Degree distribution and assortativity in line graphs of complex networks

Journal article (2016)

Authors

X. Wang Network Architectures and Services - EEMCS
S. Trajanovski Network Architectures and Services - EEMCS
Robert Kooij TNO, Network Architectures and Services - EEMCS
P.F.A. Van Mieghem Network Architectures and Services - EEMCS
Research Group
Network Architectures and Services (EEMCS) (TU Delft)
More Info
expand_more

Published Date

2016

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

Abstract

Topological characteristics of links of complex networks influence the dynamical processes executed on networks triggered by links, such as cascading failures triggered by links in power grids and epidemic spread due to link infection. The line graph transforms links in the original graph into nodes. In this paper, we investigate how graph metrics in the original graph are mapped into those for its line graph. In particular, we study the degree distribution and the assortativity of a graph and its line graph. Specifically, we show, both analytically and numerically, the degree distribution of the line graph of an Erdős–Rényi graph follows the same distribution as its original graph. We derive a formula for the assortativity of line graphs and indicate that the assortativity of a line graph is not linearly related to its original graph. Additionally, line graphs of various graphs, e.g. Erdős–Rényi graphs, scale-free graphs, show positive assortativity. In contrast, we find certain types of trees and non-trees whose line graphs have negative assortativity.