The Friendship Paradox: Implications In Statistical Inference Of Social Networks

The friendship paradox is a type of observation bias in undirected social networks: “on average, the number of friends of a random friend is always greater than or equal to the number of friends of a random individual”. This paper discusses friendship paradox, its recent generalizations to directed networks as well as its applications. Specifically, we discuss how the friendship paradox can be exploited in two important statistical inference problems in social networks: (i) polling a social network where the aim is to estimate the fraction of nodes in the network with a specific label (e.g. gender, political affiliation, etc.) by querying (sampling) only some of the nodes and, (ii) estimating the power-law exponent in social networks with a power-law degree distribution.

[1]  Kristina Lerman,et al.  Friendship Paradox Redux: Your Friends Are More Interesting Than You , 2013, ICWSM.

[2]  Desmond J. Higham,et al.  Centrality-Friendship Paradoxes: When Our Friends Are More Important Than Us , 2018, J. Complex Networks.

[3]  Jonathan Cutler,et al.  The Multistep Friendship Paradox , 2016, Am. Math. Mon..

[4]  S. Feld.  Why Your Friends Have More Friends Than You Do , 1991, American Journal of Sociology.

[5]  Michael G. Rabbat,et al.  Generalized Friendship Paradox: An Analytical Approach , 2014, SocInfo Workshops.

[6]  Vikram Krishnamurthy,et al.  Information Diffusion in Social Networks: Friendship Paradox based Models and Statistical Inference , 2018, Modeling, Stochastic Control, Optimization, and Applications.

[7]  Donald F. Towsley,et al.  Estimating and sampling graphs with multidimensional random walks , 2010, IMC '10.

[8]  Hang-Hyun Jo,et al.  Generalized friendship paradox in complex networks: The case of scientific collaboration , 2014, Scientific Reports.

[9]  W. Just,et al.  The friendship paradox , 2015 .

[10]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[11]  Minas Gjoka,et al.  Walking in Facebook: A Case Study of Unbiased Sampling of OSNs , 2010, 2010 Proceedings IEEE INFOCOM.

[12]  J. Wolfers,et al.  Forecasting Elections: Voter Intentions Versus Expectations , 2011 .

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

[14]  Minas Gjoka,et al.  Practical Recommendations on Crawling Online Social Networks , 2011, IEEE Journal on Selected Areas in Communications.

[15]  Kristina Lerman,et al.  The "Majority Illusion" in Social Networks , 2015, PloS one.

[16]  Kristina Lerman,et al.  Friendship paradox biases perceptions in directed networks , 2019, Nature Communications.

[17]  Johan Bollen,et al.  The happiness paradox: your friends are happier than you , 2016, EPJ Data Science.

[18]  Kristina Lerman,et al.  Contagions in Social Networks: Effects of Monophilic Contagion, Friendship Paradox and Reactive Networks , 2018, ArXiv.

[19]  Vikram Krishnamurthy,et al.  “What Do Your Friends Think?”: Efficient Polling Methods for Networks Using Friendship Paradox , 2018, IEEE Transactions on Knowledge and Data Engineering.

[20]  Rick Durrett,et al.  Probability: Theory and Examples, 4th Edition , 2010 .

[21]  Hang-Hyun Jo,et al.  Tail-scope: Using friends to estimate heavy tails of degree distributions in large-scale complex networks , 2014, Scientific Reports.

[22]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[23]  Christos Faloutsos,et al.  Sampling from large graphs , 2006, KDD '06.

[24]  Vikram Krishnamurthy,et al.  Maximum Likelihood Estimation of Power-law Degree Distributions via Friendship Paradox-based Sampling , 2019, ACM Trans. Knowl. Discov. Data.