# networkx.generators.harary_graph.hnm_harary_graph¶

hnm_harary_graph(n, m, create_using=None)[source]

Returns the Harary graph with given numbers of nodes and edges.

The Harary graph $$H_{n,m}$$ is the graph that maximizes node connectivity with $$n$$ nodes and $$m$$ edges.

This maximum node connectivity is known to be floor($$2m/n$$). 1

Parameters
• n (integer) – The number of nodes the generated graph is to contain

• m (integer) – The number of edges the generated graph is to contain

• create_using (NetworkX graph constructor, optional Graph type) – to create (default=nx.Graph). If graph instance, then cleared before populated.

Returns

The Harary graph $$H_{n,m}$$.

Return type

NetworkX graph

Notes

This algorithm runs in $$O(m)$$ time. It is implemented by following the Reference 2.

References

1

F. T. Boesch, A. Satyanarayana, and C. L. Suffel, “A Survey of Some Network Reliability Analysis and Synthesis Results,” Networks, pp. 99-107, 2009.

2

Harary, F. “The Maximum Connectivity of a Graph.” Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.