Fingerprint for Network Topologies

TL;DR

This paper introduces a novel visualization called BOSAM for network topologies, revealing self-similar patterns that enable network reconstruction and are analogous to human fingerprints in their uniqueness and simplicity.

Contribution

The paper mathematically proves the self-similar property of BOSAM envelopes, enabling network topology reconstruction from a single envelope, and draws an analogy between BOSAM and human fingerprints.

Findings

BOSAM visualizations exhibit self-similarity in network topologies.

A single BOSAM envelope can predict all other envelopes.

BOSAM shares key features with human fingerprints for network identification.

Abstract

A network's topology information can be given as an adjacency matrix. The bitmap of sorted adjacency matrix(BOSAM) is a network visualisation tool which can emphasise different network structures by just looking at reordered adjacent matrixes. A BOSAM picture resembles the shape of a flower and is characterised by a series of 'leaves'. Here we show and mathematically prove that for most networks, there is a self-similar relation between the envelope of the BOSAM leaves. This self-similar property allows us to use a single envelope to predict all other envelopes and therefore reconstruct the outline of a network's BOSAM picture. We analogise the BOSAM envelope to human's fingerprint as they share a number of common features, e.g. both are simple, easy to obtain, and strongly characteristic encoding essential information for identification.