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_usingNetworkX graph constructor, optional Graph type

to create (default=nx.Graph). If graph instance, then cleared before populated.

Returns

NetworkX graph

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

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.