In social networks, counting the number of different cycle sizes can be used to measure the entropy of the network that represents its robustness. The exact algorithms to compute cycles in a graph can generate exact results but they are not guaranteed to run in a polynomial time. We present an approximation algorithm for counting the number of cycles in an undirected graph. The algorithm is regression-based and guaranteed to run in a polynomial time. A set of experiments are conducted to compare the results of our approximate algorithm with the results of an exact algorithm based on the Donald-Johnson backtracking algorithm.