Navigability is a Robust Property

TL;DR

This paper demonstrates that navigability is an inherent property of many random networks, emerging naturally without coordination or independence assumptions, extending Kleinberg's RBA model.

Contribution

It proves that navigability arises inherently in many random networks without the need for explicit coordination or independence assumptions.

Findings

Navigability is an inherent property of many random networks.

It occurs without coordination or independence assumptions.

Supports Kleinberg's RBA model as a natural phenomenon.

Abstract

The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random destination selected from a carefully crafted probability distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it allows greedy routing to successfully deliver messages between any two vertices in a polylogarithmic number of steps. We prove that navigability is an inherent property of many random networks, arising without coordination, or even independence assumptions.