The Degree Distribution of Random k-Trees

TL;DR

This paper proves that a specific random graph model based on k-trees exhibits a power law degree distribution, highlighting limitations of using degree distribution alone to characterize complex networks.

Contribution

It introduces a k-tree-based graph evolution model that captures features of preferential attachment and copying mechanisms, providing a rigorous proof of power law distribution.

Findings

Power law degree distribution established for the k-tree model

Model captures characteristics of preferential attachment and copying

Highlights that degree distribution alone is insufficient to characterize networks

Abstract

A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential attachment and copying mechanisms that existing evolving graph processes fail to model due to technical obstacles. The result also serves as a further cautionary note reinforcing the point of view that a power law degree distribution should not be regarded as the only important characteristic of a complex network, as has been previously argued.