Striations in PageRank-Ordered Matrices

TL;DR

This paper uncovers a new striation pattern in PageRank-ordered adjacency matrices of real-world networks, linking it to known graph generation processes and revealing insights into network topology and anomalies.

Contribution

It identifies and explains a novel regular striation pattern in PageRank-ordered matrices, connecting it to underlying graph generation mechanisms.

Findings

Striation patterns are linked to specific graph generation processes.

Re-ordered matrices reveal network properties and anomalies.

Spectral analysis encodes extensive topological information.

Abstract

Patterns often appear in a variety of large, real-world networks, and interesting physical phenomena are often explained by network topology as in the case of the bow-tie structure of the World Wide Web, or the small world phenomenon in social networks. The discovery and modelling of such regular patterns has a wide application from disease propagation to financial markets. In this work we describe a newly discovered regularly occurring striation pattern found in the PageRank ordering of adjacency matrices that encode real-world networks. We demonstrate that these striations are the result of well-known graph generation processes resulting in regularities that are manifest in the typical neighborhood distribution. The spectral view explored in this paper encodes a tremendous amount about the explicit and implicit topology of a given network, so we also discuss the interesting network properties, outliers and anomalies that a viewer can determine from a brief look at the re-ordered matrix.