8, Total 115203
## Node 808, Reach 1, Total 115204
## Node 809, Reach 4, Total 115208
## Node 810, Reach 1, Total 115209
## Node 811, Reach 2, Total 115211
## Node 812, Reach 439, Total 115650
## Node 813, Reach 6, Total 115656
## Node 814, Reach 5, Total 115661
## Node 815, Reach 1, Total 115662
## Node 816, Reach 4, Total 115666
## Node 817, Reach 439, Total 116105
## Node 818, Reach 439, Total 116544
## Node 819, Reach 3, Total 116547
## Node 820, Reach 1, Total 116548
## Node 821, Reach 3, Total 116551
## Node 822, Reach 5, Total 116556
## Node 823, Reach 1, Total 116557
## Node 824, Reach 1, Total 116558
## Node 825, Reach 1, Total 116559
## Node 826, Reach 7, Total 116566
## Node 827, Reach 1, Total 116567
## Node 828, Reach 439, Total 117006
## Node 829, Reach 1, Total 117007
## Node 830, Reach 439, Total 117446
## Node 831, Reach 1, Total 117447
## Node 832, Reach 439, Total 117886
## Node 833, Reach 439, Total 118325
## Node 834, Reach 1, Total 118326
## Node 835, Reach 1, Total 118327
## Node 836, Reach 439, Total 118766
## Node 837, Reach 1, Total 118767
## Node 838, Reach 2, Total 118769
## Node 839, Reach 3, Total 118772
## Node 840, Reach 1, Total 118773
## Node 841, Reach 2, Total 118775
## Node 842, Reach 3, Total 118778
## Node 843, Reach 1, Total 118779
## Node 844, Reach 2, Total 118781
## Node 845, Reach 1, Total 118782
## Node 846, Reach 439, Total 119221
## Node 847, Reach 439, Total 119660
## Node 848, Reach 2, Total 119662
## Node 849, Reach 1, Total 119663
## Node 850, Reach 439, Total 120102
## Node 851, Reach 1, Total 120103
## Node 852, Reach 1, Total 120104
## Node 853, Reach 439, Total 120543
## Node 854, Reach 3, Total 120546
## Node 855, Reach 439, Total 120985
## Node 856, Reach 9, Total 120994
## Node 857, Reach 439, Total 121433
## Node 858, Reach 1, Total 121434
## Node 859, Reach 19, Total 121453
## Node 860, Reach 439, Total 121892
## Node 861, Reach 439, Total 122331
## Node 862, Reach 439, Total 122770
## Node 863, Reach 1, Total 122771
## Node 864, Reach 3, Total 122774
## Node 865, Reach 3, Total 122777
## Node 866, Reach 1, Total 122778
## Node 867, Reach 5, Total 122783
## Node 868, Reach 1, Total 122784
## Node 869, Reach 439, Total 123223
## Node 870, Reach 6, Total 123229
## Node 871, Reach 1, Total 123230
## Node 872, Reach 1, Total 123231
## Node 873, Reach 1, Total 123232
## Node 874, Reach 7, Total 123239
## Node 875, Reach 1, Total 123240
## Node 876, Reach 23, Total 123263
## Node 877, Reach 1, Total 123264
## Node 878, Reach 1, Total 123265
## Node 879, Reach 1, Total 123266
## Node 880, Reach 1, Total 123267
## Node 881, Reach 5, Total 123272
## Node 882, Reach 1, Total 123273
## Node 883, Reach 1, Total 123274
## Node 884, Reach 2, Total 123276
## Node 885, Reach 3, Total 123279
## Node 886, Reach 6, Total 123285
## Node 887, Reach 1, Total 123286
## Node 888, Reach 4, Total 123290
## Node 889, Reach 1, Total 123291
## Node 890, Reach 439, Total 123730
## Node 891, Reach 1, Total 123731
## Node 892, Reach 1, Total 123732
## Node 893, Reach 