Shortest Paths

Compute the shortest paths and path lengths between nodes in the graph.

These algorithms work with undirected and directed graphs.

shortest_path(G[, source, target, weight, ...])	Compute shortest paths in the graph.
all_shortest_paths(G, source, target[, ...])	Compute all shortest simple paths in the graph.
shortest_path_length(G[, source, target, ...])	Compute shortest path lengths in the graph.
average_shortest_path_length(G[, weight, method])	Returns the average shortest path length.
has_path(G, source, target)	Returns True if G has a path from source to target.

Advanced Interface

Shortest path algorithms for unweighted graphs.

single_source_shortest_path(G, source[, cutoff])	Compute shortest path between source and all other nodes reachable from source.
single_source_shortest_path_length(G, source)	Compute the shortest path lengths from source to all reachable nodes.
single_target_shortest_path(G, target[, cutoff])	Compute shortest path to target from all nodes that reach target.
single_target_shortest_path_length(G, target)	Compute the shortest path lengths to target from all reachable nodes.
bidirectional_shortest_path(G, source, target)	Returns a list of nodes in a shortest path between source and target.
all_pairs_shortest_path(G[, cutoff])	Compute shortest paths between all nodes.
all_pairs_shortest_path_length(G[, cutoff])	Computes the shortest path lengths between all nodes in G.
predecessor(G, source[, target, cutoff, ...])	Returns dict of predecessors for the path from source to all nodes in G.

Shortest path algorithms for weighted graphs.

dijkstra_predecessor_and_distance(G, source)	Compute weighted shortest path length and predecessors.
dijkstra_path(G, source, target[, weight])	Returns the shortest weighted path from source to target in G.
dijkstra_path_length(G, source, target[, weight])	Returns the shortest weighted path length in G from source to target.
single_source_dijkstra(G, source[, target, ...])	Find shortest weighted paths and lengths from a source node.
single_source_dijkstra_path(G, source[, ...])	Find shortest weighted paths in G from a source node.
single_source_dijkstra_path_length(G, source)	Find shortest weighted path lengths in G from a source node.
multi_source_dijkstra(G, sources[, target, ...])	Find shortest weighted paths and lengths from a given set of source nodes.
multi_source_dijkstra_path(G, sources[, ...])	Find shortest weighted paths in G from a given set of source nodes.
multi_source_dijkstra_path_length(G, sources)	Find shortest weighted path lengths in G from a given set of source nodes.
all_pairs_dijkstra(G[, cutoff, weight])	Find shortest weighted paths and lengths between all nodes.
all_pairs_dijkstra_path(G[, cutoff, weight])	Compute shortest paths between all nodes in a weighted graph.
all_pairs_dijkstra_path_length(G[, cutoff, ...])	Compute shortest path lengths between all nodes in a weighted graph.
bidirectional_dijkstra(G, source, target[, ...])	Dijkstra's algorithm for shortest paths using bidirectional search.
bellman_ford_path(G, source, target[, weight])	Returns the shortest path from source to target in a weighted graph G.
bellman_ford_path_length(G, source, target)	Returns the shortest path length from source to target in a weighted graph.
single_source_bellman_ford(G, source[, ...])	Compute shortest paths and lengths in a weighted graph G.
single_source_bellman_ford_path(G, source[, ...])	Compute shortest path between source and all other reachable nodes for a weighted graph.
single_source_bellman_ford_path_length(G, source)	Compute the shortest path length between source and all other reachable nodes for a weighted graph.
all_pairs_bellman_ford_path(G[, weight])	Compute shortest paths between all nodes in a weighted graph.
all_pairs_bellman_ford_path_length(G[, weight])	Compute shortest path lengths between all nodes in a weighted graph.
bellman_ford_predecessor_and_distance(G, source)	Compute shortest path lengths and predecessors on shortest paths in weighted graphs.
negative_edge_cycle(G[, weight, heuristic])	Returns True if there exists a negative edge cycle anywhere in G.
find_negative_cycle(G, source[, weight])	Returns a cycle with negative total weight if it exists.
goldberg_radzik(G, source[, weight])	Compute shortest path lengths and predecessors on shortest paths in weighted graphs.
johnson(G[, weight])	Uses Johnson's Algorithm to compute shortest paths.

Dense Graphs

Floyd-Warshall algorithm for shortest paths.

floyd_warshall(G[, weight])	Find all-pairs shortest path lengths using Floyd's algorithm.
floyd_warshall_predecessor_and_distance(G[, ...])	Find all-pairs shortest path lengths using Floyd's algorithm.
floyd_warshall_numpy(G[, nodelist, weight])	Find all-pairs shortest path lengths using Floyd's algorithm.
reconstruct_path(source, target, predecessors)	Reconstruct a path from source to target using the predecessors dict as returned by floyd_warshall_predecessor_and_distance

A* Algorithm

Shortest paths and path lengths using the A* (“A star”) algorithm.

astar_path(G, source, target[, heuristic, ...])	Returns a list of nodes in a shortest path between source and target using the A* ("A-star") algorithm.
astar_path_length(G, source, target[, ...])	Returns the length of the shortest path between source and target using the A* ("A-star") algorithm.