Quilting Stochastic Kronecker Product Graphs to Generate Multiplicative Attribute Graphs

TL;DR

This paper introduces a novel, efficient sub-quadratic algorithm for sampling large multiplicative attribute graphs by leveraging the connection to Kronecker product graphs and quilting smaller samples, enabling scalability to billions of edges.

Contribution

The paper presents the first sub-quadratic sampling algorithm for MAGM, utilizing a quilting approach with KPGM graphs, significantly improving scalability for large graph generation.

Findings

Algorithm runs in $O((\log_2(n))^3 |E|)$ time under certain conditions.

Can sample graphs with 8 million nodes and 20 billion edges in under 6 hours.

Demonstrates scalability through extensive empirical evaluation.

Abstract

We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices to sample small number of KPGM graphs and \emph{quilt} them together. Under a restricted set of technical conditions our algorithm runs in $O((\log_2(n))^3 |E|)$ time, where $n$ is the number of nodes and $|E|$ is the number of edges in the sampled graph. We demonstrate the scalability of our algorithm via extensive empirical evaluation; we can sample a MAGM graph with 8 million nodes and 20 billion edges in under 6 hours.