hkn_harary_graph#

hkn_harary_graph(k, n, create_using=None)[source]#

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 $$H_{k,n}$$.

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.