Yield the articulation points, or cut vertices, of a graph.
An articulation point or cut vertex is any node whose removal (along with all its incident edges) increases the number of connected components of a graph. An undirected connected graph without articulation points is biconnected. Articulation points belong to more than one biconnected component of a graph.
Notice that by convention a dyad is considered a biconnected component.
- GNetworkX Graph
An undirected graph.
An articulation point in the graph.
If the input graph is not undirected.
The algorithm to find articulation points and biconnected components is implemented using a non-recursive depth-first-search (DFS) that keeps track of the highest level that back edges reach in the DFS tree. A node
nis an articulation point if, and only if, there exists a subtree rooted at
nsuch that there is no back edge from any successor of
nthat links to a predecessor of
nin the DFS tree. By keeping track of all the edges traversed by the DFS we can obtain the biconnected components because all edges of a bicomponent will be traversed consecutively between articulation points.
Hopcroft, J.; Tarjan, R. (1973). “Efficient algorithms for graph manipulation”. Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
>>> G = nx.barbell_graph(4, 2) >>> print(nx.is_biconnected(G)) False >>> len(list(nx.articulation_points(G))) 4 >>> G.add_edge(2, 8) >>> print(nx.is_biconnected(G)) True >>> len(list(nx.articulation_points(G))) 0