7, Total 123739
## Node 894, Reach 1, Total 123740
## Node 895, Reach 439, Total 124179
## Node 896, Reach 1, Total 124180
## Node 897, Reach 6, Total 124186
## Node 898, Reach 4, Total 124190
## Node 899, Reach 12, Total 124202
## Node 900, Reach 1, Total 124203
## Node 901, Reach 7, Total 124210
## Node 902, Reach 1, Total 124211
## Node 903, Reach 1, Total 124212
## Node 904, Reach 1, Total 124213
## Node 905, Reach 23, Total 124236
## Node 906, Reach 439, Total 124675
## Node 907, Reach 1, Total 124676
## Node 908, Reach 7, Total 124683
## Node 909, Reach 3, Total 124686
## Node 910, Reach 1, Total 124687
## Node 911, Reach 2, Total 124689
## Node 912, Reach 439, Total 125128
## Node 913, Reach 439, Total 125567
## Node 914, Reach 439, Total 126006
## Node 915, Reach 2, Total 126008
## Node 916, Reach 4, Total 126012
## Node 917, Reach 3, Total 126015
## Node 918, Reach 4, Total 126019
## Node 919, Reach 439, Total 126458
## Node 920, Reach 1, Total 126459
## Node 921, Reach 3, Total 126462
## Node 922, Reach 1, Total 126463
## Node 923, Reach 1, Total 126464
## Node 924, Reach 1, Total 126465
## Node 925, Reach 1, Total 126466
## Node 926, Reach 439, Total 126905
## Node 927, Reach 1, Total 126906
## Node 928, Reach 4, Total 126910
## Node 929, Reach 1, Total 126911
## Node 930, Reach 3, Total 126914
## Node 931, Reach 23, Total 126937
## Node 932, Reach 1, Total 126938
## Node 933, Reach 1, Total 126939
## Node 934, Reach 1, Total 126940
## Node 935, Reach 3, Total 126943
## Node 936, Reach 5, Total 126948
## Node 937, Reach 1, Total 126949
## Node 938, Reach 1, Total 126950
## Node 939, Reach 439, Total 127389
## Node 940, Reach 439, Total 127828
## Node 941, Reach 439, Total 128267
## Node 942, Reach 439, Total 128706
## Node 943, Reach 439, Total 129145
## Node 944, Reach 9, Total 129154
## Node 945, Reach 1, Total 129155
## Node 946, Reach 1, Total 129156
## Node 947, Reach 439, Total 129595
## Node 948, Reach 1, Total 129596
## Node 949, Reach 9, Total 129605
## Node 950, Reach 1, Total 129606
## Node 951, Reach 1, Total 129607
## Node 952, Reach 8, Total 129615
## Node 953, Reach 1, Total 129616
## Node 954, Reach 439, Total 130055
## Node 955, Reach 5, Total 130060
## Node 956, Reach 439, Total 130499
## Node 957, Reach 1, Total 130500
## Node 958, Reach 2, Total 130502
## Node 959, Reach 439, Total 130941
## Node 960, Reach 3, Total 130944
## Node 961, Reach 1, Total 130945
## Node 962, Reach 439, Total 131384
## Node 963, Reach 439, Total 131823
## Node 964, Reach 2, Total 131825
## Node 965, Reach 1, Total 131826
## Node 966, Reach 2, Total 131828
## Node 967, Reach 439, Total 132267
## Node 968, Reach 439, Total 132706
## Node 969, Reach 439, Total 133145
## Node 970, Reach 439, Total 133584
## Node 971, Reach 5, Total 133589
## Node 972, Reach 439, Total 134028
## Node 973, Reach 439, Total 134467
## Node 974, Reach 3, Total 134470
## Node 975, Reach 2, Total 134472
## Node 976, Reach 439, Total 134911
## Node 977, Reach 4, Total 134915
## Node 978, Reach 8, Total 134923
