MODIT: MOtif DIscovery in Temporal Networks.

Roberto Grasso,Alfredo Ferro,Giovanni Micale,Alfredo Pulvirenti

doi:10.3389/fdata.2021.806014

Abstract

Temporal networks are graphs where each edge is linked with a timestamp, denoting when an interaction between two nodes happens. According to the most recently proposed definitions of the problem, motif search in temporal networks consists in finding and counting all connected temporal graphs Q (called motifs) occurring in a larger temporal network T, such that matched target edges follow the same chronological order imposed by edges in Q. In the last few years, several algorithms have been proposed to solve motif search, but most of them are limited to very small or specific motifs due to the computational complexity of the problem. In this paper, we present MODIT (MOtif DIscovery in Temporal Networks), an algorithm for counting motifs of any size in temporal networks, inspired by a very recent algorithm for subgraph isomorphism in temporal networks, called TemporalRI. Experiments show that for big motifs (more than 3 nodes and 3 edges) MODIT can efficiently retrieve them in reasonable time (up to few hours) in many networks of medium and large size and outperforms state-of-the art algorithms.

Highlights

We present a new motif search algorithm, called MODIT (MOtif DIscovery in Temporal networks)
In what follows we introduce a new algorithm for solving the Temporal Motif Search (TMS) problem, called MODIT (MOtif DIscovery in Temporal networks)
MODIT has been implemented in Java and tested on two datasets of real temporal networks of different sizes, denoted as Dataset 1 and Dataset 2, respectively

Summary

Introduction

AND RELATED WORKSNetworks ( named graphs) are tools for the description and analysis of entities, called nodes, that interact with each other by means of edges. A wide range of domains can be modeled and studied with static networks but many complex systems are fully dynamic, interactions between entities change over time. Systems of this type can be modeled as temporal networks, in which edges between nodes are associated with temporal information such as, for example, the duration of the interaction and the instant in which the interaction begins. Several definitions of temporal networks have been proposed (Holme and Saramaki, 2012; Masuda and Lambiotte, 2020) In few works, these are referenced as dynamic (Carley et al, 2007), evolutionary (Aggarwal and Subbian, 2014) or time-varying (Casteigts et al, 2011) networks. Each edge is associated with an integer, called timestamp, which denotes when two nodes interact

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Conclusion