62 lines
1.9 KiB
Matlab
62 lines
1.9 KiB
Matlab
% Betweenness centrality measure: number of shortest paths running through a vertex.
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% Reference: Ulrik Brandes, "A Faster Algorithm for Betweenness
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% Centrality", Journal of Mathematical Sociology 25(2):163-177,(2001)
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% Source: http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf
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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: kneighbors.m
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% GB: July 18 2015
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function betw = nodeBetweennessFaster(adj)
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betw = zeros(1,size(adj,1));
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for s=1:size(adj,1) % over all nodes
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S = []; % S <- empty stack
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P = {}; P{size(adj,1)} = []; % P{w} <- empty list, w in V;
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sigma = zeros(1,size(adj,1)); sigma(s) = 1;
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d = (-1)*ones(1,size(adj,1)); d(s) = 0;
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Q = []; % Q - empty queue
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Q = [Q s]; % enqueue s -> Q
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while length(Q)>0 % while Q not empty do
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v = Q(1); Q = Q(2:length(Q)); % dequeue v <- Q;
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S = [v S]; % push v -> S
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knei = kneighbors(adj,v,1);
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for ii=1:length(knei) % for each neighbor w of v
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w = knei(ii);
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% w found for the first time?
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if d(w)<0
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Q = [Q w];
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d(w) = d(v) + 1;
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end
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% shortest path to w via v?
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if d(w) == d(v) + 1
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sigma(w) = sigma(w) + sigma(v);
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P{w} = [P{w} v];
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end
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end
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end
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delta = zeros(1,size(adj,1));
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% S returns vertices in order of non-increasing distance from s
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while length(S)>0 % while S not empty
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w = S(1); S = S(2:length(S)); % pop w <- S
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for ii=1:length(P{w})
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v = P{w}(ii);
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delta(v) = delta(v) + (sigma(v)/sigma(w))*(1+delta(w));
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end
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if w~=s; betw(w) = betw(w) + delta(w); end
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end
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end
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% this last step is just additional normalization, and is arbitrary
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betw=betw/(2*nchoosek(size(adj,1),2)); |