5.3.2. networkx.generators.expanders.chordal_cycle_graph¶

networkx.generators.expanders.chordal_cycle_graph(p, create_using=None)[source]¶

Return the chordal cycle graph on p nodes.

The returned graph is a cycle graph on p nodes with chords joining each vertex x to its inverse modulo p. This graph is a (mildly explicit) 3-regular expander [R1028].

p must be a prime number.

Parameters:	p : a prime number The number of vertices in the graph. This also indicates where the chordal edges in the cycle will be created. create_using : graph-like A graph-like object that receives the constructed edges. If None, then a MultiGraph instance is used.
Returns:	G : graph The constructed undirected multigraph.
Raises:	NetworkXError If the graph provided in create_using is directed or not a multigraph.

References

[R1028]

(1, 2) Theorem 4.4.2 in A. Lubotzky. “Discrete groups, expanding graphs and invariant measures”, volume 125 of Progress in Mathematics. Birkhäuser Verlag, Basel, 1994.