research-article

Measuring the mixing time of social graphs

Authors:

Abedelaziz Mohaisen,

Yongdae KimAuthors Info & Claims

IMC '10: Proceedings of the 10th ACM SIGCOMM conference on Internet measurement

Pages 383 - 389

https://doi.org/10.1145/1879141.1879191

Published: 01 November 2010 Publication History

Abstract

Social networks provide interesting algorithmic properties that can be used to bootstrap the security of distributed systems. For example, it is widely believed that social networks are fast mixing, and many recently proposed designs of such systems make crucial use of this property. However, whether real-world social networks are really fast mixing is not verified before, and this could potentially affect the performance of such systems based on the fast mixing property. To address this problem, we measure the mixing time of several social graphs, the time that it takes a random walk on the graph to approach the stationary distribution of that graph, using two techniques. First, we use the second largest eigenvalue modulus which bounds the mixing time. Second, we sample initial distributions and compute the random walk length required to achieve probability distributions close to the stationary distribution. Our findings show that the mixing time of social graphs is much larger than anticipated, and being used in literature, and this implies that either the current security systems based on fast mixing have weaker utility guarantees or have to be less efficient, with less security guarantees, in order to compensate for the slower mixing.

References

[1]

L. Bilge, T. Strufe, D. Balzarotti, and E. Kirda. All your contacts are belong to us: automated identity theft attacks on social networks. In WWW '09: Proceedings of the 18th international conference on World wide web, pages 551--560, New York, NY, USA, 2009. ACM.

Digital Library

[2]

E. M. Daly and M. Haahr. Social network analysis for routing in disconnected delay-tolerant manets. In MobiHoc'07: Proceedings of the 8th ACM international symposium on Mobile ad hoc networking and computing, pages 32--40, New York, NY, USA, 2007. ACM.

Digital Library

[3]

G. Danezis and P. Mittal. SybilInfer: Detecting sybil nodes using social networks. In The 16th Annual Network & Distributed System Security Conference, 2009.

[4]

J. R. Douceur. The sybil attack. In IPTPS '01: Revised Papers from the First International Workshop on Peer-to-Peer Systems, pages 251--260, London, UK, 2002. Springer-Verlag.

Digital Library

[5]

C. Dwyer, S. Hiltz, and K. Passerini. Trust and privacy concern within social networking sites: A comparison of Facebook and MySpace. In Proceedings of AMCIS, 2007.

[6]

M. Jerrum and A. Sinclair. Conductance and the rapid mixing property for markov chains: the approximation of the permanent resolved (preliminary version). In STOC, pages 235--244. ACM, 1988.

Digital Library

[7]

H. A. Kautz, B. Selman, and M. A. Shah. Referral web: Combining social networks and collaborative filtering. Commun. ACM, 40(3):63--65, 1997.

Digital Library

[8]

J. Leskovec, D. P. Huttenlocher, and J. M. Kleinberg. Predicting positive and negative links in online social networks. In M. Rappa, P. Jones, J. Freire, and S. Chakrabarti, editors, WWW, pages 641--650. ACM, 2010.

Digital Library

[9]

J. Leskovec, J. Kleinberg, and C. Faloutsos. Graphs over time: densification laws, shrinking diameters and possible explanations. In KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining, pages 177--187, New York, NY, USA, 2005. ACM.

Digital Library

[10]

J. Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney. Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. CoRR,abs/0810.1355, 2008.

[11]

C. Lesniewski-Laas. A Sybil-proof one-hop DHT. In Proceedings of the 1st workshop on Social network systems, pages 19--24. ACM, 2008.

Digital Library

[12]

C. Lesniewski-Lass and M. F. Kaashoek. Whanau: A sybil-proof distributed hash table. In 7th USENIX Symposium on Network Design and Implementation, pages 3--17, 2010.

Digital Library

[13]

M. Ley. The DBLP computer science bibliography: Evolution, research issues, perspectives. In String Processing and Information Retrieval, pages 481--486. Springer, 2009.

Digital Library

[14]

A. Mislove, M. Marcon, P. K. Gummadi, P. Druschel, and B. Bhattacharjee. Measurement and analysis of online social networks. In Internet Measurement Comference, pages 29--42, 2007.

Digital Library

[15]

A. Mohaisen, N. Hopper, and Y. Kim. Designs to account for trust in social network-based sybil defenses. In 17th ACM Conference on Computer and Communications Security, Chicago, IL, USA, 2010. ACM.

Digital Library

[16]

A. Mohaisen, N. Hopper, and Y. Kim. Keep your friends close: Incorporating trust in social network-based Sybil defenses. Technical report, University of Minnesota, 2010.

