Accessibility: A Generalization of the Node Degree (A Tutorial)

TL;DR

This paper introduces the concept of accessibility as a generalization of node degree, incorporating network dynamics and neighborhoods, and demonstrates its effectiveness in characterizing various complex networks.

Contribution

It presents the accessibility measure, extending node degree to include dynamics and neighborhoods, with examples and a toolbox for large networks.

Findings

Accessibility complements traditional topological measurements.

Effective in analyzing Erdos-Renyi, Watts-Strogatz, Barabasi-Albert, and Geometric networks.

Provides a practical toolbox for large network analysis.

Abstract

Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an introduction to one of these measurements, namely the accessibility of a node, which can be understood as a generalization of the concept of node degree not only to incorporate successive neighborhoods of that node, but also to reflect specific types of dynamics unfolding in the network. After discussing the node degree and its hierarchical extension, we present the concepts of random walk, entropy, and then the accessibility. Several examples of its numeric calculation are provided, as well as some experimental results indicating that it can effectively complement the information provided by other topological measurements of four types of complex networks, namely Erdos-Renyi, Watts-Strogatz, Barabasi-Albert, and Geometric. We also describe how a recently developed toolbox can be used for the calculation of accessibility in relatively large networks.