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- function [I,Q,F]=motif3struct_wei(W)
- %MOTIF3STRUCT_WEI Intensity and coherence of structural class-3 motifs
- %
- % [I,Q,F] = motif3struct_wei(W);
- %
- % 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 motif intensity and coherence
- % are weighted generalizations of the motif frequency. The motif
- % intensity is equivalent to the geometric mean of weights of links
- % comprising each motif. The motif coherence is equivalent to the ratio
- % of geometric and arithmetic means of weights of links comprising each
- % motif.
- %
- % Input: W, weighted directed connection matrix
- % (all weights must be between 0 and 1)
- %
- % Output: I, node motif intensity fingerprint
- % Q, node motif coherence fingerprint
- % F, node motif frequency fingerprint
- %
- % Notes:
- % 1. The function find_motif34.m outputs the motif legend.
- % 2. Average intensity and coherence are given by I./F and Q./F
- % 3. All weights must be between 0 and 1. This may be achieved using
- % the weight_conversion.m function, as follows:
- % W_nrm = weight_conversion(W, 'normalize');
- %
- % References: Onnela et al. (2005), Phys Rev E 71:065103
- % 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 M3 M3n ID3 N3
- if isempty(N3)
- load motif34lib M3 M3n ID3 N3 %load motif data
- end
- n=length(W); %number of vertices in W
- I=zeros(13,n); %intensity
- Q=zeros(13,n); %coherence
- F=zeros(13,n); %frequency
- A=1*(W~=0); %adjacency matrix
- As=A|A.'; %symmetrized adjacency
- for u=1:n-2 %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=([false(1,v1) As(u,v1+1:n)])|V2; %and all neibs of u (>v1)
- for v2=find(V2)
- w=[W(v1,u) W(v2,u) W(u,v1) W(v2,v1) W(u,v2) W(v1,v2)];
- s=uint32(sum(10.^(5:-1:0).*[A(v1,u) A(v2,u) A(u,v1)...
- A(v2,v1) A(u,v2) A(v1,v2)]));
- ind=(s==M3n);
- M=w.*M3(ind,:);
- id=ID3(ind);
- l=N3(ind);
- x=sum(M,2)/l; %arithmetic mean
- M(M==0)=1; %enable geometric mean
- i=prod(M,2)^(1/l); %intensity
- q=i/x; %coherence
- %then add to cumulative count
- I(id,[u v1 v2])=I(id,[u v1 v2])+[i i i];
- Q(id,[u v1 v2])=Q(id,[u v1 v2])+[q q q];
- F(id,[u v1 v2])=F(id,[u v1 v2])+[1 1 1];
- end
- end
- end
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