## Node 979, Reach 1, Total 134924
## Node 980, Reach 439, Total 135363
## Node 981, Reach 439, Total 135802
## Node 982, Reach 1, Total 135803
## Node 983, Reach 1, Total 135804
## Node 984, Reach 2, Total 135806
## Node 985, Reach 1, Total 135807
## Node 986, Reach 1, Total 135808
## Node 987, Reach 1, Total 135809
## Node 988, Reach 3, Total 135812
## Node 989, Reach 1, Total 135813
## Node 990, Reach 439, Total 136252
## Node 991, Reach 439, Total 136691
## Node 992, Reach 2, Total 136693
## Node 993, Reach 1, Total 136694
## Node 994, Reach 439, Total 137133
## Node 995, Reach 6, Total 137139
## Node 996, Reach 439, Total 137578
## Node 997, Reach 7, Total 137585
## Node 998, Reach 1, Total 137586
## Node 999, Reach 1, Total 137587
## Node 1000, Reach 19, Total 137606
## Node 1001, Reach 2, Total 137608
## Node 1002, Reach 2, Total 137610
## Node 1003, Reach 6, Total 137616
## Node 1004, Reach 6, Total 137622
## Node 1005, Reach 439, Total 138061
## Node 1006, Reach 1, Total 138062
## Node 1007, Reach 5, Total 138067
## Node 1008, Reach 439, Total 138506
## Node 1009, Reach 439, Total 138945
## Node 1010, Reach 439, Total 139384
## Node 1011, Reach 4, Total 139388
## Node 1012, Reach 439, Total 139827
## Node 1013, Reach 3, Total 139830
## Node 1014, Reach 439, Total 140269
## Node 1015, Reach 1, Total 140270
## Node 1016, Reach 1, Total 140271
## Node 1017, Reach 5, Total 140276
## Node 1018, Reach 1, Total 140277
## Node 1019, Reach 439, Total 140716
## Node 1020, Reach 1, Total 140717
## Node 1021, Reach 1, Total 140718
## Node 1022, Reach 1, Total 140719
## Node 1023, Reach 439, Total 141158
## Node 1024, Reach 439, Total 141597
## Node 1025, Reach 1, Total 141598
## Node 1026, Reach 1, Total 141599
## Node 1027, Reach 1, Total 141600
## Node 1028, Reach 6, Total 141606
## Node 1029, Reach 1, Total 141607
## Node 1030, Reach 5, Total 141612
## Node 1031, Reach 439, Total 142051
## Node 1032, Reach 1, Total 142052
## Node 1033, Reach 439, Total 142491
## Node 1034, Reach 1, Total 142492
## Node 1035, Reach 439, Total 142931
## Node 1036, Reach 2, Total 142933
## Node 1037, Reach 2, Total 142935
## Node 1038, Reach 7, Total 142942
## Node 1039, Reach 4, Total 142946
## Node 1040, Reach 439, Total 143385
## Node 1041, Reach 439, Total 143824
## Node 1042, Reach 7, Total 143831
## Node 1043, Reach 1, Total 143832
## Node 1044, Reach 1, Total 143833
## Node 1045, Reach 1, Total 143834
## Node 1046, Reach 1, Total 143835
## Node 1047, Reach 1, Total 143836
## Node 1048, Reach 1, Total 143837
## Node 1049, Reach 439, Total 144276
## Node 1050, Reach 1, Total 144277
## Node 1051, Reach 439, Total 144716
## Node 1052, Reach 1, Total 144717
## Node 1053, Reach 439, Total 145156
## Node 1054, Reach 439, Total 145595
## Node 1055, Reach 7, Total 145602
## Node 1056, Reach 439, Total 146041
## Node 1057, Reach 439, Total 146480
## Node 1058, Reach 4, Total 146484
## Node 1059, Reach 7, Total 146491
## Node 1060, Reach 1, Total 146492
## Node 1061, Reach 439, Total 146931
## Node 1062, Reach 