Calculating all paths from a given node in a digraph

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Hey all,
I am using the digraph function and trying to find all paths from a given source node, i was wondering if there already exist a object function to do this such as the shortest path object functions.
As an example:
The output i would like:
[1 2 4]
[1 2 5]
[1 2 6]
[1 3 7 9]
[1 3 7 8]

Accepted Answer

Guillaume
Guillaume on 4 Sep 2018
I've not tested it thoroughly but I think this should work:
function paths = getpaths(g)
%return all paths from a DAG.
%the function will error in toposort if the graph is not a DAG
paths = {}; %path computed so far
endnodes = []; %current end node of each path for easier tracking
for nid = toposort(g) %iterate over all nodes
if indegree(g, nid) == 0 %node is a root, simply add it for now
paths = [paths; nid]; %#ok<AGROW>
endnodes = [endnodes; nid]; %#ok<AGROW>
end
%find successors of current node and replace all paths that end with the current node with cartesian product of paths and successors
toreplace = endnodes == nid; %all paths that need to be edited
s = successors(g, nid);
if ~isempty(s)
[p, tails] = ndgrid(paths(toreplace), s); %cartesian product
paths = [cellfun(@(p, t) [p, t], p(:), num2cell(tails(:)), 'UniformOutput', false); %append paths and successors
paths(~toreplace)];
endnodes = [tails(:); endnodes(~toreplace)];
end
end
end
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More Answers (2)

Walter Roberson
Walter Roberson on 4 Sep 2018
Mathworks does not provide any function for that purpose. Perhaps the graph theory toolbox in the File Exchange?
Your text asks for "all paths", and your example is a digraph that happens to have "in degree" 1 for all nodes. In the special case of a digraph with "in degree" 1 for all nodes, then "all paths" becomes the same as all shortest path tree https://www.mathworks.com/help/matlab/ref/graph.shortestpathtree.html .
This routine will not work for cases where the in degree is more than 1, such as if node 3 also pointed to node 9: in that case the "shortest" path choices in the routine would prune out some of the paths.
  3 Comments
Niels de Vries
Niels de Vries on 4 Sep 2018
Edited: Niels de Vries on 4 Sep 2018
It indeed is, backtracking is needed, but i am not sure how to implement something like that in Matlab. An example digraph is added, and unfortunately couldn't find something in the file exchange

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Pierre Harouimi
Pierre Harouimi on 29 Dec 2021
R2021a: allpaths

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