Dynamic Exploration of Networks: from general principles to the traceroute process

TL;DR

This paper develops a mean-field theory to understand how exploration processes like traceroute reveal the evolving topology of large networks such as the Internet, highlighting the interplay between dynamics and structure.

Contribution

It introduces a general theoretical framework for analyzing dynamical exploration processes on networks, specifically focusing on tree-like sampling methods like traceroute.

Findings

Provides a mean-field model for network exploration dynamics

Improves understanding of sampling effects on observed network topology

Applies theory to traceroute, revealing insights into Internet topology

Abstract

Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on a class of tree-like processes, such as those used to explore the Internet's topology. A general theory based on mean-field arguments is proposed, both for single-source and multiple-source cases, and applied to the specific example of the traceroute exploration of networks. Our results provide a qualitative improvement in the understanding of dynamical sampling and of the interplay between dynamics and topology in large networks like the Internet.