graphscope.nx.generators.harary_graph.hkn_harary_graph

graphscope.nx.generators.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_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