articulation_points(G)
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.
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 :None:None:`n` is an articulation point if, and only if, there exists a subtree rooted at :None:None:`n` such that there is no back edge from any successor of :None:None:`n` that links to a predecessor of :None:None:`n` in 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.
An undirected graph.
If the input graph is not undirected.
Yield the articulation points, or cut vertices, of a graph.
An articulation point in the graph.
>>> 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))) 0See :
The following pages refer to to this document either explicitly or contain code examples using this.
networkx.algorithms.components.biconnected.is_biconnected
networkx.algorithms.components.biconnected.articulation_points
networkx.algorithms.components.biconnected.biconnected_component_edges
networkx.algorithms.components.biconnected.biconnected_components
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