# networkx.generators.small.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 $$h·i+j$$ 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