max_clique#
- max_clique(G)[source]#
Find the Maximum Clique
Finds the \(O(|V|/(log|V|)^2)\) apx of maximum clique/independent set in the worst case.
- Parameters:
- GNetworkX graph
Undirected graph
- Returns:
- cliqueset
The apx-maximum clique of the graph
- Raises:
- NetworkXNotImplemented
If the graph is directed or is a multigraph.
Notes
A clique in an undirected graph G = (V, E) is a subset of the vertex set
C subseteq V
such that for every two vertices in C there exists an edge connecting the two. This is equivalent to saying that the subgraph induced by C is complete (in some cases, the term clique may also refer to the subgraph).A maximum clique is a clique of the largest possible size in a given graph. The clique number
omega(G)
of a graph G is the number of vertices in a maximum clique in G. The intersection number of G is the smallest number of cliques that together cover all edges of G.https://en.wikipedia.org/wiki/Maximum_clique
References
[1]Boppana, R., & Halldórsson, M. M. (1992). Approximating maximum independent sets by excluding subgraphs. BIT Numerical Mathematics, 32(2), 180–196. Springer. doi:10.1007/BF01994876
Examples
>>> G = nx.path_graph(10) >>> nx.approximation.max_clique(G) {8, 9}