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
- Number of single cycle components in an undirected graph
- Tarjan's Algorithm to find Strongly Connected Components
- Sum of the minimum elements in all connected components of an undirected graph
- Clone an undirected graph with multiple connected components
- Maximum number of edges among all connected components of an undirected graph
- Program to count Number of connected components in an undirected graph
- Minimum number of colors required to color a graph
- Shortest Path Faster Algorithm
- Check whether the cost of going from any node to any other node via all possible paths is same
- Check if alternate path exists from U to V with smaller individual weight in a given Graph
- Maximum number of edges that N-vertex graph can have such that graph is Triangle free | Mantel's Theorem