Distance-based accessibility indices

TL;DR

This paper develops a new family of accessibility indices for networks, generalizing the distance sum measure by incorporating additional factors and a tunable parameter to better reflect network vulnerability.

Contribution

It introduces the generalized distance sum, a novel accessibility index that considers node accessibility beyond distances and allows parameter tuning for different applications.

Findings

Generalized distance sum can reflect network vulnerability to link disruptions.

It maintains anonymity and dominance preservation under certain conditions.

The measure offers a flexible tool for assessing network accessibility.

Abstract

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at least as accessible. We argue for the need of eliminating the independence property in certain applications. Therefore generalized distance sum, a family of accessibility indices, will be suggested. It is linear, considers the accessibility of vertices besides their distances and depends on a parameter in order to control its deviation from distance sum. Generalized distance sum is anonymous and satisfies dominance preservation if its parameter meets a sufficient condition. Two detailed examples demonstrate its ability to reflect the vulnerability of accessibility to link disruptions.