44 lines
1.4 KiB
Matlab
44 lines
1.4 KiB
Matlab
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% This function returns the betweenness measure of all vertices.
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% Betweenness centrality measure: number of shortest paths running through a vertex.
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%
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% Note 1: Valid for a general graph (multiple shortest paths possible).
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% Note 2: Currently this function is quite slow, because of
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% findAllShortestPaths.m. This is especially true for dense
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% graphs.
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%
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% INPUTS: adjacency or distances matrix (nxn)
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% OUTPUTS: betweeness vector for all vertices (1xn)
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%
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% Other routines used: numNodes.m, adj2adjL.m, simpleDijkstra.m, findAllShortestPaths.m
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% GB: July 3, 2014
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function betw = nodeBetweenness(adj)
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n = numNodes(adj);
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spaths=inf(n,n);
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betw = zeros(1,n);
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adjL = adj2adjL(adj);
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for i=1:n
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uB = simpleDijkstra(adj,i);
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for j=1:n
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if i==j; continue; end
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[allPaths, ~] = findAllShortestPaths(adjL,i,j, uB(j), allPaths={},path=[]);
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spaths(i,j) = length(allPaths);
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% for all paths in allPaths, parse out the path:
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for p=1:length(allPaths)
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path = strsplit(allPaths{p},'-');
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pathvec = [];
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for x=2:length(path) % skip the first one
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pathvec = [pathvec str2num(path{x})];
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end
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betw(pathvec(2:length(pathvec)-1)) = betw(pathvec(2:length(pathvec)-1)) + 1/spaths(i,j);
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end
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end % end of j=1:n
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end % end of i=1:n
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% this last step is just additional normalization, and is arbitrary
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betw=betw/(2*nchoosek(n,2));
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