I need to write a method to find the count of 4 cycles(cycles containing 4 edges) in an undirected graph. Please give me some advices if you have any idea about the algorithm.

See Robert Sedgewick[^]'s book list: Part 5: Graph Algorithms is the book to read (you choose: C, C++, Java). It would be a nice exercise if you write all the code of the book in C#. ;-)
Cheers
Andi

I have done this myself. The algorithm uses DFS. And on every step it goes 4 levels and finds if the found vertex is the same as the one for which is done the step. In formal language it should be something like this:

for path in dfs(start=node, max_depth=4):
if len(path) == 4 and path[1] == path[4]:
output.append(path)

Andi