Theoretical results on the topological properties of the limited penetrable horizontal visibility graph family

TL;DR

This paper extends the limited penetrable horizontal visibility graph algorithm to directed and image variants, providing theoretical insights into their topological properties and demonstrating their effectiveness in analyzing real-valued time series and matrices.

Contribution

It introduces new directed and image versions of the limited penetrable horizontal visibility graph with theoretical topological analysis and practical applications.

Findings

Theoretical topological properties are established for the new graph variants.

Numerical simulations confirm the accuracy of the theoretical results.

Applications successfully discriminate noise from chaos and measure time series irreversibility.

Abstract

The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. We extend this visibility graph and create a directed limited penetrable horizontal visibility graph and an image limited penetrable horizontal visibility graph. We define the two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series (or matrices). We perform several numerical simulations to further check the accuracy of our theoretical results. Finally we present an application of the directed limited penetrable horizontal visibility graph for measuring real-value time series irreversibility, and an application of the image limited penetrable horizontal visibility graph that discriminates noise from chaos. The empirical results show the effectiveness of our proposed algorithms.