odeN: Simultaneous Approximation of Multiple Motif Counts in Large Temporal Networks

TL;DR

This paper introduces odeN, a sampling-based algorithm that efficiently approximates counts of multiple temporal motifs in large networks, significantly reducing computation time while maintaining accuracy.

Contribution

The work presents a novel method for simultaneous motif counting in temporal networks, with theoretical bounds and superior empirical performance over existing approaches.

Findings

odeN provides accurate approximations with fewer samples.

It reduces computational time compared to state-of-the-art methods.

The method is effective for large-scale temporal network analysis.

Abstract

Counting the number of occurrences of small connected subgraphs, called temporal motifs, has become a fundamental primitive for the analysis of temporal networks, whose edges are annotated with the time of the event they represent. One of the main complications in studying temporal motifs is the large number of motifs that can be built even with a limited number of vertices or edges. As a consequence, since in many applications motifs are employed for exploratory analyses, the user needs to iteratively select and analyze several motifs that represent different aspects of the network, resulting in an inefficient, time-consuming process. This problem is exacerbated in large networks, where the analysis of even a single motif is computationally demanding. As a solution, in this work we propose and study the problem of simultaneously counting the number of occurrences of multiple temporal motifs, all corresponding to the same (static) topology (e.g., a triangle). Given that for large temporal networks computing the exact counts is unfeasible, we propose odeN, a sampling-based algorithm that provides an accurate approximation of all the counts of the motifs. We provide analytical bounds on the number of samples required by odeN to compute rigorous, probabilistic, relative approximations. Our extensive experimental evaluation shows that odeN enables the approximation of the counts of motifs in temporal networks in a fraction of the time needed by state-of-the-art methods, and that it also reports more accurate approximations than such methods.