标签：dex empty 修改 att clear set 针对 代码 基于
WS小世界网络生成算法，一般小世界网络生成算法速度慢，节点度分布与数学推导不符，在网络仿真中造成不便，这里针对实际网络动力学仿真过程撰写了WS小世界网络的MATLAB生成算法，并考虑了矩阵化，具有较高的速度。
以下是対应的代码：
% The simulation of WS-smallworld network
% the algorithm of WS-smallworld‘s generation has been improved in speed,
% and tend to be easily understood
% writen by winter-my-dream@hotmail.com
% Example:
% N = 100; %network size (number of nodes)
% m = 6; %2*m is the average edges of each nodes
% p = 0.1; %rewiring probability
% matrix = small_world_WS_new(N,m,p);
function matrix = small_world_WS_new(N,m,p)
rng(‘default‘)
rng(‘shuffle‘)
matrix=zeros(N,N);
% generate regular network
for i=m+1:N-m
matrix(i,i-m:i+m)=1;
end
for i=1:m
matrix(i,1:i+m)=1;
end
for i=N-m+1:N
matrix(i,i-m:N)=1;
end
for i=1:m
matrix(i,N-m+i:N)=1;
matrix(N-m+i:N,i)=1;
end
% rewiring the network
for i = 1:N
% then rewiring the edges with the probability of p
[series1,series2] = range_sort(N,m,i);
index0 = series1(rand(2*m,1)>1-p);
if(~isempty(index0))
matrix(i,index0) = 0;
matrix(i,series2(randperm(length(series2),length(index0))))=1;
end
end
matrix = matrix -diag(diag(matrix));
end
function [series1,series2] = range_sort(N,m,i)
% select the index of nodes in row i for rewiring
if(i-m>0 && i+m<=N)
series1 = i-m:i+m;
series2 = setdiff(1:N,series1);
elseif(i-m<=0)
series1 = [1:i+m,N-m+i:N];
series2 = setdiff(1:N,series1);
else
series1 = [1:m-N+i,i-m:N];
series2 = setdiff(1:N,series1);
end
% Without considering the connection of diagonal elements
series1(series1==i) = [];
end
参考文献：
Watts D J, Strogatz S H. Collective dynamics of ‘small-world’networks[J]. nature, 1998, 393(6684): 440-442.
NW小世界网络的生成方法相对简单，我这里附加对应代码：
% 基于Matlab 的小世界网络仿真
% 经过矩阵化修改后，生成速度已经大大加快
function matrix = small_world_NW(N,m,p)
% N=50;m=3;p=0.1;
% matrix=sparse([]);
matrix = zeros(N,N);
for i=m+1:N- m
matrix(i,i- m:i+m)=1;
end
for i=1:m
matrix(i,1:i+m)=1;
end
for i=N- m+1:N
matrix(i,i- m:N)=1;
end
for i=1:m
matrix(i,N- m+i:N)=1;
matrix(N- m+i:N,i)=1;
end
% Random add edge
kk=(rand(N,N)<p);
matrix = logical(matrix + kk);
matrix = matrix -diag(diag(matrix));
对应生成网络的测试图的代码：
clear,clc,close all
% load A.txt
N=10;
m=2;
p=0.1;
% A= small_world_WS_new(N,m,p);
A = small_world_NW(N, m, p);
t=linspace(0,2*pi,N+1);
x=sin(t);
y=cos(t);
figure
set(gcf,‘color‘,‘w‘)
plot(x,y,‘o‘,‘markerfacecolor‘,‘k‘),hold on
for i=1:N
for j=1:N
if (A(i,j)==1)
fp1=plot([x(i),x(j)],[y(i),y(j)],‘r-‘); hold on
set(fp1,‘linesmoothing‘,‘on‘)
end
end
end
axis([-1.05,1.05,-1.05,1.05])
axis square
axis off
sum(sum(A))
标签：dex empty 修改 att clear set 针对 代码 基于
原文地址：http://www.cnblogs.com/wintermydream/p/7845823.html
