Likelihood-based approach to discriminate mixtures of network models that vary in time

Naomi A. Arnold,Raul J. Mondragón,Richard G. Clegg

doi:10.1038/s41598-021-84085-0

Naomi A. Arnold, Raul J. Mondragón + Show 1 more

Open Access

https://doi.org/10.1038/s41598-021-84085-0

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Abstract

Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. The rules governing this growth are attributed to mechanisms such as preferential attachment and triangle closure, with a wealth of explanatory models based on these. These models are deliberately simple, commonly with the network growing according to a constant mechanism for its lifetime, to allow for analytical results. We use a likelihood-based framework on artificial data where the network model changes at a known point in time and demonstrate that we can recover the change point from analysis of the network. We then use real datasets and demonstrate how our framework can show the changing importance of network growth mechanisms over time.

Highlights

Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science
There is a clear need for a framework that can allow network growth models that vary in time and a need to establish the optimal parameters for such models
This paper makes three contributions: (i) We create an extremely rich class of models for network growth by allowing the mixture parameters to change in time. (ii) Using artificial data generated from a known time-varying model we demonstrate a likelihood based framework that can find the correct model and its change points in time that were responsible for the observed network data. (iii) Using real data we show how this framework can give insights into the different mechanisms responsible for network growth

Summary

Introduction

Discriminating between competing explanatory models as to which is more likely responsible for the growth of a network is a problem of fundamental importance for network science. We allow the use of existing popular models, combined into a flexible time-varying framework, either as a tool to generate new types of network or as an explanatory framework to determine the growth mechanism seen in a real data set.

Results

Conclusion