negative_edge_cycle(G, weight='weight', heuristic=True)[source]#

Returns True if there exists a negative edge cycle anywhere in G.

GNetworkX graph
weightstring or function

If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining u to v will be G.edges[u, v][weight]). If no such edge attribute exists, the weight of the edge is assumed to be one.

If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.


Determines whether to use a heuristic to early detect negative cycles at a negligible cost. In case of graphs with a negative cycle, the performance of detection increases by at least an order of magnitude.


True if a negative edge cycle exists, otherwise False.


Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

This algorithm uses bellman_ford_predecessor_and_distance() but finds negative cycles on any component by first adding a new node connected to every node, and starting bellman_ford_predecessor_and_distance on that node. It then removes that extra node.


>>> G = nx.cycle_graph(5, create_using=nx.DiGraph())
>>> print(nx.negative_edge_cycle(G))
>>> G[1][2]["weight"] = -7
>>> print(nx.negative_edge_cycle(G))

Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.