There is no direct method in MATLAB for computing the edge connectivity. Based on the Wikipedia page, you should be able to compute it quite efficiently for small graphs by calling maxflow in a loop:
% Completely connected graph:
g = graph(ones(4));
edgeConnectivity(g)
% Line graph:
g = graph(1:4, 2:5);
edgeConnectivity(g)
% Circle graph:
g = graph(1:4, [2:4 1]);
edgeConnectivity(g)
% Completely connected graph with 50 nodes:
g = graph(ones(50));
tic
edgeConnectivity(g)
toc
function k = edgeConnectivity(g)
% Make sure the graph is unweighted:
if contains("Weight", g.Edges.Properties.VariableNames)
g.Edges.Weight = [];
end
% Compute the maximum flow from node 1 to every other node
mf = zeros(1, numnodes(g)-1);
for ii=2:numnodes(g)
mf(ii-1) = maxflow(g, 1, ii);
end
% The edge connectivity is the minimum of these maximum flows
k = min(mf);
end
"A simple algorithm would, for every pair (u,v), determine the maximum flow from u to v with the capacity of all edges in G set to 1 for both directions. A graph is k-edge-connected if and only if the maximum flow from u to v is at least k for any pair (u,v), so k is the least u-v-flow among all (u,v).
[...]
An improved algorithm will solve the maximum flow problem for every pair (u,v) where u is arbitrarily fixed while v varies over all vertices. This [...] is sound since, if a cut of capacity less than k exists, it is bound to separate u from some other vertex.
"
Note this isn't the most efficient implementation in terms of code complexity, but the timing looks quite good for a graph with 50 nodes.
