A logical approach for temporal and multiplex networks analysis

TL;DR

This paper introduces a logical framework for analyzing temporal and multiplex networks directly from triplet data, enabling more comprehensive pattern detection across multiple dimensions.

Contribution

It proposes a novel formalism that processes triplet data without separating variables, extending graph theory concepts to better capture complex patterns.

Findings

Framework unifies analysis of temporal and multiplex networks

Algorithm effectively identifies informative patterns in real datasets

Extends classical graph concepts to triplet-based data

Abstract

Many systems generate data as a set of triplets (a, b, c): they may represent that user a called b at time c or that customer a purchased product b in store c. These datasets are traditionally studied as networks with an extra dimension (time or layer), for which the fields of temporal and multiplex networks have extended graph theory to account for the new dimension. However, such frameworks detach one variable from the others and allow to extend one same concept in many ways, making it hard to capture patterns across all dimensions and to identify the best definitions for a given dataset. This extended abstract overrides this vision and proposes a direct processing of the set of triplets. In particular, our work shows that a more general analysis is possible by partitioning the data and building categorical propositions that encode informative patterns. We show that several concepts from graph theory can be framed under this formalism and leverage such insights to extend the concepts to data triplets. Lastly, we propose an algorithm to list propositions satisfying specific constraints and apply it to a real world dataset.