Social climber attachment in forming networks produces a phase transition in a measure of connectivity

Dane Taylor and Daniel B. Larremore
Phys. Rev. E 86, 031140 – Published 26 September 2012


The formation and fragmentation of networks are typically studied using percolation theory, but most previous research has been restricted to studying a phase transition in cluster size, examining the emergence of a giant component. This approach does not study the effects of evolving network structure on dynamics that occur at the nodes, such as the synchronization of oscillators and the spread of information, epidemics, and neuronal excitations. We introduce and analyze an alternative link-formation rule, called social climber (SC) attachment, that may be combined with arbitrary percolation models to produce a phase transition using the largest eigenvalue of the network adjacency matrix as the order parameter. This eigenvalue is significant in the analyses of many network-coupled dynamical systems in which it measures the quality of global coupling and is hence a natural measure of connectivity. We highlight the important self-organized properties of SC attachment and discuss implications for controlling dynamics on networks.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 16 May 2012


©2012 American Physical Society

Authors & Affiliations

Dane Taylor1,*,† and Daniel B. Larremore1,2,*,‡

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Department of Epidemiology, Center for Communicable Disease Dynamics, Harvard School of Public Health, Boston, Massachusetts 02115, USA

  • *These authors contributed equally.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Vol. 86, Iss. 3 — September 2012

Reuse & Permissions
Access Options

Article Available via CHORUS

Download Accepted Manuscript
Physical Review E Scope Description to Include Biological Physics
January 14, 2016

The editors of Physical Review E are pleased to announce that the journal’s stated scope has been expanded to explicitly include the term “Biological Physics.”

Authorization Required




Sign up to receive regular email alerts from Physical Review E

Log In



Article Lookup

Paste a citation or DOI

Enter a citation