skip to main content
10.1145/2492517.2492650acmconferencesArticle/Chapter ViewAbstractPublication PageskddConference Proceedingsconference-collections
research-article

The power of consensus: random graphs have no communities

Published: 25 August 2013 Publication History

Abstract

Communities are a powerful tool to describe the structure of complex networks. Algorithms aiming at maximizing a quality function called modularity have been shown to effectively compute the community structure. However, some problems remain: in particular, it is possible to find high modularity partitions in graph without any community structure, in particular random graphs. In this paper, we study the notion of consensual communities and show that they do not exist in random graphs. For that, we exhibit a phase transition based on the strength of consensus: below a given threshold, all the nodes belongs to the same consensual community; above this threshold, each node is in its own consensual community.

References

[1]
M. Girvan and M. Newman, "Community structure in social and biological networks," Proc. of the National Academy of Sciences, vol. 99, no. 12, 2002.
[2]
C. Senshadhri, T. G. Kolda, and A. Pinar, "Community structure and scale-free collections of Erdős-Rényi graphs," Physical Review E, vol. 85, no. 056109, 2012.
[3]
S. Fortunato, "Community detection in graphs," Physics Reports, vol. 486, no. 3--5, pp. 75--174, 2010.
[4]
M. Newman and M. Girvan, "Finding and evaluating community structure in networks," Physical Review E, vol. 69, no. 2, 2004.
[5]
U. Brandes, D. Delling, M. Gaertler, R. Gorke, M. Hoefer, Z. Nikoloski, and D. Wagner, "On finding graph clusterings with maximum modularity," in Graph-Theoretic Concepts in Computer Science, 2007.
[6]
R. Guimerà, M. Sales-Pardo, and L. A. N. Amaral, "Modularity from fluctations in random graphs and complex networks," Physical Review E, vol. 70, no. 2, 2004.
[7]
E. Diday, "The dynamic clusters method and optimization in non-hierarchical clustering," Optimization Techniques, pp. 241--258, 1973.
[8]
M. Seifi, J.-L. Guillaume, I. Junier, J.-B. Rouquier, and S. Iskrov, "Stable community cores in complex networks," in 3rd Int. Workshop on Complex Networks, Melbourne, Florida, 2012.
[9]
Q. Wang and E. Fleury, "Uncovering overlapping community structure," in 2nd Int. Workshop on Complex Networks, 2010, pp. 176--186.
[10]
A. Lancichinetti and S. Fortunato, "Consensus clustering in complex networks," Scientific Reports, vol. 2, no. 336, 2012.
[11]
B. Karrer, E. Levina, and M. Newman, "Robustness of community structure in networks," Physical Review E, vol. 77, no. 4, 2008.
[12]
M. Rosvall and C. Bergstrom, "Mapping change in large networks," PloS one, vol. 5, no. 1, 2010.
[13]
D. Gfeller, J. Chappelier, and P. De Los Rios, "Finding instabilities in the community structure of complex networks," Physical Review E, vol. 72, no. 5, 2005.
[14]
V. Blondel, J.-L. Guillaume, R. Lambiotte, and E. Lefebvre, "Fast unfolding of communities in large networks," Journal of Statistical Mechanics: Theory and Experiment, 2008.
[15]
M. Newman, "The structure of scientific collaboration networks," Proc. of the National Academy of Sciences, vol. 98, no. 2, 2001.
[16]
R. Guimera, L. Danon, A. Diaz-Guilera, F. Giralt, and A. Arenas, "Self-similar community structure in a network of human interactions," Physical Review E, vol. 68, no. 6, 2003.
[17]
J. Reichardt and S. Bornholdt, "Statistical mechanics of community detection," Physical Review E, vol. 74, no. 1, 2006.
[18]
F. de Montgolfier, M. Soto, and L. Viennot, "Asymptotic modularity of some graph classes," in ISAAC, 2011, pp. 435--444.
[19]
P. Erdős and A. Rényi, "On random graphs," Publicationes Mathematicae, vol. 6, pp. 290--297, 1959.
[20]
E. A. Bender and E. R. Canfield, "The asymptotic number of labeled graphs with given degree sequences," Journal of Combinatorial Theory A, vol. 24, pp. 296--307, 1978.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
ASONAM '13: Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
August 2013
1558 pages
ISBN:9781450322409
DOI:10.1145/2492517
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 August 2013

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Research-article

Conference

ASONAM '13
Sponsor:
ASONAM '13: Advances in Social Networks Analysis and Mining 2013
August 25 - 28, 2013
Ontario, Niagara, Canada

Acceptance Rates

Overall Acceptance Rate 116 of 549 submissions, 21%

Upcoming Conference

KDD '25

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)9
  • Downloads (Last 6 weeks)1
Reflects downloads up to 14 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2025)Insights into the Structured Coordination Game with Neutral Options Through SimulationDynamic Games and Applications10.1007/s13235-024-00612-4Online publication date: 11-Jan-2025
  • (2023)On Filtering the Noise in Consensual CommunitiesComputational Science – ICCS 202310.1007/978-3-031-36027-5_52(655-670)Online publication date: 26-Jun-2023
  • (2018)Multiresolution Consensus Clustering in NetworksScientific Reports10.1038/s41598-018-21352-78:1Online publication date: 19-Feb-2018
  • (2015)From Local to Global Communities in Large Networks Through ConsensusProgress in Pattern Recognition, Image Analysis, Computer Vision, and Applications10.1007/978-3-319-25751-8_79(659-666)Online publication date: 25-Oct-2015
  • (2015)The Power of Consensus: Random Graphs Still Have No CommunitiesSocial Network Analysis - Community Detection and Evolution10.1007/978-3-319-12188-8_7(145-164)Online publication date: 14-Jan-2015
  • (2014)All for one, one for all: Consensus community detection in networks2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)10.1109/ICASSP.2014.6853762(1075-1079)Online publication date: May-2014

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media