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kl_connected_subgraph(G, k, l, low_memory=False, same_as_graph=False)[source]

Returns the maximum locally \((k, l)\)-connected subgraph of G.

A graph is locally \((k, l)\)-connected if for each edge \((u, v)\) in the graph there are at least \(l\) edge-disjoint paths of length at most \(k\) joining \(u\) to \(v\).

  • G (NetworkX graph) – The graph in which to find a maximum locally \((k, l)\)-connected subgraph.
  • k (integer) – The maximum length of paths to consider. A higher number means a looser connectivity requirement.
  • l (integer) – The number of edge-disjoint paths. A higher number means a stricter connectivity requirement.
  • low_memory (bool) – If this is True, this function uses an algorithm that uses slightly more time but less memory.
  • same_as_graph (bool) – If this is True then return a tuple of the form (H, is_same), where H is the maximum locally \((k, l)\)-connected subgraph and is_same is a Boolean representing whether G is locally \((k, l)\)-connected (and hence, whether H is simply a copy of the input graph G).

If same_as_graph is True, then this function returns a two-tuple as described above. Otherwise, it returns only the maximum locally \((k, l)\)-connected subgraph.

Return type:

NetworkX graph or two-tuple