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Isolation concepts applied to temporal clique enumeration

Published online by Cambridge University Press:  16 October 2020

Hendrik Molter Open the ORCID record for Hendrik Molter [Opens in a new window] ,
Rolf Niedermeier  and
Malte Renken
Hendrik Molter*
Affiliation:
TU Berlin, Faculty IV, Algorithmics and Computational Complexity (emails: rolf.niedermeier@tu-berlin.de, m.renken@tu-berlin.de)
Rolf Niedermeier
Affiliation:
TU Berlin, Faculty IV, Algorithmics and Computational Complexity (emails: rolf.niedermeier@tu-berlin.de, m.renken@tu-berlin.de)
Malte Renken
Affiliation:
TU Berlin, Faculty IV, Algorithmics and Computational Complexity (emails: rolf.niedermeier@tu-berlin.de, m.renken@tu-berlin.de)
*
*Corresponding author. Email: h.molter@tu-berlin.de
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Abstract

Isolation is a concept originally conceived in the context of clique enumeration in static networks, 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 transform the isolation concept to the temporal setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of parameterized enumeration algorithms for five of these six isolation types for clique enumeration, employing the parameter “degree of isolation.” In a nutshell, this means that the more isolated these cliques are, the faster we can find them. On the empirical side, we implemented and tested these algorithms on (temporal) social network data, obtaining encouraging results.

Keywords

community detectiondense subgraphssocial network analysistime-evolving dataenumeration algorithmsfixed-parameter tractability
Type
Research Article
Information
Network Science , Volume 9 , Special Issue S1: Complex Networks 2019 , October 2021 , pp. S83 - S105
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Special Issue Editor: Hocine Cherifi

*

An extended abstract of this work appeared under the title “Enumerating Isolated Cliques in Temporal Networks” in the proceedings of the 8th International Conference on Complex Networks and their Applications (Molter et al., 2019). This version contains full proof details and a comprehensive empirical evaluation. This work was supported by the DFG, project MATE (NI 369/17).

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