Mining (maximal) span-cores from temporal networks

TL;DR

This paper introduces efficient algorithms for identifying maximal span-cores in temporal networks, enabling the analysis of dense, time-bound structures crucial for understanding social dynamics and detecting anomalies.

Contribution

It presents novel algorithms for computing all span-cores and specifically the maximal span-cores efficiently, leveraging containment properties and theoretical insights.

Findings

Algorithms are efficient and scalable on real-world data.

Maximal span-cores effectively reveal social dynamics.

Applications include anomaly detection in face-to-face interaction networks.

Abstract

When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). We tackle this task by introducing a notion of temporal core decomposition where each core is associated with its span: we call such cores span-cores. As the total number of time intervals is quadratic in the size of the temporal domain $T$ under analysis, the total number of span-cores is quadratic in $|T|$ as well. Our first contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the maximal span-cores, i.e., span-cores that are not dominated by any other span-core by both the coreness property and the span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly compute the maximal ones without computing all span-cores. Experimentation on several real-world temporal networks confirms the efficiency and scalability of our methods. Applications on temporal networks, gathered by a proximity-sensing infrastructure recording face-to-face interactions in schools, highlight the relevance of the notion of (maximal) span-core in analyzing social dynamics and detecting/correcting anomalies in the data.