cycle detection graph

hi folks,
the "?" is how to detect a cycle in a graph.
Ofcourse there is this time-tested method of using DFS.

I figured a way out by determining the indegree of every vertex in the graph. if there is a cycle , at 1 stage of the algorithm , there will be no vertex of in-degree 0. which wud mean there is a cycle

My question is, is there a better way to detect the cycle?

Your way have O(n) as complexity indicator, it's not so bad!

I'm not shure this is correct,
consider the graph A->B , B->C, C->B
Then A's indegree is 0,
the cycle is between B and C