Exponential random graph models for networks with community structure

Piotr Fronczak , Agata Fronczak , Maksymilian Bujok

Abstract

Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field. © 2013 American Physical Society.
Author Piotr Fronczak (FP / PCSD)
Piotr Fronczak,,
- Physics of Complex Systems Divison
, Agata Fronczak (FP / PCSD)
Agata Fronczak,,
- Physics of Complex Systems Divison
, Maksymilian Bujok (FP / PCSD)
Maksymilian Bujok,,
- Physics of Complex Systems Divison
Journal seriesPhysical Review E, ISSN 1539-3755
Issue year2013
Vol88
No3
Pages032810
ASJC Classification3104 Condensed Matter Physics; 2613 Statistics and Probability; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1103/PhysRevE.88.032810
URL http://www.scopus.com/inward/record.url?eid=2-s2.0-84885129223&partnerID=40&md5=109e2691c15447695d853eb381facc52
LanguageEnglish
Score (nominal)35
Score sourcejournalList
ScoreMinisterial score = 35.0, 10-06-2020, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 10-06-2020, ArticleFromJournal
Publication indicators Scopus Citations = 13; WoS Citations = 9; Scopus SNIP (Source Normalised Impact per Paper): 2014 = 1.123; WoS Impact Factor: 2013 = 2.326 (2) - 2013=2.302 (5)
Citation count*4 (2015-07-21)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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