What is a fast algorithm for finding critical nodes?

I'm looking for a quick method/algorithm for finding which nodes in a graph is critical.

For example, in this graph:

Node number 2 and 5 are critical.

My current method is to try removing one non-endpoint 开发者_运维技巧node from the graph at a time and then check if the entire network can be reached from all other nodes. This method is obvious not very efficient.

What are a better way?

---

See biconnected components. Calling them articulation points instead of critical nodes seems to yield better search results.

In any case, the algorithm consists of a simple depth first search where you maintain certain information for each node.

---

there are several better ways. research is always helpful

but since this is homework, the point of the exercise is likely to be to figure it out yourself

hint: how could you decorate the graph to tell you what nodes depend on what other nodes, and would this information perhaps be useful to spot the critical nodes?