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].

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.

NetworkX graph

The Harary graph \(H_{k,n}\).

See also



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



Weisstein, Eric W. “Harary Graph.” From MathWorld–A Wolfram Web Resource.


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