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Quantifying the Strength of the Friendship Paradox

  • Siddharth Pal
  • Feng Yu
  • Yitzchak Novick
  • Ananthram Swami
  • Amotz Bar-Noy
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 813)

Abstract

The friendship paradox is the observation that friends of individuals tend to have more friends or be more popular than the individuals themselves. In this work, we first develop local metrics that quantify the strength and the direction of the paradox from the perspective of individual nodes, i.e., is the individual more or less popular than its friends. We aggregate the local measures to define global metrics that capture the friendship paradox at the network scale. Theoretical results are shown that support the global metrics to be well-behaved enough to capture the friendship paradox. Furthermore, through experiments, we identify regimes in network models, and real networks, where the friendship paradox is prominent. By conducting a correlation study between the proposed metrics and assortativity, we experimentally demonstrate that the phenomenon of the friendship paradox is related to the well-known phenomenon of homophily or assortative mixing.

Keywords

Friendship paradox Assortativity Assortative mixing Homophily Network Analysis 

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Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  • Siddharth Pal
    • 1
  • Feng Yu
    • 2
  • Yitzchak Novick
    • 2
    • 4
  • Ananthram Swami
    • 3
  • Amotz Bar-Noy
    • 2
  1. 1.Raytheon BBN TechnologiesCambridgeUSA
  2. 2.City University of New YorkNew YorkUSA
  3. 3.U.S. Army Research LabAdelphiUSA
  4. 4.Touro College and University SystemNew YorkUSA

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