The Wedge Picking Model: A dynamic graph model based on triadic closure

TL;DR

This paper introduces a probabilistic dynamic graph model based on triadic closure, providing theoretical analysis and practical algorithms to efficiently process evolving social networks and improve existing graph algorithms.

Contribution

The paper presents a novel probabilistic model for dynamic graphs inspired by triadic closure, along with theoretical bounds and an efficient scheduling method to enhance graph processing algorithms.

Findings

Bounded growth rate of graph characteristics like vertex degree.

Speedup of state-of-the-art algorithms with minimal approximation loss.

Successful application to densest subgraph and tri-densest subgraph problems.

Abstract

Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept of triadic closure, we propose a probabilistic mechanism to model the evolution of these dynamic graphs. Although triadic closure is ubiquitous in social networks and its presence helps forming communities, probabilistic models encapsulating it have not been studied adequately. We theoretically analyze our model and show how to bound the growth rate of some characteristics of the graph, such as degree of vertices. Leveraging our theoretical results, we develop a scheduling subroutine to process modifications of the graph in batches. Our scheduling subroutine is then used to speed up the state-of-the-art algorithms with negligible loss in their approximation guarantees. We demonstrate the applicability of our method by applying it to the densest subgraph and tri-densest subgraph discovery problem.