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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 . 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 .

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 $Q_i$ .

Returns

G : networkx Graph

Hoffman–Singleton Graph with 50 nodes and 175 edges

Returns the Hoffman-Singleton Graph.

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/generators/small.py#523
type: <class 'function'>
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