How can I get the root node of a given node from a directed graph ?
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Anatole Jimenez
le 18 Déc 2019
Commenté : Guillaume
le 19 Déc 2019
Hello,
I am using graph for image processing, 1 node = 1 pixel.
I computed the graph but I need to find for each node its root node.
Is there any function or a quite performant solution as the number of nodes is quite high ?
Thank you,
Anatole Jimenez
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Guillaume
le 18 Déc 2019
the first element of the vector returned by toposort would be your root node. Of course, your graph must be acyclic and if your graph has several roots, this will only be one of them.
Perhaps easier would be to look in the edge table and find which nodes don't appear at all as target nodes. Assuming the Nodes table is empty:
rootnodes = setdiff(1:height(yourgraph.Nodes), yourgraph.Edges.EndNodes(:, 2))
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Guillaume
le 19 Déc 2019
Indeed, I made an assumption that the terminals would be in the same order as the bins, which is generally incorrect. Fixed code:
bins = G.conncomp('Type', 'weak'); %since the graph is DAG all connections are weak
terminalidx = find(G.outdegree == 0); %which nodes are terminal
terminalbin = bins(terminalidx)
assert(isequal(unique(terminalbin), 1:numel(terminalbin)), 'At least one subgraph has more than one terminal') %optional check
[~, termorder] = sort(terminalbin); %find ordering of terminals according to the bin they're in
terminalidx = terminalidx(termorder); %and reorder them accordingly
matchingterminal = terminalidx(bins); %replicate terminal index in each bin
Note that I would store all this information, together with the nodes X and Y location into the node table:
G.Nodes.Isterminal = G.outdegree == 0;
G.Nodes.MatchingTerminal = matchingterminal;
G.Nodes.Subgraph = bins;
G.Nodes.X = ??? %Nx1 column vector
G.Nodes.Y = ??? %Nx1 column vector
which makes for easy plotting
plot(G, 'XData', G.Nodes.X, 'YData', G.Nodes.Y, 'NodeCdata', G.Nodes.IsTerminal+1); %to highlight the terminals
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