average_shortest_path_length

average_shortest_path_length(G, weight=None, method=None)

Returns the average shortest path length.

The average shortest path length is

\[\begin{split}a =\sum_{\substack{s,t \in V \\ s\neq t}} \frac{d(s, t)}{n(n-1)}\end{split}\]

where V is the set of nodes in G, d(s, t) is the shortest path from s to t, and n is the number of nodes in G.

Changed in version 3.0: An exception is raised for directed graphs that are not strongly connected.

Parameters:

GNetworkX graph

weightNone, string or function, optional (default = None)

If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1. If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.

methodstring, optional (default = ‘unweighted’ or ‘dijkstra’)

The algorithm to use to compute the path lengths. Supported options are ‘unweighted’, ‘dijkstra’, ‘bellman-ford’, ‘floyd-warshall’ and ‘floyd-warshall-numpy’. Other method values produce a ValueError. The default method is ‘unweighted’ if weight is None, otherwise the default method is ‘dijkstra’.

Raises:

NetworkXPointlessConcept

If G is the null graph (that is, the graph on zero nodes).

NetworkXError

If G is not connected (or not strongly connected, in the case of a directed graph).

ValueError

If method is not among the supported options.

Examples

>>> G = nx.path_graph(5)
>>> nx.average_shortest_path_length(G)
2.0

For disconnected graphs, you can compute the average shortest path length for each component

>>> G = nx.Graph([(1, 2), (3, 4)])
>>> for C in (G.subgraph(c).copy() for c in nx.connected_components(G)):
...     print(nx.average_shortest_path_length(C))
1.0
1.0