38 lines
1.1 KiB
Matlab
38 lines
1.1 KiB
Matlab
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% Prim's minimal spanning tree algorithm
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% Prim's alg idea:
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% start at any node, find closest neighbor and mark edges
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% for all remaining nodes, find closest to previous cluster, mark edge
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% continue until no nodes remain
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%
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% INPUTS: graph defined by adjacency matrix, nxn
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% OUTPUTS: matrix specifying minimum spanning tree (subgraph), nxn
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%
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% Other routines used: isConnected.m
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% GB: Oct 7, 2012
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function tr = minSpanTree(adj)
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% check if graph is connected:
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if not(isConnected(adj)); printf('This graph is not connected. No spanning tree exists.\n'); return; end
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n = length(adj); % number of nodes
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tr = zeros(n); % initialize tree
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adj(find(adj==0))=inf; % set all zeros in the matrix to inf
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conn_nodes = 1; % nodes part of the min-span-tree
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rem_nodes = [2:n]; % remaining nodes
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while length(rem_nodes)>0
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[minlink]=min(min(adj(conn_nodes,rem_nodes)));
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ind=find(adj(conn_nodes,rem_nodes)==minlink);
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[ind_i,ind_j] = ind2sub([length(conn_nodes),length(rem_nodes)],ind(1));
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i=conn_nodes(ind_i); j=rem_nodes(ind_j); % gets back to adj indices
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tr(i,j)=1; tr(j,i)=1;
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conn_nodes = [conn_nodes j];
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rem_nodes = setdiff(rem_nodes,j);
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end
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