is_chordal

is_chordal(G)

Checks whether G is a chordal graph.

A graph is chordal if every cycle of length at least 4 has a chord (an edge joining two nodes not adjacent in the cycle).

Parameters :

G : graph

A NetworkX graph.

Returns :

chordal : bool

True if G is a chordal graph and False otherwise.

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.

Notes

The routine tries to go through every node following maximum cardinality search. It returns False when it finds that the separator for any node is not a clique. Based on the algorithms in [R137].

References

[R137]

(1, 2) R. E. Tarjan and M. Yannakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput., 13 (1984), pp. 566–579.

Examples

>>> import networkx as nx
>>> e=[(1,2),(1,3),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)]
>>> G=nx.Graph(e)
>>> nx.is_chordal(G)
True