The Limitations of the BP Algorithm for Counting Cycles in Random Networks

We study the computation capability of the BP cycles counting algorithm in random networks by estimating the required convergence error to find the maximum number of points in the cycles distribution which helps to interpolate accurately the cycles counts for different sizes. The algorithm shows that the convergence error required to get all possible points is almost constant through all possible connection probability values. The number of points possible can not reach the maximum even with high convergence error values.