Scalable Approximation Algorithm for Graph Summarization

TL;DR

This paper introduces a scalable randomized algorithm for graph summarization that minimizes reconstruction error, enabling efficient analysis of large real-world graphs with high accuracy.

Contribution

The paper presents a novel weighted sampling scheme and analytical bounds, making graph summarization scalable and effective for large graphs unlike previous methods.

Findings

Algorithm is scalable to very large graphs

Summaries achieve low reconstruction error

High accuracy in answering structural queries

Abstract

Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a compressed version of the graph that removes several details, yet preserves it's essential structure. Generally, some predefined quality measure of the summary is optimized to bound the approximation error incurred by working on the summary instead of the whole graph. All known summarization algorithms are computationally prohibitive and do not scale to large graphs. In this paper we present an efficient randomized algorithm to compute graph summaries with the goal to minimize reconstruction error. We propose a novel weighted sampling scheme to sample vertices for merging that will result in the least reconstruction error. We provide analytical bounds on the running time of the algorithm and prove approximation guarantee for our score computation. Efficiency of our algorithm makes it scalable to very large graphs on which known algorithms cannot be applied. We test our algorithm on several real world graphs to empirically demonstrate the quality of summaries produced and compare to state of the art algorithms. We use the summaries to answer several structural queries about original graph and report their accuracies.