On the mixing time of directed social graphs and security implications

Many graphs in general, and social graphs in particular, are directed by nature. However, applications built on top of social networks, including Sybil defenses, information routing and dissemination, and anonymous communication require mutual relationships which produce undirected graphs. When undirected graphs are used as testing tools for these applications to bring insight on their usability and potential deployment, directed graphs are converted into undirected graphs by omitting edge directions or by augmenting graphs. Unfortunately, it is unclear how altering these graphs affects the quality of their mixing time. Motivated by the lack of prior work on this problem, we investigate mathematical tools for measuring the mixing time of directed social graphs and its associated error bounds. We use these tools to measure the mixing time of several benchmarking directed graphs and their undirected counterparts. We then measure how this difference impacts two applications built on top of social networks: a Sybil defense mechanism and an anonymous communication system.

[1]  Alistair Sinclair,et al.  Improved Bounds for Mixing Rates of Markov Chains and Multicommodity Flow , 1992, Combinatorics, Probability and Computing.

[2]  Carmela Troncoso,et al.  Drac: An Architecture for Anonymous Low-Volume Communications , 2010, Privacy Enhancing Technologies.

[3]  M. Frans Kaashoek,et al.  Whanau: A Sybil-proof Distributed Hash Table , 2010, NSDI.

[4]  Jure Leskovec,et al.  Statistical properties of community structure in large social and information networks , 2008, WWW.

[5]  Hector Garcia-Molina,et al.  DHT Routing Using Social Links , 2004, IPTPS.

[6]  Christopher T. Lesniewski-Laas.  Design and applications of a secure and decentralized DHT , 2011 .

[7]  Krishna P. Gummadi,et al.  An analysis of social network-based Sybil defenses , 2010, SIGCOMM 2010.

[8]  Aziz Mohaisen,et al.  Mistaking friends for foes: an analysis of a social network-based Sybil defense in mobile networks , 2011, ICUIMC '11.

[9]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[10]  George Danezis,et al.  Sybil-Resistant DHT Routing , 2005, ESORICS.

[11]  Aziz Mohaisen,et al.  Measuring bias in the mixing time of social graphs due to graph sampling , 2012, MILCOM 2012 - 2012 IEEE Military Communications Conference.

[12]  Krishna P. Gummadi,et al.  Measurement and analysis of online social networks , 2007, IMC '07.

[13]  Michael Kaminsky,et al.  SybilGuard: defending against sybil attacks via social networks , 2006, SIGCOMM.

[14]  Aziz Mohaisen,et al.  Understanding Social Networks Properties for Trustworthy Computing , 2011, 2011 31st International Conference on Distributed Computing Systems Workshops.

[15]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[16]  Alistair Sinclair,et al.  Improved Bounds for Mixing Rates of Marked Chains and Multicommodity Flow , 1992, LATIN.

[17]  Matteo Dell Amico.  A Measurement of Mixing Time in Social Networks , 2009 .

[18]  Michael Kaminsky,et al.  SybilLimit: A Near-Optimal Social Network Defense against Sybil Attacks , 2008, S&P 2008.

[19]  A. Granas,et al.  Fixed Point Theory , 2003 .

[20]  Yongdae Kim,et al.  Trust in Social Network-based Sybil Defenses , 2010 .

[21]  Aziz Mohaisen,et al.  Measuring the mixing time of social graphs , 2010, IMC '10.

[22]  Chandra Prakash,et al.  SybilInfer: Detecting Sybil Nodes using Social Networks , 2011 .

[23]  Igor Pak.  Mixing time and long paths in graphs , 2002, SODA '02.

[24]  Haifeng Yu,et al.  Sybil defenses via social networks: a tutorial and survey , 2011, SIGA.

[25]  Chris Jermaine,et al.  The Latent Community Model for Detecting Sybils in Social Networks , 2012, NDSS.

[26]  Ian T. Foster,et al.  Mapping the Gnutella Network , 2002, IEEE Internet Comput..

[27]  Lakshminarayanan Subramanian,et al.  Sybil-Resilient Online Content Voting , 2009, NSDI.

[28]  Shishir Nagaraja,et al.  Anonymity in the Wild: Mixes on Unstructured Networks , 2007, Privacy Enhancing Technologies.

[29]  Hector Garcia-Molina,et al.  SPROUT: P2P Routing with Social Networks , 2004, EDBT Workshops.

[30]  Chris Lesniewski-Laas,et al.  A Sybil-proof one-hop DHT , 2008, SocialNets '08.

[31]  Lakshminarayanan Subramanian,et al.  Optimal Sybil-resilient node admission control , 2011, 2011 Proceedings IEEE INFOCOM.

[32]  Matthew Richardson,et al.  Trust Management for the Semantic Web , 2003, SEMWEB.

[33]  Jiye Yu,et al.  iLink: search and routing in social networks , 2007, KDD '07.

[34]  Jure Leskovec,et al.  Predicting positive and negative links in online social networks , 2010, WWW '10.

[35]  Prateek Mittal,et al.  X-Vine: Secure and Pseudonymous Routing Using Social Networks , 2011, ArXiv.