Estimation of the Number of Cliques in a Random Graph

This paper examines methods for predicting and estimating the number of maximal cliques in a random graph. A clique is a subgraph where each vertex is connected to every other vertex in the subgraph. A maximal clique is a clique which is not a proper subgraph of another clique. There are many algorithms that enumerate all maximal cliques in a graph, but since the task can take exponential time, there are practical limits on the size of the input. In this paper, we examine three methods that could be used to estimate the number of cliques in a random graph. One method is based on sampling, another on probability arguments and the third uses curve fitting. We compare the methods for accuracy and efficiency.