kernighan_lin_bisection(G, partition=None, max_iter=10, weight='weight', seed=None)[source]

Partition a graph into two blocks using the Kernighan–Lin algorithm.

This algorithm partitions a network into two sets by iteratively swapping pairs of nodes to reduce the edge cut between the two sets. The pairs are chosen according to a modified form of Kernighan-Lin, which moves node individually, alternating between sides to keep the bisection balanced.

  • G (graph)

  • partition (tuple) – Pair of iterables containing an initial partition. If not specified, a random balanced partition is used.

  • max_iter (int) – Maximum number of times to attempt swaps to find an improvemement before giving up.

  • weight (key) – Edge data key to use as weight. If None, the weights are all set to one.

  • seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness. Only used if partition is None


partition – A pair of sets of nodes representing the bipartition.

Return type



NetworkXError – If partition is not a valid partition of the nodes of the graph.



Kernighan, B. W.; Lin, Shen (1970). “An efficient heuristic procedure for partitioning graphs.” Bell Systems Technical Journal 49: 291–307. Oxford University Press 2011.