networkx.algorithms.sparsifiers.spanner

spanner(G, stretch, weight=None, seed=None)[source]

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:
  • G (NetworkX graph) – An undirected simple graph.
  • stretch (float) – The stretch of the spanner.
  • weight (object) – The edge attribute to use as distance.
  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.
Returns:

A spanner of the given graph with the given stretch.

Return type:

NetworkX graph

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).