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1、復(fù)雜網(wǎng)絡(luò)聚類系數(shù)和 平均路徑長(zhǎng)度計(jì)算的 MATLAB源代碼 復(fù)雜網(wǎng)絡(luò)聚類系數(shù)和平均路徑長(zhǎng)度計(jì)算的MATLAB源代碼 申明：文章來自百度用戶carrot_hy 復(fù)雜網(wǎng)絡(luò)的代碼總共是三個(gè)m文件，復(fù)制如下： 第一個(gè)文件，CCM_ClusteringCoef.m function [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(gMatrix, Types) % CCM_ClusteringCoef calculates clustering coefficients. % Input: % gMatrix adjacency matrix

2、% Types type of graph: '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('

3、nograph'); % [Cp_Global, 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, jus

4、t 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 Rubinov's BCT toolkit. % Refer: % [1] Barrat et al. (2004) The architecture of the complex weighted networks. % [2] Wasserman,S.,Faust,K.(1994) Social Network

5、 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

6、(NLPR), % 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) 2007 error(nargchk(1,2,nargin,'struct')); if(nargin < 2), Types = 'all'; end N = length(gMatrix); gMatrix(1:(N+1):en

7、d) = 0;%Clear self-edges Cp_Nodal = zeros(N,1); %Preallocate switch(upper(Types)) case 'BINARY'%Binary network gMatrix = double(gMatrix > 0);%Ensure binary network for i = 1:N neighbor = (gMatrix(i,:) > 0); Num = sum(neighbor);%number of neighbor nodes temp = gMatrix(neighbor, neighbor); if

8、(Num > 1), Cp_Nodal(i) = sum(temp(:))/Num/(Num-1); end 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_weigh

9、t + n_weight'; n_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)廣3);) % A(A == 0) = inf; %close-triplet no exist,let CpNode=0 (A=in

10、f) % CpNode = G3./(A.*(A-1)); case ,DIRECTED', % Directed network for i = 1:N inset = (gMatrix(:,i) > 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

11、(inset)*sum(outset) - sum(allset); tri sum(sum(gMatrix(inset, outset))); Cp_Nodal(i) = tri./total; end end %case 'DIRECTED', % Directed network — clarity format (from Mika Rubinov, UNSW) gMatrix + gMatrix'; %symmetrized sum(G,2); %total degree g3 = diag(G”3)/2; %number of triplet D(g3 =

12、= 0) = inf; %3-cycles no exist,let Cp=0 % c3 = D.*(D-1) - 2*diag(gMatrix"2); %number of all possible 3-cycles % Cp_Nodal = g3./c3; %Note: Directed & weighted network (from Mika Rubinov)

13、 case 'ALL',%All type A = (gMatrix~= 0); %adjacency matrix G = gMatrix.”(1/3) + (gMatrix.').”(1/3); D = sum(A + A.',2); %total degree g3 = diag(G”3)/2; %number of triplet D(g3 == 0) = inf; %3-cycles no exist,let Cp=0 c3 = D.*(D-1) - 2*diag(A”2); Cp_Nodal = g3./c3; otherwise,%Eorr Msg

14、 error('Type only four: 〃Binary〃，〃Weighted〃，〃Directed〃,and "All"'); end Cp_Global = sum(Cp_Nodal)/N; %% 第二個(gè)文件：CCM_AvgShortestPath.m function [D_Global, D_Nodal] = CCM_AvgShortestPath(gMatrix, s, t) % CCM_AvgShortestPath generates the shortest distance matrix of source nodes % indice s to th

15、e target nodes indice t. % Input: % gMatrix symmetry binary connect matrix or weighted connect matrix 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,a

16、nd 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, MEAN, SUM % Written by Yong Liu, Oct,2007 % Modified by Hu Yong, Nov 2010 % Center for Computational Medicine (CCM), %

17、Based on Matlab 2008a % $Revision: 1.0, Copywrite (c) 2007 % ###### Input check ######### error(nargchk(1,3,nargin,'struct')); N = length(gMatrix); if(nargin < 2 | isempty(s)), s = (1:N)'; else s = s(:); end if(nargin < 3 | isempty(t)), t = (1:N)'; else t = t(:); end % Calculate the shortes

18、t-path from s to all node D = dijk(gMatrix,s);%D(isinf(D)) = 0; %To target nodes D_Nodal = (sum(D,2)./sum(D>0,2)); % D_Nodal(isnan(D_Nodal))=[]; D_Global = mean(D_Nodal); 第三個(gè)文件：dijk.m function D = dijk(A,s,t) %DIJK Shortest paths from nodes 's to nodes 't' using Dijkstra algorithm. %

19、 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 0 weight) s = FROM node indices =[](default), paths from all nodes t = TO node indices =[](default), paths to all nodes |s

20、| 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 computationally intensive node % selection step not needed since graph is acyclic (triangularity is a % sufficient, but not a necessary, condit

21、ion for a graph to be acyclic) and A can have non-negative elements) % (If | s| >> 11|, 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. 1

22、09.) % 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 ****************************************************** error(nargchk(1,3,nargin,'struct')); [n,cA] = size(A); if nargin < 2 | isempty(s), s =

23、 (1:n)'; else s = s(:); end if nargin < 3 | isempty(t), t = (1:n)'; else t = t(:); end if ~any(any(tril(A) ~= 0)) % A is upper triangular isAcyclic = 1; elseif ~any(any(triu(A) ~= 0)) % A is lower triangular isAcyclic = 2; else % Graph may not be acyclic isAcyclic = 0; end if n ~= cA error

24、('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 (Inp

25、ut Error Checking) ************************************************ A = A'; % Use transpose to speed-up FIND for sparse A D = 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(zeros(length(t),1)); if isAcyclic ==

26、1 nLab = j - 1; elseif isAcyclic == 2 nLab = n - j; else nLab = 0; UnLab = 1:n; isUnLab = logical(ones(n,1)); end while nLab < n & ~all(isLab) if isAcyclic Dj = Di(j); else % Node selection [Dj,jj] = min(Di(isUnLab)); j = UnLab(jj); UnLab(jj)=[]; isUnLab(j) = 0; end nLab = nLab

27、+ 1; if length(t) < n, isLab = isLab | (j == t); end [jA,kA,Aj] = find(A(:,j)); Aj(isnan(Aj)) = 0; if isempty(Aj), Dk = Inf; else Dk = Dj + Aj; end P(i,jA(Dk < Di(jA))) = j; Di(jA) = min(Di(jA),Dk); if isAcyclic == 1 % Increment node index for upper triangular A j = j + 1; elseif isAcyclic == 2 % Decrement node index for lower triangular A j = j - 1； end %disp( num2str( nLab )); end D(i,:) = Di(t)'; end