[17]

A. Mohaisen, A. Yun, and Y. Kim. Measuring the mixing time of social graphs. Technical report, University of Minnesota, 2010.

[18]

S. Nagaraja. Anonymity in the wild: Mixes on unstructured networks. In N. Borisov and P. Golle, editors, Privacy Enhancing Technologies, volume 4776 of Lecture Notes in Computer Science, pages 254--271. Springer, 2007.

Digital Library

[19]

D. Quercia and S. Hailes. Sybil attacks against mobile users: friends and foes to the rescue. In INFOCOM'10: Proceedings of the 29th conference on Information communications, pages 336--340, Piscataway, NJ, USA, 2010. IEEE Press.

Digital Library

[20]

M. Richardson, R. Agrawal, and P. Domingos. Trust management for the semantic web. In D. Fensel, K. P. Sycara, and J. Mylopoulos, editors, International Semantic Web Conference, volume 2870 of Lecture Notes in Computer Science, pages 351--368. Springer, 2003.

[21]

A. Sinclair. Improved bounds for mixing rates of markov chains and multicommodity flow. Combinatorics, Probability & Computing, 1:351--370, 1992.

[22]

N. Tran, J. Li, L. Subramanian, and S. S. M. Chow. Brief announcement: improving social-network-based Sybil-resilient node admission control. In A. W. Richa and R. Guerraoui, editors, PODC, pages 241--242. ACM, 2010.

Digital Library

[23]

N. Tran, B. Min, J. Li, and L. Subramanian. Sybil-resilient online content voting. In USENIX NSDI, 2009.

Digital Library

[24]

E. Vasserman. Towards freedom of speech on the Internet: Censorship-resistant communication and storage. PhD thesis, UNIVERSITY OF MINNESOTA, 2010.

Digital Library

[25]

E. Vasserman, R. Jansen, J. Tyra, N. Hopper, and Y. Kim. Membership-concealing overlay networks. In Proceedings of the 16th ACM conference on Computer and communications security, pages 390--399. ACM, 2009.

Digital Library

[26]

B. Viswanath, A. Mislove, M. Cha, and K. P. Gummadi. On the evolution of user interaction in facebook. In Proceedings of the 2nd ACM SIGCOMM Workshop on Social Networks (WOSN'09), August 2009.

Digital Library

[27]

B. Viswanath, A. Post, K. P. Gummadi, and A. Mislove. An analysis of social network-based sybil defenses. In SIGCOMM, 2010.

Digital Library

[28]

C. Wilson, B. Boe, A. Sala, K. P. Puttaswamy, and B. Y. Zhao. User interactions in social networks and their implications. In EuroSys '09: Proceedings of the 4th ACM European conference on Computer systems, pages 205--218, New York, NY, USA, 2009. ACM.

Digital Library

[29]

S. Xu, X. Li, and P. Parker. Exploiting social networks for threshold signing: attack-resilience vs. availability. In ASIACCS '08: Proceedings of the 2008 ACM symposium on Information, computer and communications security, pages 325--336, New York, NY, USA, 2008. ACM.

Digital Library

[30]

H. Yu, P. B. Gibbons, M. Kaminsky, and F. Xiao. SybilLimit: A near-optimal social network defense against sybil attacks. In IEEE Symposium on Security and Privacy, pages 3--17, 2008.

Digital Library

[31]

H. Yu, M. Kaminsky, P. B. Gibbons, and A. Flaxman. SybilGuard: defending against sybil attacks via social networks. In SIGCOMM, pages 267--278, 2006.

Digital Library

[32]

H. Yu, M. Kaminsky, P. B. Gibbons, and A. D. Flaxman. SybilGuard: defending against sybil attacks via social networks. IEEE/ACM Trans. Netw., 16(3):576--589, 2008.

Digital Library

Cited By

Kasana SSharma MGupta S(2025)A Systematic Security Analysis of Existing Sybil Attack-Resilient Defensive Methodologies in Blockchain NetworkConvergence of Cybersecurity and Cloud Computing10.4018/979-8-3693-6859-6.ch009(191-224)Online publication date: 10-Jan-2025
https://doi.org/10.4018/979-8-3693-6859-6.ch009
Liao MZhou JLi RDai QChen HWang G(2024)Efficient and Provable Effective Resistance Computation on Large Graphs: An Index-based ApproachProceedings of the ACM on Management of Data10.1145/36549362:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654936
Peng JLei RWei ZSerra ESpezzano F(2024)Beyond Over-smoothing: Uncovering the Trainability Challenges in Deep Graph Neural NetworksProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679776(1878-1887)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1145/3627673.3679776
Show More Cited By

Index Terms

Measuring the mixing time of social graphs
1. General and reference
  1. Cross-computing tools and techniques
    1. Measurement
    2. Metrics

