Micro-, meso-, macroscales: The effect of triangles on communities in networks

Sophie Wharrie, Lamiae Azizi, and Eduardo G. Altmann
Phys. Rev. E 100, 022315 – Published 21 August 2019

Abstract

Mesoscale structures (communities) are used to understand the macroscale properties of complex networks, such as their functionality and formation mechanisms. Microscale structures are known to exist in most complex networks (e.g., large number of triangles or motifs), but they are absent in the simple random-graph models considered (e.g., as null models) in community-detection algorithms. In this paper we investigate the effect of microstructures on the appearance of communities in networks. We find that alone the presence of triangles leads to the appearance of communities even in methods designed to avoid the detection of communities in random networks. This shows that communities can emerge spontaneously from simple processes of motiff generation happening at a microlevel. Our results are based on four widely used community-detection approaches (stochastic block model, spectral method, modularity maximization, and the Infomap algorithm) and three different generative network models (triadic closure, generalized configuration model, and random graphs with triangles).

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 22 April 2019

DOI:https://doi.org/10.1103/PhysRevE.100.022315

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsInterdisciplinary PhysicsNetworks

Authors & Affiliations

Sophie Wharrie, Lamiae Azizi, and Eduardo G. Altmann

  • School of Mathematics and Statistics, University of Sydney, 2006 NSW, Australia

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 100, Iss. 2 — August 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×