复杂网络聚类系数和平均路径长度计算的MATLAB源代码

1、申明：文章来自百度用户 carrot_hy复杂网络的代码总共是三个 m文件，复制如下:第一个文件，function Cp_Global, Cp_Nodal = CCM_ClusteringCoef(gMatrix, Types)% CCM_ClusteringCoef calculates clustering coefficients.% Input:%gMatrixadjacency matrix%Types type of graph:binary,weighted,directed,all(default).% Usage:% Cp_Global, Cp_Nodal = CCM_Clu

2、steringCoef(gMatrix, Types) returns%clustering coefficients for all nodes Cp_Nodal and average clustering%coefficient of network Cp_Global.% Example:%G = CCM_TestGraph1(nograph);%Cp_Global, Cp_Nodal = CCM_ClusteringCoef(G);% Note:% 1) one node have vaule 0, while which only has a neighbour or none.%

3、2) The dircted network termed triplets that fulfill the follow condition% as non-vacuous: j-i-k and k-i-j,if dont satisfy with that as% vacuous, just like: j-i,k-i and i-j,i-k. and the closed triplets% only j-i-k = j-k and k-i-j = k-j.%3) ALL type network code from Mika Rubinovs BCT toolkit.% Refer:

4、% 1 Barrat et al. (2004) The architecture of the complex weighted networks.% 2 Wasserman,S.,Faust,K.(1994) Social Network Analysis: Methods and %Applications.% 3 Tore Opsahl and Pietro Panzarasa (2009). Clustering in Weighted%Networks. Social Networks31(2).% See also CCM_Transitivity% Written by Yon

5、g Liu, Oct,2007% Center for Computational Medicine (CCM),% National Laboratory of Pattern Recognition (NLPR),% Institute of Automation,Chinese Academy of Sciences (IACAS), China.% Revise by Hu Yong, Nov, 2010% E-mail:% based on Matlab 2006a% $Revision: , Copywrite (c) 2007error(nargchk(1,2,nargin,st

6、ruct);if(nargin 0);%Ensure binary networkfor i = 1:Nneighbor = (gMatrix(i,:) 0);Num= sum(neighbor);%number of neighbor nodestemp = gMatrix(neighbor, neighbor);endneighbor) 0);if(Num 1),Cp_Nodal(i) = sum(temp(:)/Num/(Num-1);endcase WEIGHTED% Weighted network - arithmetic mean for i = 1:Nneighbor = (g

7、Matrix(i,:) 0); n_weight = gMatrix(i,neighbor); Si= sum(n_weight);Num = sum(neighbor); if(Num 1),n_weight = ones(Num,1)*n_weight;n_weight = n_weight + n_weight;n_weight = n_weight.*(gMatrix(neighbor, Cp_Nodal(i) = sum(n_weight(:)/(2*Si*(Num-1); endend %case WEIGHTED% Weighted network - geometric mea

8、n% A = (gMatrix= 0);% G3 = diag(gMatrix.A(1 )人3);)% A(A = 0) = inf;%close-triplet no exist,let CpNode=0 (A=inf)% CpNode = G3./(A.*(A-1);case DIRECTED, % Directed network%in-nodes setfor i = 1:Ninset = (gMatrix(:,i) 0);outset = (gMatrix(i,:) 0); %out-nodes setif(any(inset & outset) allset = and(inset

9、, outset);% Ensure aji*aik 0,j belongs to inset,and k belongs tooutsettotal= sum(inset)*sum(outset) - sum(allset);tri = sum(sum(gMatrix(inset, outset); Cp_Nodal(i) = tri./total;endend%G= gMatrix + gMatrix;%symmetrized%D= sum(G,2);%total degree%g3 =diag(GA3)/2;%number of triplet%D(g3= 0) = inf;%3-cyc

10、les no exist,let%c3 =D.*(D-1) - 2*diag(gMatrixA2); %number of all possible 3-cycles%Cp_Nodal= g3./c3;%case DIRECTED, % Directed network - clarity format (from Mika Rubinov, UNSW)Cp=0%adjacency matrix%total degree %number of triplet%3-cycles no exist,let%Note: Directed & weighted network (from Mika R

