networkx.generators.harary_graph.hkn_harary_graph

hkn_harary_graph(k, n, create_using=None)

Returns the Harary graph with given node connectivity and node number.

The Harary graph $H_{k,n}$ is the graph that minimizes the number of edges needed with given node connectivity $k$ and node number $n$.

This smallest number of edges is known to be ceil($kn/2$) 1.

Parameters

• k (integer) – The node connectivity of the generated graph

• n (integer) – The number of nodes 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 $H_{k,n}$.

Return type

NetworkX graph

See also

hnm_harary_graph()

Notes

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

References

1

Weisstein, Eric W. “Harary Graph.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/HararyGraph.html.

2

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