spanner

spanner(G, stretch, weight=None, seed=None)

Returns a spanner of the given graph with the given stretch.

A spanner of a graph G = (V, E) with stretch t is a subgraph H = (V, E_S) such that E_S is a subset of E and the distance between any pair of nodes in H is at most t times the distance between the nodes in G.

Parameters:

GNetworkX graph

An undirected simple graph.

stretchfloat

The stretch of the spanner.

weightobject

The edge attribute to use as distance.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

Returns:

NetworkX graph

A spanner of the given graph with the given stretch.

Raises:

ValueError

If a stretch less than 1 is given.

Notes

This function implements the spanner algorithm by Baswana and Sen, see [1].

This algorithm is a randomized las vegas algorithm: The expected running time is O(km) where k = (stretch + 1) // 2 and m is the number of edges in G. The returned graph is always a spanner of the given graph with the specified stretch. For weighted graphs the number of edges in the spanner is O(k * n^(1 + 1 / k)) where k is defined as above and n is the number of nodes in G. For unweighted graphs the number of edges is O(n^(1 + 1 / k) + kn).

References

[1] S. Baswana, S. Sen. A Simple and Linear Time Randomized Algorithm for Computing Sparse Spanners in Weighted Graphs. Random Struct. Algorithms 30(4): 532-563 (2007).