Fast Computation of Empirically Tight Bounds for the Diameter of Massive Graphs

TL;DR

This paper introduces a new, fast method for computing tight bounds on the diameter of massive graphs, enabling accurate estimation in large complex networks where previous algorithms were too slow or resource-intensive.

Contribution

It presents a simple, efficient algorithmic approach that produces very tight bounds for graph diameter, improving estimation accuracy for large-scale networks.

Findings

Bounds are very tight on real-world complex networks

Method enables diameter estimation for previously intractable graphs

Bounds can be equal, providing exact diameter estimates

Abstract

The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones producing approximate values, have too high a time and/or space complexity to be used in such cases. We propose here a new approach relying on very simple and fast algorithms that compute (upper and lower) bounds for the diameter. We show empirically that, on various real-world cases representative of complex networks studied in the literature, the obtained bounds are very tight (and even equal in some cases). This leads to rigorous and very accurate estimations of the actual diameter in cases which were previously untractable in practice.