In above graph, following are the biconnected components:
- 4–2 3–4 3–1 2–3 1–2
- 8–5 7–8 5–7
- 6–0 5–6 1–5 0–1
Algorithm is based on Disc and Low Values discussed in Strongly Connected Components Article.
Idea is to store visited edges in a stack while DFS on a graph and keep looking for Articulation Points (highlighted in above figure). As soon as an Articulation Point u is found, all edges visited while DFS from node u onwards will form one biconnected component. When DFS completes for one connected component, all edges present in stack will form a biconnected component.
If there is no Articulation Point in graph, then graph is biconnected and so there will be one biconnected component which is the graph itself.
4--2 3--4 3--1 2--3 1--2 8--9 8--5 7--8 5--7 6--0 5--6 1--5 0--1 10--11 Above are 5 biconnected components in graph
This article is contributed by Anurag Singh. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
- Biconnected graph
- Strongly Connected Components
- Connected Components in an undirected graph
- Clone an undirected graph with multiple connected components
- Tarjan's Algorithm to find Strongly Connected Components
- Sum of the minimum elements in all connected components of an undirected graph
- Number of single cycle components in an undirected graph
- Maximum number of edges among all connected components of an undirected graph
- Uniform-Cost Search (Dijkstra for large Graphs)
- Sum of degrees of all nodes of a undirected graph
- Spanning Tree With Maximum Degree (Using Kruskal's Algorithm)
- Check if the array can be sorted using swaps between given indices only
- Find the weight of the minimum spanning tree
- Longest path in a directed Acyclic graph | Dynamic Programming