复杂网络聚类系数和平均路径长度计算的MATLAB源代码

1、复杂网络聚类系数和平均路径长度计算的MATLA醐代码申明：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%Typestype of graph:'binary','weighted

2、9;,'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_G

3、lobal, Cp_Nodal = CCM_ClusteringCoef(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 don't satisfy with that as%vacuous, just like: j->i,k->

4、;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 Rubinov's BCT toolkit.% Refer:% 1 Barrat et al. (2004) The architecture of the complex weighted networks.% 2 Wasserman,S.,Faust,K.(1994) Social N

5、etwork Analysis: Methods and%Applications.% 3 Tore Opsahl and Pietro Panzarasa (2009). "Clustering in 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 (N

6、LPR),% Institute of Automation,Chinese Academy of Sciences (IACAS), China.% Revise by Hu Yong, Nov, 2010% E-mail:% based on Matlab 2006a% $Revision: 1.0, Copywrite (c) 2007error(nargchk(1,2,nargin,'struct');if(nargin < 2),Types = 'all'endN = length(gMatrix);gMatrix(1:(N+1):end) =

7、0;%Clear self-edgesCp_Nodal = zeros(N,1);%Preallocateswitch(upper(Types) case 'BINARY'%Binary network gMatrix = double(gMatrix > 0);%Ensure binary network for i = 1:Nneighbor = (gMatrix(i,:) > 0);Num= sum(neighbor);%number of neighbor nodestemp= gMatrix(neighbor, neighbor);if(Num >

8、1), Cp_Nodal(i) = sum(temp(:)/Num/(Num-1);endendcase 'WEIGHTED'% Weighted network - arithmetic mean for 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_

9、weight=n_weight.*(gMatrix(neighbor,neighbor) > 0);Cp_Nodal(i) = sum(n_weight(:)/(2*Si*(Num-1); end end%case 'WEIGHTED'% Weighted network - geometric mean% A = (gMatrix= 0);% G3 = diag(gMatrix.，(1/3) )A3);)% A(A = 0) = inf; %close-triplet no exist,let CpNode=0 (A=inf)% CpNode = G3./(A.*(A-

10、1);case 'DIRECTED', % Directed networkfor i = 1:Ninset = (gMatrix(:,i) > 0);%in-nodes setoutset = (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 outsettotal=sum(inset)*sum(outset)

11、- sum(allset);tri= sum(sum(gMatrix(inset, outset);Cp_Nodal(i) = tri./total;endend%case 'DIRECTED', % Directed network - clarity 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

12、 no exist,let Cp=0% c3 = D.*(D-1) - 2*diag(gMatrixA2); %number of all possible 3-cycles% Cp_Nodal = g3./c3;%Note: Directed & weighted network (from Mika Rubinov) case 'ALL',%All typeA = (gMatrix= 0);G = gMatrix.A(l/3) + (gMatrix.').A(l/3);D = sum(A + A.',2);g3 = diag(GA3)/2;D(g3

13、= 0) = inf;Cp=0c3 = D.*(D-1) - 2*diag(AA2);Cp_Nodal = g3./c3;otherwise,%Eorr Msg%adjacency matrix%total degree%number of triplet%3-cycles no exist,leterror('Type only four: "Binary","Weighted","Directed",and "All"');endCp_Global = sum(Cp_Nodal)/N;%第二个文

14、件：CCM_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 matrix%ssource nodes, default

15、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 network% Example:%G = CCM_TestGraph1('nograph');%D_Global, D_Nodal = CCM_AvgS

16、hortestPath(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 #error(nargchk(1,3,nargin,'struct');N = length(gMatrix);if(nargin < 2

17、 | isempty(s),s = (1:N)'else s = s(:);endif(nargin < 3 | isempty(t),t = (1:N)'else t = t(:);end% Calculate the shortest-path from s to all nodeD = dijk(gMatrix,s);%D(isinf(D) = 0;D = D(:,t);%To target nodesD_Nodal = (sum(D,2)./sum(D>0,2);% D_Nodal(isnan(D_Nodal) = 口；D_Global = mean(D_N

18、odal);第三个文件：dijk.mfunction 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 (i,j) exists with

19、0 weight)%s = FROM node indices%= 口(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 ma

20、trix, 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 can have non-negative elements) % (If |s| >> |t|, then DIJK is faster if DIJK(A',t,s) used, where D is

21、 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% Modified by JBT, Dec 2000, to delete paths% Input Error Checking*err

22、or(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(triu(A) = 0)% A is lower triangularisAcycl

23、ic = 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 < 1 | s > n)error("'s" must be an integer between 1 and ',num2str(n);elseif any(t < 1 | 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),lengt