Enumerating Isolated Cliques in Temporal Networks

TL;DR

This paper extends the concept of isolated cliques to temporal networks, developing fixed-parameter algorithms for their enumeration based on the degree of isolation, and demonstrates their effectiveness on social network data.

Contribution

It introduces six natural isolation concepts in temporal networks and provides fixed-parameter algorithms for five of them, advancing clique enumeration methods.

Findings

Algorithms successfully enumerate isolated cliques in temporal networks.

Empirical tests show promising performance on social network data.

Six distinct isolation concepts are identified for temporal cliques.

Abstract

Isolation is a concept from the world of clique enumeration that is mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we lift the isolation concept to this setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of fixed-parameter enumeration algorithms for five of these six clique types employing the parameter "degree of isolation". On the empirical side, we implement and test these algorithms on (temporal) social network data, obtaining encouraging preliminary results.