hyper_wiener_index

hyper_wiener_index(G, weight=None)

Returns the Hyper-Wiener index of the graph G.

The Hyper-Wiener index of a connected graph G is defined as

\[WW(G) = \frac{1}{2} \sum_{u,v \in V(G)} (d(u,v) + d(u,v)^2)\]

where d(u, v) is the shortest-path distance between nodes u and v.

Parameters:

GNetworkX graph

An undirected, connected graph.

weightstring or None, optional (default: None)

The edge attribute to use for calculating shortest-path distances. If None, all edges are considered to have a weight of 1.

Returns:

float

The Hyper-Wiener index of the graph G. Returns float(“inf”) if the graph is not connected.

References

[1]

M. Randić, “Novel molecular descriptor for structure-property studies,” Chemical Physics Letters, vol. 211, pp. 478-483, 1993.

[2]

Wikipedia: Hyper-Wiener Index

Examples

>>> G = nx.path_graph(4)
>>> nx.hyper_wiener_index(G)
30.0

>>> G = nx.cycle_graph(4)
>>> nx.hyper_wiener_index(G)
20.0