ネットワークの作成方法の例と距離の測りかた
Regular Networks, Small-World Networks
mkRegG=function(n_node,n_edge){
# input
# n_node: number of nodes
# n_edge: number of edges / 2
M=matrix(0,n_node,n_node)
for (i_loop in 1:n_edge){
M=M+diag(1,n_node,n_node)[, c((i_loop+1):n_node,1:i_loop)]
}
return(M+t(M))
}
# small-world network
G=mkRegG(100,2);
n_node=ncol(G);
prob=0.05;
for (i_node in 1:n_node) {
node=G[i_node,]
linked=which(node==1)
woLinked=which(node==0)
woLinked=woLinked[woLinked!=i_node]
rwVec=linked[which(runif(length(linked)) < prob)]
nRW=length(rwVec)
if (nRW>0) {
newLink=sample(woLinked,nRW)
G[i_node,newLink]=1;G[newLink,i_node]=1
G[i_node,rwVec]=0;G[rwVec,i_node]=0
}
}
# cal. shortest path
dijkstra2<-function(G,nodeID){
n_node=nrow(G)
G[which(G==0)]=Inf;diag(G)=0
d=rep(Inf,n_node);d[nodeID]=0
M=1:n_node;M=M[-nodeID]
while(length(M)>0) {
for (j in 1:n_node)
{
d[j]=min(d[j],d[nodeID]+G[nodeID,j])
}
nodeID=M[which(d[M]==min(d[M]))]
n_remove=length(nodeID)
for (i_remove in 1:n_remove){
M=M[-which(M==nodeID[i_remove])]
}
}
return(d)
}
昔のバージョン（多分）
# regular network
mkRegG=function(n_node,n_edge){
# input
# n_node: number of nodes
# n_edge: number of edges / 2
M=matrix(0,n_node,n_node)
for (i_loop in 1:n_edge){
M=M+diag(1,n_node,n_node)[, c((i_loop+1):n_node,1:i_loop)]
}
return(M+t(M))
}
# WS model (small-world)
mkWSG=function(regG,prob){
# input
# regG: regular network
# prob: probability of rewiring / 2
n_node=ncol(regG)
M=regG;
for (i_node in 1:n_node){
edge=which(M[i_node,]==1)
rwVec=edge[which(runif(length(edge)) < prob)]
nRW=length(rwVec);
if (nRW>0) {
newEdge=sample(seq(n_node)[-i_node],nRW);
while (any(M[i_node,newEdge]==1) & any(M[i_node,rwVec]==1)){
newEdge=sample(seq(n_node)[-i_node],nRW);
}
M[i_node,newEdge]=1;M[newEdge,i_node]=1;
M[i_node,rwVec]=0;M[rwVec,i_node]=0;
}
}
return(M);
}
# scale-free network
mkFSG=function(n_node,n_edge) {
# input
# n_node: number of nodes
# n_edge: minimum number of edges
M=matrix(1,n_edge+1,n_edge+1)-diag(n_edge+1)
for (i_node in (n_edge+2):n_node) {
Pnode=rowSums(M)/sum(M)
cumPnode=c(0,cumsum(Pnode))
vec=matrix(0,1,i_node-1)
while (sum(vec) < n_edge) {
vec[max(which(cumPnode<=runif(1)))]=1
}
M=rbind(M,vec);
M=cbind(M,c(vec,0));
}
return(M)
}
