# 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.

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 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. 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. 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. 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. 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.