Journal Article

A network complexity metric based on planarity and community structure

Douglas Rigterink and David J. Singer

in Journal of Complex Networks

Volume 2, issue 3, pages 299-312
Published in print September 2014 | ISSN: 2051-1310
Published online February 2014 | e-ISSN: 2051-1329 | DOI: https://dx.doi.org/10.1093/comnet/cnu005
A network complexity metric based on planarity and community structure

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This article proposes a network complexity metric based on the concepts of planarity and network communities. This work considers planarity as an analogue for network complexity. It compares the number of network communities that contain non-planar subgraph expansions with the total number of network communities, and considers the networks with less non-planar communities to be less complex. The metric is then used to analyse four networks, three representing real systems and one representing a more abstract system. Finally, the metric itself is analysed according to nine criteria for judging the effectiveness of a complexity metric. Using the network analyses and the effectiveness criteria, this metric is shown to be fast, versatile and effective and to fill a current gap in network tools for assessing the degree of planarity of a system.

Keywords: network complexity; planarity; real networks

Journal Article.  5767 words.  Illustrated.

Subjects: Mathematics ; Computer Science

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