Returns the k-component structure of a graph G.
A \(k\)-component is a maximal subgraph of a graph G that has, at least, node connectivity \(k\): we need to remove at least \(k\) nodes to break it into more components. \(k\)-components have an inherent hierarchical structure because they are nested in terms of connectivity: a connected graph can contain several 2-components, each of which can contain one or more 3-components, and so forth.
- G (NetworkX graph) –
- flow_func (function) – Function to perform the underlying flow computations. Default value
edmonds_karp(). This function performs better in sparse graphs with right tailed degree distributions.
shortest_augmenting_path()will perform better in denser graphs.
k_components – Dictionary with all connectivity levels \(k\) in the input Graph as keys and a list of sets of nodes that form a k-component of level \(k\) as values.
Return type: Raises:
NetworkXNotImplemented: – If the input graph is directed.
>>> # Petersen graph has 10 nodes and it is triconnected, thus all >>> # nodes are in a single component on all three connectivity levels >>> G = nx.petersen_graph() >>> k_components = nx.k_components(G)
Moody and White  (appendix A) provide an algorithm for identifying k-components in a graph, which is based on Kanevsky’s algorithm  for finding all minimum-size node cut-sets of a graph (implemented in
- Compute node connectivity, k, of the input graph G.
- Identify all k-cutsets at the current level of connectivity using Kanevsky’s algorithm.
- Generate new graph components based on the removal of these cutsets. Nodes in a cutset belong to both sides of the induced cut.
- If the graph is neither complete nor trivial, return to 1; else end.
This implementation also uses some heuristics (see  for details) to speed up the computation.
 Moody, J. and D. White (2003). Social cohesion and embeddedness: A hierarchical conception of social groups. American Sociological Review 68(1), 103–28. http://www2.asanet.org/journals/ASRFeb03MoodyWhite.pdf  Kanevsky, A. (1993). Finding all minimum-size separating vertex sets in a graph. Networks 23(6), 533–541. http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract  Torrents, J. and F. Ferraro (2015). Structural Cohesion: Visualization and Heuristics for Fast Computation. http://arxiv.org/pdf/1503.04476v1