is_reachable#

is_reachable(G, s, t)[source]#

Decides whether there is a path from s to t in the tournament.

This function is more theoretically efficient than the reachability checks than the shortest path algorithms in networkx.algorithms.shortest_paths.

The given graph must be a tournament, otherwise this function’s behavior is undefined.

Parameters:

GNetworkX graph: A directed graph representing a tournament.
snode: A node in the graph.
tnode: A node in the graph.

Returns:

bool: Whether there is a path from s to t in G.

Notes

Although this function is more theoretically efficient than the generic shortest path functions, a speedup requires the use of parallelism. Though it may in the future, the current implementation does not use parallelism, thus you may not see much of a speedup.

This algorithm comes from [1].

References

[1]

Tantau, Till. “A note on the complexity of the reachability problem for tournaments.” Electronic Colloquium on Computational Complexity. 2001. <http://eccc.hpi-web.de/report/2001/092/>

Examples

>>> G = nx.DiGraph([(1, 0), (1, 3), (1, 2), (2, 3), (2, 0), (3, 0)])
>>> nx.is_tournament(G)
True
>>> nx.tournament.is_reachable(G, 1, 3)
True
>>> nx.tournament.is_reachable(G, 3, 2)
False

Additional backends implement this function

parallelParallel backend for NetworkX algorithms: The function parallelizes the calculation of two neighborhoods of vertices in G and checks closure conditions for each neighborhood subset in parallel.

[Source]