64 lines
1.8 KiB
Matlab
64 lines
1.8 KiB
Matlab
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% Test whether a graph is bipartite. If so, return the two vertex sets.
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% A bipartite graph is a graph for which the nodes can be split in two sets A and B,
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% such that there are no edges that connect nodes within A or within B.
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%
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% Inputs: graph in the form of adjacency list (neighbor list, see adj2adjL.m)
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% Outputs: true/false (boolean), empty set (if false) or two sets of vertices
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%
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% Note: This only works for undirected graphs.
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% GB: last updated, Dec 6, 2015
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function [isit,A,B]=isBipartite(L)
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isit=true; % default
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A=[]; B=[];
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queue=[1]; % initialize to first vertex arbitrarily
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visited=[]; % initilize to empty
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A=[1]; % put the first node on the queue in A, arbitrarily
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while not(isempty(queue))
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i=queue(1);
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visited=[visited, i];
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if length(find(A==i))>0
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for j=1:length(L{i})
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B=[B,L{i}(j)];
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if length(find(visited==L{i}(j)))==0; queue=[queue, L{i}(j)]; end
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end
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elseif length(find(B==i))>0
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for j=1:length(L{i})
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A=[A,L{i}(j)];
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if length(find(visited==L{i}(j)))==0; queue=[queue, L{i}(j)]; end
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end
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end
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queue=queue(2:length(queue)); % remove the visited node
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% if A and B overlap, return false, [],[] ....
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A=unique(A); B=unique(B);
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if not(isempty(intersect(A,B))); isit=false; A=[]; B=[]; return; end
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% ............................................
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end
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% Alternative for isBipartite(), without returning
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% the two vertex sets.
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%
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% function [isit] = isBipartite(adj)
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%
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% # This function uses the signlessLaplacian() function.
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% # Note that instead of checking directly for zeros,
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% # due to numeric approximation - the code checks for
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% # really small positive numbers instead.
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%
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% [~,E] = eig(signlessLaplacian(adj));
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% isit = true;
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% if sum( abs(diag(E))>10^(-10) )==size(adj,1); isit = false; end
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