Multi-View Structural Graph Summaries

TL;DR

This paper introduces multi-view structural graph summaries, proposes an efficient merging algorithm, and evaluates its performance across diverse datasets and models, demonstrating linear-time complexity under practical assumptions.

Contribution

It presents a novel multi-view graph summary method, an algorithm for merging summaries, and a comprehensive analysis of its complexity and efficiency across different domains.

Findings

Merging summaries has an upper bound of quadratic complexity, but is often linear in practice.

Merging the smallest summaries first is the most efficient strategy.

Experiments on diverse datasets validate the linear-time performance under reasonable assumptions.

Abstract

A structural graph summary is a small graph representation that preserves structural information necessary for a given task. The summary is used instead of the original graph to complete the task faster. We introduce multi-view structural graph summaries and propose an algorithm for merging two summaries. We conduct a theoretical analysis of our algorithm. We run experiments on three datasets, contributing two new ones. The datasets are of different domains (web graph, source code, and news) and sizes; the interpretation of multi-view depends on the domain and are pay-level domains on the web, control vs.\@ data flow of the code, and news broadcasters. We experiment with three graph summary models: attribute collection, class collection, and their combination. We observe that merging two structural summaries has an upper bound of quadratic complexity; but under reasonable assumptions, it has linear-time worst-case complexity. The running time of merging has a strong linear correlation with the number of edges in the two summaries. Therefore, the experiments support the assumption that the upper bound of quadratic complexity is not tight and that linear complexity is possible. Furthermore, our experiments show that always merging the two smallest summaries by the number of edges is the most efficient strategy for merging multiple structural summaries.