Recommendations

Understanding Social Networks Properties for Trustworthy Computing
ICDCSW '11: Proceedings of the 2011 31st International Conference on Distributed Computing Systems Workshops

The ever-increasing popularity of social networks opens new directions for leveraging social networks to build primitives for security and communication, in many contexts. Such primitives utilize the trust in these social networks to ensure ...
Improving Social Network-Based Sybil Defenses by Rewiring and Augmenting Social Graphs
WISA 2013: Revised Selected Papers of the 14th International Workshop on Information Security Applications - Volume 8267

Recent solutions to defend against the Sybil attack, in which a node generates multiple identities, using social networks. In these solutions, social networks are assumed to be fast mixing, and Sybil nodes–which disrupt the fast mixing property of social ...
On the mixing time of geographical threshold graphs

We study the mixing time of random graphs in the d-dimensional toric unit cube [0,1]^d generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

IMC '10: Proceedings of the 10th ACM SIGCOMM conference on Internet measurement

November 2010

496 pages

ISBN:9781450304832

DOI:10.1145/1879141

Program Chair:
Mark Allman
International Computer Science Institute

Copyright © 2010 ACM.

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 ACM 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

In-Cooperation

USENIX Assoc: USENIX Assoc

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 November 2010

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

IMC '10

Sponsor:

IMC '10: Internet Measurement Conference

November 1 - 30, 2010

Melbourne, Australia

Acceptance Rates

Overall Acceptance Rate 277 of 1,083 submissions, 26%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

176
Total Citations
View Citations
748
Total Downloads

Downloads (Last 12 months)40
Downloads (Last 6 weeks)1

Reflects downloads up to 27 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Kasana SSharma MGupta S(2025)A Systematic Security Analysis of Existing Sybil Attack-Resilient Defensive Methodologies in Blockchain NetworkConvergence of Cybersecurity and Cloud Computing10.4018/979-8-3693-6859-6.ch009(191-224)Online publication date: 10-Jan-2025
https://doi.org/10.4018/979-8-3693-6859-6.ch009
Liao MZhou JLi RDai QChen HWang G(2024)Efficient and Provable Effective Resistance Computation on Large Graphs: An Index-based ApproachProceedings of the ACM on Management of Data10.1145/36549362:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654936
Peng JLei RWei ZSerra ESpezzano F(2024)Beyond Over-smoothing: Uncovering the Trainability Challenges in Deep Graph Neural NetworksProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679776(1878-1887)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1145/3627673.3679776
Farach-Colton GFarach-Colton MGoldberg LKomlos HLapinskas JLevi RMedina MMosteiro MLeyton-Brown KSamuelson LHartline J(2023)Graph Ranking and the Cost of Sybil DefenseProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597782(586-625)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597782
Xie YQiu JDhulipala LYu WTang JPeng RWang C(2023)Towards Lightweight and Automated Representation Learning System for NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2023.324316935:9(9613-9627)Online publication date: 1-Sep-2023
https://doi.org/10.1109/TKDE.2023.3243169
Gao YXu GLi LLuo XWang CSui YRoychoudhury ACadar CKim M(2022)Demystifying the underground ecosystem of account registration botsProceedings of the 30th ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering10.1145/3540250.3549090(897-909)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1145/3540250.3549090
Cui YLi XLi JWang HChen X(2022)A Survey of Sampling Method for Social Media Embeddedness RelationshipACM Computing Surveys10.1145/352410555:4(1-39)Online publication date: 21-Nov-2022
https://dl.acm.org/doi/10.1145/3524105
Ben-Eliezer OEden TOren JFotakis DSelcuk Candan KLiu HAkoglu LLuna Dong XTang J(2022)Sampling Multiple Nodes in Large NetworksProceedings of the Fifteenth ACM International Conference on Web Search and Data Mining10.1145/3488560.3498383(37-47)Online publication date: 11-Feb-2022
https://dl.acm.org/doi/10.1145/3488560.3498383
Khaund TKirdemir BAgarwal NLiu HMorstatter F(2022)Social Bots and Their Coordination During Online Campaigns: A SurveyIEEE Transactions on Computational Social Systems10.1109/TCSS.2021.31035159:2(530-545)Online publication date: Apr-2022
https://doi.org/10.1109/TCSS.2021.3103515
Jia NBagam LFabijanczyk PCeesay E(2022)Machine Learning models for Customer Relationship Analysis to Improve Satisfaction Rate in Banking2022 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS)10.1109/IEMTRONICS55184.2022.9795855(1-9)Online publication date: 1-Jun-2022
https://doi.org/10.1109/IEMTRONICS55184.2022.9795855
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Figures

Tables

Media

View Table of Conten