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Geometric Deep Learning sub-network extraction for Maximum Clique Enumeration.

Vincenza Carchiolo¹, Marco Grassia¹, Michele Malgeri¹

¹Dipartimento Ingegneria Elettrica Elettronica Informatica Università di Catania, Catania, Italy.

|January 16, 2024

Summary

This study introduces LGP-MCE, a novel algorithm using Geometric Deep Learning to efficiently solve the Maximum Clique Enumeration problem. Experiments show LGP-MCE significantly speeds up computation while preserving all maximum cliques.

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Area of Science:

Graph Theory
Machine Learning
Computational Complexity

Background:

Maximum Clique Enumeration (MCE) is a critical NP-hard problem with diverse real-world applications.
Existing algorithms often struggle with scalability on large, complex networks.

Purpose of the Study:

To develop an efficient algorithm for Maximum Clique Enumeration.
To leverage Geometric Deep Learning for pruning large networks.

Main Methods:

Proposed LGP-MCE algorithm combining Geometric Deep Learning with exact methods.
Applied a node-filtering strategy based on Geometric Deep Learning.
Tested on a substantial dataset of real-world networks with varying characteristics.

Main Results:

LGP-MCE drastically reduces the running time for Maximum Clique Enumeration.
The algorithm successfully retains all maximum cliques.
Performance validated across networks of diverse sizes and densities.

Conclusions:

LGP-MCE offers a significant advancement in solving the Maximum Clique Enumeration problem.
Geometric Deep Learning provides an effective approach for network pruning in MCE.
The method demonstrates practical efficiency for real-world network analysis.