Multiresolution community detection for megascale networks by information-based replica correlations

Peter Ronhovde and Zohar Nussinov
Phys. Rev. E 80, 016109 – Published 14 July 2009

Abstract

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies (“replicas”) of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation in information, and other measures, in principle, give a quantitative estimate of the “best” resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can, in principle, be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the “resolution limit” that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40×106 nodes and more than 1×109 edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10×106 edges on a single processor with exceptionally high accuracy. For typical cases, we find a superlinear scaling O(L1.3) for community detection and O(L1.3logN) for the multiresolution algorithm, where L is the number of edges and N is the number of nodes in the system.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
7 More
  • Received 22 December 2008

DOI:https://doi.org/10.1103/PhysRevE.80.016109

©2009 American Physical Society

Authors & Affiliations

Peter Ronhovde and Zohar Nussinov

  • Department of Physics, Washington University in St. Louis, Campus Box 1105, 1 Brookings Drive, St. Louis, Missouri 63130, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 80, Iss. 1 — July 2009

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
×