439, Total 147370
## Node 1063, Reach 439, Total 147809
## Node 1064, Reach 439, Total 148248
## Node 1065, Reach 1, Total 148249
## Node 1066, Reach 1, Total 148250
## Node 1067, Reach 439, Total 148689
## Node 1068, Reach 1, Total 148690
## Node 1069, Reach 19, Total 148709
## Node 1070, Reach 1, Total 148710
## Node 1071, Reach 11, Total 148721
## Node 1072, Reach 11, Total 148732
## Node 1073, Reach 439, Total 149171
## Node 1074, Reach 439, Total 149610
## Node 1075, Reach 439, Total 150049
## Node 1076, Reach 2, Total 150051
## Node 1077, Reach 1, Total 150052
## Node 1078, Reach 1, Total 150053
## Node 1079, Reach 1, Total 150054
## Node 1080, Reach 439, Total 150493
## Node 1081, Reach 1, Total 150494
## Node 1082, Reach 439, Total 150933
## Node 1083, Reach 1, Total 150934
## Node 1084, Reach 11, Total 150945
## Node 1085, Reach 11, Total 150956
## Node 1086, Reach 1, Total 150957
## Node 1087, Reach 439, Total 151396
## Node 1088, Reach 4, Total 151400
## Node 1089, Reach 1, Total 151401
## Node 1090, Reach 1, Total 151402
## Node 1091, Reach 1, Total 151403
## Node 1092, Reach 1, Total 151404
## Node 1093, Reach 1, Total 151405
## Node 1094, Reach 1, Total 151406
## Node 1095, Reach 439, Total 151845
## Node 1096, Reach 1, Total 151846
## Node 1097, Reach 439, Total 152285
## Node 1098, Reach 1, Total 152286
## Node 1099, Reach 439, Total 152725
## Node 1100, Reach 1, Total 152726
## Node 1101, Reach 1, Total 152727
## Node 1102, Reach 5, Total 152732
## Node 1103, Reach 3, Total 152735
## Node 1104, Reach 439, Total 153174
## Node 1105, Reach 1, Total 153175
## Node 1106, Reach 1, Total 153176
## Node 1107, Reach 439, Total 153615
## Node 1108, Reach 3, Total 153618
## Node 1109, Reach 1, Total 153619
## Node 1110, Reach 439, Total 154058
## Node 1111, Reach 1, Total 154059
## Node 1112, Reach 5, Total 154064
## Node 1113, Reach 1, Total 154065
## Node 1114, Reach 3, Total 154068
## Node 1115, Reach 5, Total 154073
## Node 1116, Reach 1, Total 154074
## Node 1117, Reach 439, Total 154513
## Node 1118, Reach 19, Total 154532
## Node 1119, Reach 5, Total 154537
## Node 1120, Reach 1, Total 154538
## Node 1121, Reach 439, Total 154977
## Node 1122, Reach 7, Total 154984
## Node 1123, Reach 19, Total 155003
## Node 1124, Reach 7, Total 155010
## Node 1125, Reach 12, Total 155022
## Node 1126, Reach 439, Total 155461
## Node 1127, Reach 5, Total 155466
## Node 1128, Reach 2, Total 155468
## Node 1129, Reach 439, Total 155907
## Node 1130, Reach 2, Total 155909
## Node 1131, Reach 1, Total 155910
## Node 1132, Reach 3, Total 155913
## Node 1133, Reach 1, Total 155914
## Node 1134, Reach 439, Total 156353
## Node 1135, Reach 8, Total 156361
## Node 1136, Reach 19, Total 156380
## Node 1137, Reach 1, Total 156381
## Node 1138, Reach 5, Total 156386
## Node 1139, Reach 2, Total 156388
## Node 1140, Reach 1, Total 156389
## Node 1141, Reach 2, Total 156391
## Node 1142, Reach 439, Total 156830
## Node 1143, Reach 439, Total 157269
## Node 1144, Reach 439, Total 157708
## Node 1145, Reach 8, Total 