# Path between 2 nodes in a graph

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Hari on 28 Sep 2020
How to check if a path exists between two nodes in a graph?

Michael Croucher on 28 Sep 2020
Edited: Michael Croucher on 28 Sep 2020
One way to proceed would be to use concomp.
Take this example graph
s = [1 2 2 3 3 3 4 5 5 5 8 8];
t = [2 3 4 1 4 5 5 3 6 7 9 10];
G = graph(s,t);
plot(G,'Layout','layered')
>> components=conncomp(G)
ans =
1 1 1 1 1 1 1 2 2 2
We can see that there are two connected components. To see it nodes 4 and 7 are connected (for example), just see if they are members of the same component.
components(4)==components(7)
ans =
logical
1
Hari on 4 Oct 2020
This did work for me. Thanks
Christine Tobler on 5 Oct 2020
Note this works well for an undirected graph, but for directed graphs it would be more complicated: In that case, you'd want to look into digraph/transclosure to get connection between every pair of nodes.

Christine Tobler on 28 Sep 2020
Compute a path between the nodes, then check if the result is empty (this is returned by shortestpath if no path exists):
path = shortestpath(G, firstNode, secondNode)
pathExists = ~isempty(path);
Hari on 4 Oct 2020
Will this be computationally intensive if I need to check paths between every node pair (say there 100 nodes)?
Bruno Luong on 4 Oct 2020