在图形中，如何确定两个顶点是否形成桥，一旦断开桥，哪些顶点将成为哪个子图的一部分？

Question

I'm using an adjacency list to create my graph in C#.

In this graph, #4 and #5 form a bridge that when disconnected will create two subgraphs:

• {1,2,3,4}
• {5,6,7,8}

My question is two parts:

1. How do I determine if #4 and #5 form a bridge?
2. How do I find out which vertices belong to which subgraph so that I can create new graphs for each of the subgraph?

Answer 1

You can find all bridges in a graph in O(V+E) , read here

After that, mark the bridges and find the connected components using DFS:

for each node:
        if (not visited)
            components++
            dfs(node)

In the dfs traversal don't pass through edges that are marked as bridges.