Randomness criteria in binary visibility graph perspective

TL;DR

This paper introduces a new method using binary visibility graphs to analyze the randomness of binary sequences by examining their topological properties, providing a novel criterion for randomness detection.

Contribution

It proposes, for the first time, three topological properties of binary visibility graphs as criteria for assessing randomness in binary sequences.

Findings

Topological properties accurately characterize randomness.

Numerical simulations confirm theoretical theorems.

New criteria effectively distinguish random sequences.

Abstract

By means of a binary visibility graph, we present a novel method to study random binary sequences. The behavior of the some topological properties of the binary visibility graph, such as the degree distribution, the clustering coefficient, and the mean path length have been investigated. Several examples are then provided to show that the numerical simulations confirm the accuracy of the theorems for finite random binary sequences. Finally, in this paper we propose, for the first time, three topological properties of the binary visibility graph as a randomness criteria.