65 lines
1.8 KiB
Matlab
65 lines
1.8 KiB
Matlab
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% Determine if a graph is connected
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% Idea by Ed Scheinerman, circa 2006,
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% source: http://www.ams.jhu.edu/~ers/matgraph/
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% routine: matgraph/@graph/isconnected.m
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%
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% INPUTS: adjacency matrix, nxn
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% OUTPUTS: Boolean variable, 0 or 1
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%
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% Note: This function works only for undirected graphs.
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% GB: last updated, Sep 23 2012
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function S = isConnected(adj)
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if not(isempty(find(sum(adj)==0))); S = false; return; end
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n = length(adj);
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x = [1; zeros(n-1,1)]; % [1,0,...0] nx1 vector
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while 1
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y = x;
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x = adj*x + x;
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x = x>0;
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if x==y; break; end
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end
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S = true;
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if sum(x)<n; S = false; end
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% Alternative 1 ..........................................................
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% If the algebraic connectivity is > 0 then the graph is connected
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% a=algebraic_connectivity(adj);
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% S = false; if a>0; S = true; end
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% Alternative 2 ..........................................................
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% Uses the fact that multiplying the adj matrix to itself k times give the
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% number of ways to get from i to j in k steps. If the end of the
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% multiplication in the sum of all matrices there are 0 entries then the
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% graph is disconnected. Computationally intensive, but can be sped up by
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% the fact that in practice the diameter is very short compared to n, so it
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% will terminate in order of log(n)? steps.
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% function S=isconnected(el):
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%
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% S=false;
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%
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% adj=edgeL2adj(el);
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% n=numnodes(adj); % number of nodes
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% adjn=zeros(n);
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%
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% adji=adj;
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% for i=1:n
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% adjn=adjn+adji;
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% adji=adji*adj;
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%
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% if length(find(adjn==0))==0
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% S=true;
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% return
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% end
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% end
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% Alternative 3 ............................................................
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% Find all connected components, if their number is 1, the graph is
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% connected. Use find_conn_comp(adj).
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