复杂网络聚类系数和平均路径长度计算的MATLAB源代码

1、-作者xxxx-日期xxxx复杂网络聚类系数和平均路径长度计算的MATLAB源代码【精品文档】复杂网络聚类系数和平均路径长度计算的MATLAB源代码申明：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：function Cp_Global, Cp_Nodal = CCM_ClusteringCoef(gMatrix, Types)% CCM_ClusteringCoef calculates clustering coefficients.% Input:% gMatrix adjacency matrix% Types type of graph: binary,

2、weighted,directed,all(default).% Usage:% Cp_Global, Cp_Nodal = CCM_ClusteringCoef(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);% N

3、ote:% 1) one node have vaule 0, while which only has a neighbour or none.% 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

4、k-i-j = k-j.% 3) ALL type network code from Mika Rubinovs BCT toolkit.% Refer:% 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 Weig

5、hted % Networks. Social Networks31(2).% See also CCM_Transitivity% Written by Yong 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: %

6、 based on Matlab 2006a% $Revision: 1.0, Copywrite (c) 2007error(nargchk(1,2,nargin,struct);if(nargin 0);%Ensure binary networkfor i = 1:N neighbor = (gMatrix(i,:) 0); Num = sum(neighbor);%number of neighbor nodes temp = gMatrix(neighbor, neighbor); if(Num 1), Cp_Nodal(i) = sum(temp(:)/Num/(Num-1); e

7、nd end case WEIGHTED% Weighted network - arithmetic mean for i = 1:N neighbor = (gMatrix(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, neighbor) 0);

8、 Cp_Nodal(i) = sum(n_weight(:)/(2*Si*(Num-1); endend %case WEIGHTED% Weighted network - geometric mean%A = (gMatrix= 0);%G3 = diag(gMatrix.(1/3) )3);)%A(A = 0) = inf; %close-triplet no exist,let CpNode=0 (A=inf)%CpNode = G3./(A.*(A-1);case DIRECTED, % Directed networkfor i = 1:N inset = (gMatrix(:,i

9、) 0); %in-nodes set outset = (gMatrix(i,:) 0); %out-nodes set if(any(inset & outset) allset = and(inset, outset); % Ensure aji*aik 0,j belongs to inset,and k belongs to outset total = sum(inset)*sum(outset) - sum(allset); tri = sum(sum(gMatrix(inset, outset); Cp_Nodal(i) = tri./total; end end %case

10、DIRECTED, % Directed network - clarity format (from Mika Rubinov, UNSW)%G = gMatrix + gMatrix; %symmetrized%D = sum(G,2); %total degree%g3 = diag(G3)/2; %number of triplet%D(g3 = 0) = inf; %3-cycles no exist,let Cp=0%c3 = D.*(D-1) - 2*diag(gMatrix2); %number of all possible 3-cycles%Cp_Nodal = g3./c

11、3; %Note: Directed & weighted network (from Mika Rubinov)case ALL,%All typeA = (gMatrix= 0); %adjacency matrixG = gMatrix.(1/3) + (gMatrix.).(1/3);D = sum(A + A.,2); %total degreeg3 = diag(G3)/2; %number of tripletD(g3 = 0) = inf; %3-cycles no exist,let Cp=0c3 = D.*(D-1) - 2*diag(A2);Cp_Nodal = g3./

12、c3;otherwise,%Eorr Msg error(Type only four: Binary,Weighted,Directed,and All);endCp_Global = sum(Cp_Nodal)/N; %function 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:

13、% gMatrix symmetry binary connect matrix or weighted connect matrix% s source nodes, default is 1:N% t target nodes, default 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 no

14、de in the network% Example:% G = CCM_TestGraph1(nograph);% D_Global, D_Nodal = CCM_AvgShortestPath(G);% See also dijk, MEAN, SUM% Written by Yong Liu, Oct,2007% Modified by Hu Yong, Nov 2010% Center for Computational Medicine (CCM), % Based on Matlab 2008a% $Revision: 1.0, Copywrite (c) 2007% # Inpu

15、t check #error(nargchk(1,3,nargin,struct);N = length(gMatrix);if(nargin 2 | isempty(s), s = (1:N);else s = s(:); endif(nargin 0,2);% D_Nodal(isnan(D_Nodal) = ;D_Global = mean(D_Nodal);function D = dijk(A,s,t)%DIJK Shortest paths from nodes s to nodes t using Dijkstra algorithm.% D = dijk(A,s,t)% A =

16、 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 (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 p

17、ath 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 computationally 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 c

18、an 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 represents 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

19、Version 1.3 29-Aug-2000% % Modified by JBT, Dec 2000, to delete paths% Input Error Checking *error(nargchk(1,3,nargin,struct);n,cA = size(A);if nargin 2 | isempty(s), s = (1:n); else s = s(:); endif nargin 3 | isempty(t), t = (1:n); else t = t(:); endif any(any(tril(A) = 0)% A is upper triangular is

20、Acyclic = 1;elseif any(any(triu(A) = 0)% A is lower triangular isAcyclic = 2;else% Graph may not be acyclic isAcyclic = 0;endif n = cA error(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 = logical(ze