hoffman_singleton_graph¶

hoffman_singleton_graph()[source]¶

Returns the Hoffman-Singleton Graph.

The Hoffman–Singleton graph is a symmetrical undirected graph with 50 nodes and 175 edges. All indices lie in Z % 5: that is, the integers mod 5 [1]. It is the only regular graph of vertex degree 7, diameter 2, and girth 5. It is the unique (7,5)-cage graph and Moore graph, and contains many copies of the Petersen graph [2].

Returns

Gnetworkx Graph: Hoffman–Singleton Graph with 50 nodes and 175 edges

Notes

Constructed from pentagon and pentagram as follows: Take five pentagons $P_{h}$ and five pentagrams $Q_{i}$ . Join vertex $j$ of $P_{h}$ to vertex $h \cdot i + j$ of $Q_{i}$ [3].

References

1: https://blogs.ams.org/visualinsight/2016/02/01/hoffman-singleton-graph/
2: https://mathworld.wolfram.com/Hoffman-SingletonGraph.html
3: https://en.wikipedia.org/wiki/Hoffman%E2%80%93Singleton_graph