157716
## Node 1146, Reach 7, Total 157723
## Node 1147, Reach 2, Total 157725
## Node 1148, Reach 1, Total 157726
## Node 1149, Reach 439, Total 158165
## Node 1150, Reach 439, Total 158604
## Node 1151, Reach 439, Total 159043
## Node 1152, Reach 439, Total 159482
## Node 1153, Reach 439, Total 159921
## Node 1154, Reach 439, Total 160360
## Node 1155, Reach 1, Total 160361
## Node 1156, Reach 5, Total 160366
## Node 1157, Reach 439, Total 160805
## Node 1158, Reach 3, Total 160808
## Node 1159, Reach 439, Total 161247
## Node 1160, Reach 439, Total 161686
## Node 1161, Reach 439, Total 162125
## Node 1162, Reach 1, Total 162126
## Node 1163, Reach 439, Total 162565
## Node 1164, Reach 1, Total 162566
## Node 1165, Reach 439, Total 163005
## Node 1166, Reach 1, Total 163006
## Node 1167, Reach 439, Total 163445
## Node 1168, Reach 5, Total 163450
## Node 1169, Reach 1, Total 163451
## Node 1170, Reach 439, Total 163890
## Node 1171, Reach 1, Total 163891
## Node 1172, Reach 3, Total 163894
## Node 1173, Reach 1, Total 163895
## Node 1174, Reach 1, Total 163896
## Node 1175, Reach 439, Total 164335
## Node 1176, Reach 3, Total 164338
## Node 1177, Reach 12, Total 164350
## Node 1178, Reach 439, Total 164789
## Node 1179, Reach 439, Total 165228
## Node 1180, Reach 6, Total 165234
## Node 1181, Reach 6, Total 165240
## Node 1182, Reach 3, Total 165243
## Node 1183, Reach 1, Total 165244
## Node 1184, Reach 1, Total 165245
## Node 1185, Reach 1, Total 165246
## Node 1186, Reach 1, Total 165247
## Node 1187, Reach 439, Total 165686
## Node 1188, Reach 439, Total 166125
## Node 1189, Reach 6, Total 166131
## Node 1190, Reach 1, Total 166132
## Node 1191, Reach 1, Total 166133
## Node 1192, Reach 1, Total 166134
## Node 1193, Reach 1, Total 166135
## Node 1194, Reach 1, Total 166136
## Node 1195, Reach 1, Total 166137
## Node 1196, Reach 4, Total 166141
## Node 1197, Reach 439, Total 166580
## Node 1198, Reach 1, Total 166581
## Node 1199, Reach 1, Total 166582
## Node 1200, Reach 1, Total 166583
## Node 1201, Reach 8, Total 166591
## Node 1202, Reach 3, Total 166594
## Node 1203, Reach 5, Total 166599
## Node 1204, Reach 439, Total 167038
## Node 1205, Reach 8, Total 167046
## Node 1206, Reach 439, Total 167485
## Node 1207, Reach 1, Total 167486
## Node 1208, Reach 11, Total 167497
## Node 1209, Reach 2, Total 167499
## Node 1210, Reach 7, Total 167506
## Node 1211, Reach 1, Total 167507
## Node 1212, Reach 4, Total 167511
## Node 1213, Reach 1, Total 167512
## Node 1214, Reach 1, Total 167513
## Node 1215, Reach 5, Total 167518
## Node 1216, Reach 1, Total 167519
## Node 1217, Reach 439, Total 167958
## Node 1218, Reach 1, Total 167959
## Node 1219, Reach 1, Total 167960
## Node 1220, Reach 439, Total 168399
## Node 1221, Reach 439, Total 168838
## Node 1222, Reach 11, Total 168849
## Node 1223, Reach 1, Total 168850
## Node 1224, Reach 1, Total 168851
## Node 1225, Reach 1, Total 168852
## Node 1226, Reach 439, Total 169291
## Node 1227, Reach 4, Total 169295
## Node 1228, Reach 439, Total 