find_induced_nodes

find_induced_nodes(G, s, t, treewidth_bound=9223372036854775807)

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 :

I : Set of nodes

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

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.

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 [R151]. A formal definition of induced node can also be found on that reference.

References

[R151]

(1, 2) 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

Examples

>>> import networkx as nx
>>> G=nx.Graph()  
>>> G = nx.generators.classic.path_graph(10)
>>> I = nx.find_induced_nodes(G,1,9,2)
>>> list(I)
[1, 2, 3, 4, 5, 6, 7, 8, 9]