Node Accessibility Characterization of Radially-Grown Structures

TL;DR

This paper investigates the topological accessibility of radially-grown structures modeled as graphs, revealing how growth orientation influences node accessibility, with implications for understanding complex systems like urban expansion and particle deposition.

Contribution

It introduces a novel approach to characterize the accessibility of nodes in radially-grown structures, considering preferential growth orientations and their effects on topology.

Findings

Structures grown orthogonal to the axis tend to have higher accessibility.

Preferential angular growth influences the topological properties of the structure.

The method provides insights into the dynamics of complex, radially expanding systems.

Abstract

Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties change along time, as new elements are incorporated into the existing structure. In the present work, an approach is the case in which systems grown radially around some straight axis of reference, such as particle deposition on electrodes, or urban expansion along avenues, roads, coastline, or rivers, among several other possibilities. More specifically, we aim at characterizing the topological properties of simulated growing structures, which are represented as graphs, in terms of a measurement corresponding to the accessibility of each involved node. The incorporation of new elements (nodes and links) is performed preferentially to the angular orientation respectively to the reference axis. Several interesting results are reported, including the tendency of structures grown preferentially to the orientation normal to the axis to have smaller accessibility.