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 paths in the graph.
shortest_path_length(G[, source, target, …]) Compute shortest path lengths in the graph.
average_shortest_path_length(G[, weight, method]) Return the average shortest path length.
has_path(G, source, target) Return 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) Return 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 weighed 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]) Return True if there exists a negative edge cycle anywhere in G.
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, …]) Return a list of nodes in a shortest path between source and target using the A* (“A-star”) algorithm.
astar_path_length(G, source, target[, …]) Return the length of the shortest path between source and target using the A* (“A-star”) algorithm.