Long-range connections, real-world networks and rates of diffusion

TL;DR

This paper reviews the role of long-range connections in real-world networks, focusing on how different distance-dependent laws like exponential and power laws influence nonlocal diffusion processes across various systems.

Contribution

It provides a comprehensive review of evidence for long-range connections and analyzes the effects of different decay laws on diffusion in networks.

Findings

Long-range connections significantly affect network dynamics.

Power law and exponential decay laws lead to different diffusion behaviors.

Empirical evidence supports the prevalence of long-range links in real-world networks.

Abstract

Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics. Here we review the evidence for long range connections in real world networks and discuss the nature of the nonlocal diffusion arising from different distance-dependent laws. Particular attention is devoted to exponential and power laws.