Symbolic regression of generative network models

TL;DR

This paper introduces a machine learning approach inspired by natural selection to automatically discover realistic network growth models from empirical data, applicable across various network types without prior assumptions.

Contribution

The authors develop a general, model-agnostic method to identify network growth laws as computer programs, enabling better understanding of network formation mechanisms.

Findings

Successfully rediscovered known growth laws in canonical models

Identified plausible laws for real-world networks

Derived understandable programs for brain and social networks

Abstract

Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the same time, creating such models is often challenging and requires insights that may be counter-intuitive. Yet there currently exists no general method to arrive at better models. We have developed an approach to automatically detect realistic decentralised network growth models from empirical data, employing a machine learning technique inspired by natural selection and defining a unified formalism to describe such models as computer programs. As the proposed method is completely general and does not assume any pre-existing models, it can be applied "out of the box" to any given network. To validate our approach empirically, we systematically rediscover pre-defined growth laws underlying several canonical network generation models and credible laws for diverse real-world networks. We were able to find programs that are simple enough to lead to an actual understanding of the mechanisms proposed, namely for a simple brain and a social network.