On the Tomography of Networks and Multicast Trees

TL;DR

This paper analyzes the layered structure of scale-free networks and multicast trees, revealing two regimes in node distance distribution and power-law degree distributions with exponential cut-offs, supported by analytical and empirical data.

Contribution

It provides a combined analytical and empirical study of network tomography, uncovering the layered structure and degree distribution characteristics of scale-free networks and multicast trees.

Findings

Distance distribution has two regimes: rapid growth and exponential decay.

Node degree distribution at each layer follows a power law with an exponential cut-off.

Results are validated both analytically and with Internet data.

Abstract

In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show that the nodes degree distribution at each layer is a power law with an exponential cut-off. We obtain similar results for the layers surrounding the root of multicast trees cut from such networks, as well as the Internet. All of our results were obtained both analytically and on empirical Interenet data.