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 vertexx
to its inverse modulop
. 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.