First Stretch then Shrink and Bulk: A Two Phase Approach for Enumeration of Maximal (, γ)-Cliques of a Temporal Network
Abstract
A Temporal Network (also known as Link Stream or Time-Varying Graph) is often used to model a time-varying relationship among a group of agents. It is typically represented as a collection of triplets of the form (u,v,t) that denotes the interaction between the agents u and v at time t. For analyzing the contact patterns of the agents forming a temporal network, recently the notion of classical clique of a static graph has been generalized as -Clique of a Temporal Network. In the same direction, one of our previous studies introduces the notion of (, γ)-Clique, which is basically a vertex set, time interval pair, in which every pair of the clique vertices are linked at least γ times in every duration of the time interval. In this paper, we propose a different methodology for enumerating all the maximal (, γ)-Cliques of a given temporal network. The proposed methodology is broadly divided into two phases. In the first phase, each temporal link is processed for constructing (, γ)-Clique(s) with maximum duration. In the second phase, these initial cliques are expanded by vertex addition to form the maximal cliques. From the experimentation carried out on 5 real-world temporal network datasets, we observe that the proposed methodology enumerates all the maximal (,γ)-Cliques efficiently, particularly when the dataset is sparse. As a special case (γ=1), the proposed methodology is also able to enumerate (,1) -cliques with much less time compared to the existing methods.