The worst-case time complexity for generating all maximal cliques and computational experiments
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Here we study a variant of maximal clique enumeration problem by incorporating a minimum size criterion. We describe preprocessing techniques to reduce the graph size. This is of practical interest since enumerating maximal cliques is a computationally hard problem and the execution time increases rapidly with the input size. We discuss basics of an algorithm for enumerating large maximal cliques which exploits the constraint on minimum size of the desired maximal cliques. Social networks are prime examples of large sparse graphs where enumerating large maximal cliques is of interest. We present experimental results on the social network formed by the call detail records of one of the world's largest telecom service providers. Our results show that the preprocessing methods achieve significant reduction in the graph size. We also characterize the execution behaviour of our large maximal clique enumeration algorithm.