11、ubinov) case ALL,%All typeA = (gMatrix= 0);G = gMatrix.A(1/3) + (gMatrix.)4(1/3);D = sum(A + A.,2);g3 = diag(GA3)/2;D(g3 = 0) = inf;Cp=0c3 = D.*(D-1) - 2*diag(AA2);Cp_Nodal = g3./c3;otherwise,%Eorr Msgerror(Type only four: Binary,Weighted,Directed,and All);endCp_Global = sum(Cp_Nodal)/N;%第二个文件：funct

12、ion D_Global, D_Nodal = CCM_AvgShortestPath(gMatrix, s, t)% CCM_AvgShortestPath generates the shortest distance matrix of source nodes% indice s to the target nodes indice t.% Input:% gMatrixsymmetry binary connect matrix or weighted connect matrix source nodes, default is 1:N% ttarget nodes, defaul

13、t is 1:N% Usage:% D_Global, D_Nodal = CCM_AvgShortestPath(gMatrix) returns the mean% shortest-path length of whole network D_Global,and the mean shortest-path % length of each node in the network% Example:% G = CCM_TestGraph1(nograph);% D_Global, D_Nodal = CCM_AvgShortestPath(G);% See also dijk, MEA

14、N, SUM% Written by Yong Liu, Oct,2007% Modified by Hu Yong, Nov 2010% Center for Computational Medicine (CCM),% Based on Matlab 2008a% $Revision: , Copywrite (c) 2007% # Input check # error(nargchk(1,3,nargin,struct);N = length(gMatrix); if(nargin 2 | isempty(s),s = (1:N);elses = s(:);endif(nargin 0

15、,2); % D_Nodal(isnan(D_Nodal) = ; D_Global = mean(D_Nodal);第三个文件：function D = dijk(A,s,t)%DIJK Shortest paths from nodes s to nodes t using Dijkstra algorithm.% D = dijk(A,s,t)%A = n x n node-node weighted adjacency matrix of arc lengths%(Note: A(i,j) = 0= Arc (i,j) does not exist;A(i,j) = NaN = Arc

16、 (i,j) exists with 0 weight)% s = FROM node indices%= (default), paths from all nodes% t = TO node indices%= (default), paths to all nodes%D = |s| x |t| matrix of shortest path distances from s to t%= D(i,j), where D(i,j) = distance from node i to node j% % (If A is a triangular matrix, then computa

17、tionally intensive node%selection step not needed since graph is acyclic (triangularity is a%sufficient, but not a necessary, condition for a graph to be acyclic)%and A can have non-negative elements)% % (If |s| |t|, then DIJK is faster if DIJK(A,t,s) used, where D is now%transposed and P now repres

18、ents successor indices)% % (Based on Fig. 4.6 in Ahuja, Magnanti, and Orlin, Network Flows, % Prentice-Hall, 1993, p. 109.) % Copyright (c) 1998-2000 by Michael G. Kay% Matlog Version 29-Aug-2000% Modified by JBT, Dec 2000, to delete paths% Input Error Checking*error(nargchk(1,3,nargin,struct);n,cA

19、= size(A);if nargin 2 | isempty(s), s = (1:n); else s = s(:); end if nargin 3 | isempty(t), t = (1:n); else t = t(:); endif any(any(tril(A) = 0)% A is upper triangularisAcyclic = 1;elseif any(any(triu(A) = 0)% A is lower triangularisAcyclic = 2;else % Graph may not be acyclic isAcyclic = 0;end if n

20、= cAerror(A must be a square matrix); elseif isAcyclic & any(any(A 0)error(A must be non-negative); elseif any(s n)error(s must be an integer between 1 and ,num2str(n); elseif any(t n)error(t must be an integer between 1 and ,num2str(n);*end % End (Input Error Checking)A = A;% Use transpose to speed-up FIND for sparse AD = zeros(length(s),length(t);P = zeros(length(s),n);for i = 1:length(s) j = s(i);Di = Inf*ones(n,1); Di(j) = 0;isLab =