118 lines
3.8 KiB
Matlab
118 lines
3.8 KiB
Matlab
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% Edge betweenness routine, based on the number of
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% shortest paths going through an edge.
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% Source: Newman, Girvan, "Finding and evaluating community structure in networks"
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% Note: Valid for undirected graphs only.
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%
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% INPUTs: edge list, mx3, m - number of edges
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% OUTPUTs: w - betweenness per edge, mx3
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%
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% Other routines used: adj2edgeL.m, numNodes.m, numEdges.m, kneighbors.m
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% GB: last modified, Sep 29, 2012
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function ew = edgeBetweenness(adj)
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el=adj2edgeL(adj); % the corresponding edge list
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n = numNodes(adj); % number of nodes
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m = numEdges(adj); % number of edges
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ew = zeros(size(el,1),3); % edge betweenness - output
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for s=1:n % across all (source) nodes
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% compute the distances and weights starting at source node i
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d=inf(n,1); w=inf(n,1);
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d(s)=0; w(s)=1; % source node distance and weight
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queue=[s]; % add to queue
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visited=[];
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while not(isempty(queue))
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j=queue(1); % pop first member
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visited=[visited j];
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neigh=kneighbors(adj,j,1); % find all adjacent nodes, 1 step away
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for x=1:length(neigh) % add to queue if unvisited
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nei=neigh(x);
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if isempty(find(visited==nei)) && isempty(find(queue==nei)); queue=[queue nei]; end
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end
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for x=1:length(neigh)
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nei=neigh(x);
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if d(nei)==inf % not assigned yet
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d(nei)=1+d(j);
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w(nei)=w(j);
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elseif d(nei)<inf && d(nei)==d(j)+1 % assigned already, add the new path
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w(nei)=w(nei)+w(j);
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elseif d(nei)<inf && d(nei)<d(j)+1
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'do nothing';
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end
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end
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queue=queue(2:length(queue)); % remove the first element
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end
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eww = zeros(size(el,1),3); % edge betweenness for every source node (iteration)
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% find every leaf - no path from "s" to other vertices goes through the leaf
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leaves = find(d==max(d)); % farthest away from source
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for l=1:length(leaves)
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leaf=leaves(l);
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neigh=kneighbors(adj,leaf,1);
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nei2rem=[];
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for x=1:length(neigh)
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if isempty(find(leaves==neigh(x))); nei2rem=[nei2rem neigh(x)]; end
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end
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neigh=nei2rem; % remove other leaves among the neighbors
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for x=1:length(neigh)
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indi=find(el(:,1)==neigh(x));
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indj=find(el(:,2)==leaf);
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indij=intersect(indi,indj); % should be only one element at the intersection
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eww(indij,3)=w(neigh(x))/w(leaf);
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end
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end
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dsort=unique(d);
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dsort=-sort(-dsort); % reverse sort of unique distance values
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for x=1:length(dsort)
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leaves=find(d==dsort(x));
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for l=1:length(leaves)
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leaf=leaves(l);
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neigh=kneighbors(adj,leaf,1);
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up_neigh=[]; down_neigh=[];
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for x=1:length(neigh)
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if d(neigh(x))<d(leaf)
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up_neigh=[up_neigh neigh(x)];
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elseif d(neigh(x))>d(leaf)
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down_neigh=[down_neigh neigh(x)];
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end
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end
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sum_down_edges=0;
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for x=1:length(down_neigh)
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indi=find(el(:,1)==leaf);
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indj=find(el(:,2)==down_neigh(x));
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indij=intersect(indi,indj);
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sum_down_edges=sum_down_edges+eww(indij,3);
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end
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for x=1:length(up_neigh)
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indi=find(el(:,1)==up_neigh(x));
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indj=find(el(:,2)==leaf);
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indij=intersect(indi,indj);
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eww(indij,3)=w(up_neigh(x))/w(leaf)*(1+sum_down_edges);
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end
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end
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end
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for e=1:size(ew,1); ew(e,3)=ew(e,3)+eww(e,3); end
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end
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for e=1:size(ew,1)
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ew(e,1)=el(e,1);
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ew(e,2)=el(e,2);
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ew(e,3)=ew(e,3)/n/(n-1); % normalize by the total number of paths
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end
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