Organization of modular networks

S. N. Dorogovtsev, J. F. F. Mendes, A. N. Samukhin, and A. Y. Zyuzin
Phys. Rev. E 78, 056106 – Published 14 November 2008

Abstract

We examine the global organization of heterogeneous equilibrium networks consisting of a number of well-distinguished interconnected parts—“communities” or modules. We develop an analytical approach allowing us to obtain the statistics of connected components and the intervertex distance distribution in these modular networks, and to describe their global organization and structure. In particular, we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks. We demonstrate that even a relatively small number of shortcuts unite the networks into one. In more precise terms, if the number of interlinks is any finite fraction of the total number of connections, then the intervertex distance distribution approaches a δ-function peaked form, and so the network is united.

  • Figure
  • Figure
  • Figure
  • Received 24 March 2008

DOI:https://doi.org/10.1103/PhysRevE.78.056106

©2008 American Physical Society

Authors & Affiliations

S. N. Dorogovtsev1,2,*, J. F. F. Mendes1,†, A. N. Samukhin1,2,‡, and A. Y. Zyuzin2,§

  • 1Departamento de Física da Universidade de Aveiro, 3810-193 Aveiro, Portugal
  • 2A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia

  • *sdorogov@ua.pt
  • jfmendes@ua.pt
  • samukhin@ua.pt
  • §A.Zyuzin@mail.ioffe.ru

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 78, Iss. 5 — November 2008

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
×