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Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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networkx.algorithms.chordal.find_induced_nodes

find_induced_nodes(G, s, t, treewidth_bound=9223372036854775807)[source]

Returns the set of induced nodes in the path from s to t.

Parameters

  • G (graph) – A chordal NetworkX graph

  • s (node) – Source node to look for induced nodes

  • t (node) – Destination node to look for induced nodes

  • treewith_bound (float) – Maximum treewidth acceptable for the graph H. The search for induced nodes will end as soon as the treewidth_bound is exceeded.

Returns

Induced_nodes – The set of induced nodes in the path from s to t in G

Return type

Set of nodes

Raises

NetworkXError – The algorithm does not support DiGraph, MultiGraph and MultiDiGraph. If the input graph is an instance of one of these classes, a NetworkXError is raised. The algorithm can only be applied to chordal graphs. If the input graph is found to be non-chordal, a NetworkXError is raised.

Examples

>>> G = nx.Graph()
>>> G = nx.generators.classic.path_graph(10)
>>> induced_nodes = nx.find_induced_nodes(G, 1, 9, 2)
>>> sorted(induced_nodes)
[1, 2, 3, 4, 5, 6, 7, 8, 9]

Notes

G must be a chordal graph and (s,t) an edge that is not in G.

If a treewidth_bound is provided, the search for induced nodes will end as soon as the treewidth_bound is exceeded.

The algorithm is inspired by Algorithm 4 in 1. A formal definition of induced node can also be found on that reference.

References

1

Learning Bounded Treewidth Bayesian Networks. Gal Elidan, Stephen Gould; JMLR, 9(Dec):2699–2731, 2008. http://jmlr.csail.mit.edu/papers/volume9/elidan08a/elidan08a.pdf