Metric tree-like structures in real-life networks: an empirical study

TL;DR

This paper provides empirical evidence that various real-world networks exhibit tree-like metric structures, enabling efficient analysis, encoding, and estimation of network properties such as distances, diameters, and radii.

Contribution

It introduces a comprehensive set of parameters to quantify tree-likeness in networks and demonstrates their practical use in large-scale network analysis.

Findings

Networks from diverse domains are metrically close to trees.

Tree-like structures enable efficient encoding of distances and paths.

Methods improve estimation of network diameters and radii.

Abstract

Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit tree-like structures from a metric point of view. We investigate few graph parameters, namely, the tree-distortion and the tree-stretch, the tree-length and the tree-breadth, the Gromov's hyperbolicity, the cluster-diameter and the cluster-radius in a layering partition of a graph, which capture and quantify this phenomenon of being metrically close to a tree. By bringing all those parameters together, we not only provide efficient means for detecting such metric tree-like structures in large-scale networks but also show how such structures can be used, for example, to efficiently and compactly encode approximate distance and almost shortest path information and to fast and accurately estimate diameters and radii of those networks. Estimating the diameter and the radius of a graph or distances between its arbitrary vertices are fundamental primitives in many data and graph mining algorithms.