169734
## Node 1229, Reach 1, Total 169735
## Node 1230, Reach 8, Total 169743
## Node 1231, Reach 4, Total 169747
## Node 1232, Reach 3, Total 169750
## Node 1233, Reach 1, Total 169751
## Node 1234, Reach 1, Total 169752
## Node 1235, Reach 1, Total 169753
## Node 1236, Reach 1, Total 169754
## Node 1237, Reach 439, Total 170193
## Node 1238, Reach 3, Total 170196
## Node 1239, Reach 2, Total 170198
## Node 1240, Reach 439, Total 170637
## Node 1241, Reach 1, Total 170638
## Node 1242, Reach 439, Total 171077
## Node 1243, Reach 439, Total 171516
## Node 1244, Reach 9, Total 171525
## Node 1245, Reach 1, Total 171526
## Node 1246, Reach 439, Total 171965
## Node 1247, Reach 1, Total 171966
## Node 1248, Reach 2, Total 171968
## Node 1249, Reach 1, Total 171969
## Node 1250, Reach 439, Total 172408
## Node 1251, Reach 439, Total 172847
## Node 1252, Reach 4, Total 172851
## Node 1253, Reach 1, Total 172852
## Node 1254, Reach 2, Total 172854
## Node 1255, Reach 439, Total 173293
## Node 1256, Reach 4, Total 173297
## Node 1257, Reach 1, Total 173298
## Node 1258, Reach 2, Total 173300
## Node 1259, Reach 1, Total 173301
## Node 1260, Reach 439, Total 173740
## Node 1261, Reach 439, Total 174179
## Node 1262, Reach 439, Total 174618
## Node 1263, Reach 439, Total 175057
## Node 1264, Reach 5, Total 175062
## Node 1265, Reach 2, Total 175064
## Node 1266, Reach 4, Total 175068
## Node 1267, Reach 439, Total 175507
## Node 1268, Reach 1, Total 175508
## Node 1269, Reach 5, Total 175513
## Node 1270, Reach 439, Total 175952
## Node 1271, Reach 439, Total 176391
## Node 1272, Reach 439, Total 176830
## Node 1273, Reach 1, Total 176831
## Node 1274, Reach 23, Total 176854
## Node 1275, Reach 1, Total 176855
## Node 1276, Reach 1, Total 176856
## Node 1277, Reach 5, Total 176861
## Node 1278, Reach 1, Total 176862
## Node 1279, Reach 2, Total 176864
## Node 1280, Reach 6, Total 176870
## Node 1281, Reach 439, Total 177309
## Node 1282, Reach 439, Total 177748
## Node 1283, Reach 2, Total 177750
## Node 1284, Reach 439, Total 178189
## Node 1285, Reach 6, Total 178195
## Node 1286, Reach 1, Total 178196
## Node 1287, Reach 8, Total 178204
## Node 1288, Reach 7, Total 178211
## Node 1289, Reach 1, Total 178212
## Node 1290, Reach 2, Total 178214
## Node 1291, Reach 439, Total 178653
## Node 1292, Reach 2, Total 178655
## Node 1293, Reach 3, Total 178658
## Node 1294, Reach 1, Total 178659
## Node 1295, Reach 19, Total 178678
## Node 1296, Reach 1, Total 178679
## Node 1297, Reach 1, Total 178680
## Node 1298, Reach 19, Total 178699
## Node 1299, Reach 2, Total 178701
## Node 1300, Reach 8, Total 178709
## Node 1301, Reach 1, Total 178710
## Node 1302, Reach 19, Total 178729
## Node 1303, Reach 1, Total 178730
## Node 1304, Reach 1, Total 178731
## Node 1305, Reach 1, Total 178732
## Node 1306, Reach 1, Total 178733
## Node 1307, Reach 1, Total 178734
## Node 1308, Reach 7, Total 178741
## Node 1309, Reach 7, Total 178748
## Node 1310, Reach 1, Total 178749
## Node 1311, Reach 1, Total 178750
## Node 