What is a fast algorithm for finding critical nodes?

Question

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 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?

Answer 1

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.