Stochastic Graph Transformation For Social Network Modeling

TL;DR

This paper introduces a novel stochastic graph transformation framework for modeling social networks, specifically voter models, providing a formal, analyzable, and simulation-friendly approach that enhances understanding of network evolution.

Contribution

It formalizes social network models as stochastic attributed graph transformations, linking them to existing probabilistic methods and offering new analysis and simulation tools.

Findings

Successfully captures voter models as stochastic graph transformations

Demonstrates benefits of formal graph transformation approach

Proposes a new stochastic simulation algorithm variant

Abstract

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an approach inspired by the physical sciences, combining an informal description of the operations with programmed simulations, and systems of ODEs as the only abstract mathematical description. We show that we can capture a range of social network models, the so-called voter models, as stochastic attributed graph transformation systems, demonstrate the benefits of this representation and establish its relation to the non-standard probabilistic view adopted in the literature. We use the theory and tools of graph transformation to analyze and simulate the models and propose a new variant of a standard stochastic simulation algorithm to recreate the results observed.