1312, Reach 439, Total 179189
## Node 1313, Reach 3, Total 179192
## Node 1314, Reach 1, Total 179193
## Node 1315, Reach 1, Total 179194
## Node 1316, Reach 439, Total 179633
## Node 1317, Reach 439, Total 180072
## Node 1318, Reach 1, Total 180073
## Node 1319, Reach 1, Total 180074
## Node 1320, Reach 1, Total 180075
## Node 1321, Reach 1, Total 180076
## Node 1322, Reach 439, Total 180515
## Node 1323, Reach 3, Total 180518
## Node 1324, Reach 3, Total 180521
## Node 1325, Reach 1, Total 180522
## Node 1326, Reach 1, Total 180523
## Node 1327, Reach 1, Total 180524
## Node 1328, Reach 2, Total 180526
## Node 1329, Reach 1, Total 180527
## Node 1330, Reach 4, Total 180531
## Node 1331, Reach 3, Total 180534
## Node 1332, Reach 2, Total 180536
## Node 1333, Reach 7, Total 180543
## Node 1334, Reach 1, Total 180544
## Node 1335, Reach 439, Total 180983
## Node 1336, Reach 4, Total 180987
## Node 1337, Reach 5, Total 180992
## Node 1338, Reach 439, Total 181431
## Node 1339, Reach 2, Total 181433
## Node 1340, Reach 2, Total 181435
## Node 1341, Reach 2, Total 181437
## Node 1342, Reach 439, Total 181876
## Node 1343, Reach 1, Total 181877
## Node 1344, Reach 439, Total 182316
## Node 1345, Reach 439, Total 182755
## Node 1346, Reach 439, Total 183194
## Node 1347, Reach 1, Total 183195
## Node 1348, Reach 2, Total 183197
## Node 1349, Reach 439, Total 183636
## Node 1350, Reach 1, Total 183637
## Node 1351, Reach 1, Total 183638
## Node 1352, Reach 2, Total 183640
## Node 1353, Reach 439, Total 184079
## Node 1354, Reach 439, Total 184518
## Node 1355, Reach 5, Total 184523
## Node 1356, Reach 439, Total 184962
## Node 1357, Reach 4, Total 184966
## Node 1358, Reach 439, Total 185405
## Node 1359, Reach 1, Total 185406
## Node 1360, Reach 4, Total 185410
## Node 1361, Reach 439, Total 185849
## Node 1362, Reach 1, Total 185850
## Node 1363, Reach 439, Total 186289
## Node 1364, Reach 1, Total 186290
## Node 1365, Reach 439, Total 186729
## Node 1366, Reach 439, Total 187168
## Node 1367, Reach 1, Total 187169
## Node 1368, Reach 8, Total 187177
## Node 1369, Reach 11, Total 187188
## Node 1370, Reach 4, Total 187192
## Node 1371, Reach 1, Total 187193
## Node 1372, Reach 2, Total 187195
## Node 1373, Reach 1, Total 187196
## Node 1374, Reach 1, Total 187197
## Node 1375, Reach 3, Total 187200
## Node 1376, Reach 5, Total 187205
## Node 1377, Reach 439, Total 187644
## Node 1378, Reach 19, Total 187663
## Node 1379, Reach 1, Total 187664
## Node 1380, Reach 1, Total 187665
## Node 1381, Reach 439, Total 188104
## Node 1382, Reach 2, Total 188106
## Node 1383, Reach 19, Total 188125
## Node 1384, Reach 1, Total 188126
## Node 1385, Reach 439, Total 188565
## Node 1386, Reach 1, Total 188566
## Node 1387, Reach 1, Total 188567
## Node 1388, Reach 7, Total 188574
## Node 1389, Reach 439, Total 189013
## Node 1390, Reach 3, Total 189016
## Node 1391, Reach 439, Total 189455
## Node 1392, Reach 12, Total 189467
## Node 1393, Reach 1, Total 189468
## Node 1394, Reach 1, Total 189469
## Node 