smallworldnetwork.m

生成beta-小世界网络 ％ Authors: LuoNa, ECUST ％ v1.0 Created 30-May-2007

% function [adj_matr, nd_coord,clusterCof]=smallWorldNetwork(npoints,prob,degree) 
% 生成beta-小世界网络
% inputs:
%         npoints - 节点数
%         beta - 概率
%         degree - 网络的度
% Authors: LuoNa, ECUST
% v1.0 Created 30-May-2007
% number of points, npoints

clear;clc;
%  if (nargin<3) 
   npoints =10;
   beta=0.1;
   degree=4
%  end

%driven the number of points, nodes are uniformly distributed
 for i=1:npoints
     nd_coord(i, 1) = 1*cos(2*pi/npoints*i);
     nd_coord(i, 2) = 1*sin(2*pi/npoints*i);
 end
 
 dist_matr=zeros(npoints,npoints);
 % generate the adjacency matrix
 for i=1:npoints
      if i-1<1
         a1=i-1+npoints;
     else
         a1=i-1;
     end
     if i-2<1
         a2=i-2+npoints;
     else
         a2=i-2;
     end
     if i+1>npoints
         a3=i+1-npoints;
     else
         a3=i+1;
     end
     if i+2>npoints
         a4=i+2-npoints;
     else
         a4=i+2;
     end
     dist_matr(i,a1) =1;
     dist_matr(i,a2) =1;
     dist_matr(i,a3) =1;
     dist_matr(i,a4) =1;
 end 
 
 for i=1:npoints
     if i == npoints
         j=1;
     else
         j=i+1;
     end
     gama=rand;
     if gama < beta
         dist_matr(i,j)=0;
         dist_matr(j,i)=0;
         k=floor(rand*npoints)+1;
         while dist_matr(i,k)==1
             k=floor(rand*npoints)+1;
         end
         dist_matr(i,k)=1;
         dist_matr(k,i)=1;
     end
 end

 for i=1:npoints
     if i == npoints
         j=2;
     elseif i== npoints-1
         j=1;
     else
         j=i+2;
     end
     gama=rand;
     if gama < beta
         dist_matr(i,j)=0;
         dist_matr(j,i)=0;
         k=floor(rand*npoints)+1;
         while dist_matr(i,k)==1
             k=floor(rand*npoints)+1;
         end
         dist_matr(i,k)=1;
         dist_matr(k,i)=1;
     end
 end
 
 adj_matr = sparse(dist_matr);
 
 % plot the network
%  figure(1);
%  clf;
  hold on;
 plot(nd_coord(:, 1), nd_coord(:, 2), '.');
 for i=1:npoints
     text(nd_coord(i, 1), nd_coord(i, 2),int2str(i),'FontSize',18);
 end
 gplot(adj_matr, nd_coord);
 hold off;
 
% 特征路径长度(L)：将每个定点v连接到所有其他定点的最短路径长度的均值的中位数，将L定义这些值的中位数
 L=