function [f,F]=motif4struct_bin(A) %MOTIF4STRUCT_BIN Frequency of structural class-4 motifs % % [f,F] = motif4struct_bin(A); % % Structural motifs are patterns of local connectivity in complex % networks. Such patterns are particularly diverse in directed networks. % The motif frequency of occurrence around an individual node is known as % the motif fingerprint of that node. The total motif frequency of % occurrence in the whole network is correspondingly known as the % motif fingerprint of the network. % % Input: A, binary directed connection matrix % % Output: F, node motif frequency fingerprint % f, network motif frequency fingerprint % % Note: The function find_motif34.m outputs the motif legend. % % References: Milo et al. (2002) Science 298:824-827 % Sporns O, Kötter R (2004) PLoS Biol 2: e369 % % % Mika Rubinov, UNSW/U Cambridge, 2007-2015 % Modification History: % 2007: Original % 2015: Improved documentation persistent M4n ID4 if isempty(ID4) load motif34lib M4n ID4 %load motif data end n=length(A); %number of vertices in A F=zeros(199,n); %motif count of each vertex f=zeros(199,1); %motif count for whole graph As=A|A.'; %symmetric adjacency matrix for u=1:n-3 %loop u 1:n-2 V1=[false(1,u) As(u,u+1:n)]; %v1: neibs of u (>u) for v1=find(V1) V2=[false(1,u) As(v1,u+1:n)]; %v2: all neibs of v1 (>u) V2(V1)=0; %not already in V1 V2=V2|([false(1,v1) As(u,v1+1:n)]); %and all neibs of u (>v1) for v2=find(V2) vz=max(v1,v2); %vz: largest rank node V3=([false(1,u) As(v2,u+1:n)]); %v3: all neibs of v2 (>u) V3(V2)=0; %not already in V1&V2 V3=V3|([false(1,v2) As(v1,v2+1:n)]);%and all neibs of v1 (>v2) V3(V1)=0; %not already in V1 V3=V3|([false(1,vz) As(u,vz+1:n)]); %and all neibs of u (>vz) for v3=find(V3) s=uint64(sum(10.^(11:-1:0).*[A(v1,u) A(v2,u) A(v3,u)... A(u,v1) A(v2,v1) A(v3,v1) A(u,v2) A(v1,v2)... A(v3,v2) A(u,v3) A(v1,v3) A(v2,v3)])); ind=ID4(s==M4n); if nargout==2; F(ind,[u v1 v2 v3])=F(ind,[u v1 v2 v3])+1; end f(ind)=f(ind)+1; end end end end