复杂网络聚类系数和平均路径长度计算的MATLAB源代码上课讲义

1、复杂网络聚类系数和平均路径长度计算的MATL AB 源 代 码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：第一个文件， CCM_ClusteringCoef.mfunction Cp_Global, Cp_Nodal = CCM_ClusteringCoef(gMatrix, Types)% CCM_ClusteringCoef calculates clustering coefficients.% Input:%gMatrixadjacency matrix%Types type of gra

2、ph:binary,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_ClusteringC

3、oef(G);% Note:% 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

4、-k and 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

5、Weighted%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:Nneighbor = (gMatrix(i,:) 0);Num = sum(neighbor);%number of neighbor nodes temp= gMatrix(neighbor, neighbor);endif(Num 1),Cp_Nodal(i) = sum(temp(:)/Num/(Num-1);end

7、case WEIGHTED% Weighted network - arithmetic meanfor i = 1:Nneighbor = (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);Cp_Nodal(i) = sum

8、(n_weight(:)/(2*Si*(Num-1);endend%case WEIGHTED% Weighted network - geometric mean% 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 networkfor i = 1:Ninset= (gMatrix(:,i) 0);%in-nodes setou

9、tset= (gMatrix(i,:) 0); %out-nodes setif(any(inset & outset)allset = and(inset, outset);% Ensure aji*aik 0,j belongs to inset,and k belongs to outsettotal = sum(inset)*sum(outset) - sum(allset);tri = sum(sum(gMatrix(inset, outset);Cp_Nodal(i) = tri./total;endend%case DIRECTED, % Directed network - c

10、larity format (from Mika Rubinov, UNSW)% G = gMatrix + gMatrix; %symmetrized% D = sum(G,2); %total degree% g3 = diag(GA3)/2;%number of triplet% D(g3 = 0) = inf;%3-cycles no exist,letCp=0% c3 = D.*(D-1) - 2*diag(gMatrixA2); %number of all possible 3-cycles% Cp_Nodal = g3./c3;%Note: Directed & weighte

11、d network (from Mika Rubinov)%adjacency matrix%total degreeg3 = diag(GA3)/2;%number of tripletD(g3 = 0) = inf;%3-cycles no exist,letCp=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： CCM

12、_AvgShortestPath.mfunction 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 matrixcase ALL,%All typeA = (gMatri

13、x= 0);G = gMatrix.A(1/3) + (gMatrix.)4(1/3);D = sum(A + A.,2);source nodes, default is 1:N% ttarget 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 node in the

14、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% # Input check #er

15、ror(nargchk(1,3,nargin,struct);N = length(gMatrix);if(nargin 2 | isempty(s),s = (1:N);elses = s(:);endif(nargin 0,2);% D_Nodal(isnan(D_Nodal) = ;D_Global = mean(D_Nodal);第三个文件： dijk.m 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 nodest = TO node indices= (default), paths to all nodesD = |s| x |t| matrix of shortest path distances fr

17、om 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 nodeselection step not needed since graph is acyclic (triangularity is asufficient, but not a necessary, condition for a graph to be acyclic)and A can have non-negative elemen

18、ts)% (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 Version 1.3 29-Aug-2000% %

19、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 triangularisAcyclic = 1;elseif any(any(tr

20、iu(A) = 0)% A is lower triangularisAcyclic = 2;else% Graph may not be acyclicisAcyclic = 0;end if n = 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)