def pairs_of_shortest_paths(graph, weight_attribute='weight', infinity=65536):
''' Computes all pairs of shortest paths in graph.
Infinity should be specified, otherwise 65536 will be chosen.
Returns dict with shortest paths, where dict[u][v] is the length
of the shortest path between u and v, or infinity if there is no
path between them. '''
distance = {}
for node in graph:
distance[node] = defaultdict(lambda: infinity)
distance[node][node] = 0
for u, v, data in edge_iter(graph):
distance[u][v] = data[weight_attribute]
for u in graph:
for v in graph:
for w in graph:
if distance[v][u] + distance[u][w] < distance[v][w]:
distance[v][w] = distance[v][u] + distance[u][w]
return dict(distance)
def shortest_paths_from(graph, start, weight_attribute='weight'):
''' Returns (predecessors, distance). predecessors[node]
is the predecessor of node in the shortest path,
distance[node] is the shortest-path's lenght to node. No
negative cycles allowed! '''
if start not in graph:
raise NodeNotFound(
"Node {0} is not in the graph!".format(start))
distance = {start: 0}
predecessors = {start: None}
for i in range(0, graph.order()):
for u, distance_u in list(distance.items()):
for v, data in graph[u].items():
if (v not in distance or
distance[v] > distance_u + data[weight_attribute]):
distance[v] = distance_u + data[weight_attribute]
predecessors[v] = u
for (u, v, attributes) in edge_iter(graph):
if u in distance and v in distance:
if distance[v] > distance[u] + attributes[weight_attribute]:
raise NegativeCycle("Negative cycle found!")
return (predecessors, distance)
