Improving Efficiency of Maximal k-Plex Search Based on Properness of k-Plex

Abstract

In this paper, we are concerned with a problem of enumerating maximal k-plexes in a given undirected graph, where the notion of k-plex is a relaxation model of clique. An existing algorithm for this task tries to nd solution k-plexes based on a theoretical property of diameter of k-plex . In order to enjoy this propery fully, we propose to divide the class of maximal k-plexes into several subclasses based on size and properness of k-plexes . We, then, observe the maximal k-plexes in each subclass have smaller diameter, where the smaller diameter of k-plex becomes, the less the number of search branches becomes. As a result, we expect that computational cost for our enumeration task can be reduced. Our experimental results for several benchmark graphs show that the proposed approach can achieve a certain degree of improvement in efficiency.