Print Email Facebook Twitter Degree distribution and assortativity in line graphs of complex networks Title Degree distribution and assortativity in line graphs of complex networks Author Wang, X. Trajanovski, S. Kooij, R.E. van Mieghem, P. Publication year 2016 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 Erdos-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. Erdos-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. © 2015 Elsevier B.V. All rights reserved. Subject AssortativityComplex networkDegree distributionLine graphComplex networksForestryGraphic methodsTrees (mathematics)AssortativityCascading failuresDegree distributionsDynamical processEpidemic spreadLine graphScale free graphTopological characteristicsGraph theory To reference this document use: http://resolver.tudelft.nl/uuid:65b8157b-f3bd-4177-93c2-272ba75640b8 DOI https://doi.org/10.1016/j.physa.2015.10.109 TNO identifier 530921 Publisher Elsevier ISSN 0378-4371 Source Physica A: Statistical Mechanics and its Applications, 445, 343-356 Document type article Files To receive the publication files, please send an e-mail request to TNO Library.