chordal_cycle_graph#

chordal_cycle_graph(p, create_using=None)[source]#

Returns 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 [1].

p must be a prime number.

Parameters:

pa prime number: The number of vertices in the graph. This also indicates where the chordal edges in the cycle will be created.
create_usingNetworkX graph constructor, optional (default=nx.Graph): Graph type to create. If graph instance, then cleared before populated.

Returns:

Ggraph: The constructed undirected multigraph.

Raises:

NetworkXError: If create_using indicates directed or not a multigraph.

References

[1]

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