Exploring Complex Graphs by Random Walks

TL;DR

This paper introduces an algorithm for generating scale-free web-like graphs and explores their properties using random walks, including parallel interacting walks, to analyze navigation efficiency and topological features.

Contribution

It presents a novel graph growth algorithm and investigates navigation dynamics with both independent and interacting random walks on complex networks.

Findings

Betweenness and other topological properties are characterized by multiple walkers.

Navigation efficiency varies across different graph topologies.

Interacting random walks simulate information packet transport with queueing effects.

Abstract

We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local next-near-neighbor search algorithm to navigate through the graph. The topological properties such as betweenness are determined by an ensemble of independent walkers and efficiency of the search is compared on three different graph topologies. In addition we simulate interacting random walks which are created by given rate and navigated in parallel, representing transport with queueing of information packets on the graph.