Characterizing network topology using first-passage analysis

TL;DR

This paper uses first-passage analysis to study how different network topologies affect the movement and navigability of random walkers, revealing key differences among various network types.

Contribution

It introduces a novel application of First Passage analysis to characterize complex network topologies and their navigability features.

Findings

Random networks differ from scale-free networks in navigability.

Small world features can be identified using the proposed method.

First Passage Time and Simultaneity effectively differentiate network types.

Abstract

Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social systems. Here, we apply First Passage analysis tools to investigate the properties and characteristics of random walkers in networks with different topology. Starting with the simplest two-dimensional square lattice, we modify its topology incrementally by randomly reconnecting links between sites. We characterize these networks by First Passage Time from a significant number of random walkers without interaction, varying the departure and arrival locations. We also apply the concept of First Passage Simultaneity, which measures the likelihood of two walkers reaching their destination together. These measures, together with the site occupancy statistics during the processes, allowed to differentiate the studied networks, especially the random networks from the scale-free networks, by their navigability. We also show that small world features can also be highlighted with the proposed technique.