1395, Reach 4, Total 189473
## Node 1396, Reach 439, Total 189912
## Node 1397, Reach 439, Total 190351
## Node 1398, Reach 3, Total 190354
## Node 1399, Reach 1, Total 190355
## Node 1400, Reach 5, Total 190360
## Node 1401, Reach 8, Total 190368
## Node 1402, Reach 1, Total 190369
## Node 1403, Reach 1, Total 190370
## Node 1404, Reach 439, Total 190809
## Node 1405, Reach 4, Total 190813
## Node 1406, Reach 4, Total 190817
## Node 1407, Reach 1, Total 190818
## Node 1408, Reach 1, Total 190819
## Node 1409, Reach 3, Total 190822
## Node 1410, Reach 1, Total 190823
## Node 1411, Reach 2, Total 190825
## Node 1412, Reach 1, Total 190826
## Node 1413, Reach 1, Total 190827
## Node 1414, Reach 439, Total 191266
## Node 1415, Reach 439, Total 191705
## Node 1416, Reach 1, Total 191706
## Node 1417, Reach 2, Total 191708
## Node 1418, Reach 1, Total 191709
## Node 1419, Reach 439, Total 192148
## Node 1420, Reach 439, Total 192587
## Node 1421, Reach 1, Total 192588
## Node 1422, Reach 2, Total 192590
## Node 1423, Reach 7, Total 192597
## Node 1424, Reach 2, Total 192599
## Node 1425, Reach 1, Total 192600
## Node 1426, Reach 1, Total 192601
## Node 1427, Reach 1, Total 192602
## Node 1428, Reach 6, Total 192608
## Node 1429, Reach 439, Total 193047
## Node 1430, Reach 8, Total 193055
## Node 1431, Reach 1, Total 193056
## Node 1432, Reach 439, Total 193495
## Node 1433, Reach 23, Total 193518
## Node 1434, Reach 439, Total 193957
## Node 1435, Reach 1, Total 193958
## Node 1436, Reach 1, Total 193959
## Node 1437, Reach 1, Total 193960
## Node 1438, Reach 1, Total 193961
## Node 1439, Reach 2, Total 193963
## Node 1440, Reach 1, Total 193964
## Node 1441, Reach 439, Total 194403
## Node 1442, Reach 2, Total 194405
## Node 1443, Reach 1, Total 194406
## Node 1444, Reach 7, Total 194413
## Node 1445, Reach 7, Total 194420
## Node 1446, Reach 439, Total 194859
## Node 1447, Reach 9, Total 194868
## Node 1448, Reach 1, Total 194869
## Node 1449, Reach 1, Total 194870
## Node 1450, Reach 439, Total 195309
## Node 1451, Reach 1, Total 195310
## Node 1452, Reach 5, Total 195315
## Node 1453, Reach 5, Total 195320
## Node 1454, Reach 6, Total 195326
## Node 1455, Reach 1, Total 195327
## Node 1456, Reach 1, Total 195328
## Node 1457, Reach 1, Total 195329
## Node 1458, Reach 439, Total 195768
## Node 1459, Reach 439, Total 196207
## Node 1460, Reach 8, Total 196215
## Node 1461, Reach 2, Total 196217table(fmh.comp$csize)##
## 1 2 3 4 5 6 7 8 9 11 12 19 23 439
## 524 64 29 11 12 4 7 4 1 1 1 1 1 1head(fmh.comp$membership, 100)## [1] 1 2 2 2 2 3 2 4 5 6 7 8 9 2 10 2 11 12 11 13 2 14 15
## [24] 16 2 17 18 19 20 21 22 23 24 25 26 27 2 2 28 29 2 30 31 32 33 34
## [47] 2 35 36 2 37 38 2 39 40 41 42 43 44 45 2 46 2 47 2 48 49 11 2
## [70] 38 8 2 2 50 51 52 53 11 54 55 56 11 2 57 58 2 59 60 22 11 61 2
## [93] 62 63 64 65 22 66 67 68- clique
fmh.clique<-clique.census(fmh2, clique.comembership= 'bysize')- size가5인clique
fmh.clique$cliques[[5]]## [[1]]
## [1] 122 183 530 1143 1160- density
gden(fmh2)## [1] 0.000913242