Quantifying the Strength of the Friendship Paradox

Pal, Siddharth; Feng, Ying; Novick, Yitzchak; Swami, Ananthram; Bar-Noy, Amotz

doi:10.1007/978-3-030-05414-4_37

Cited by 1 publication

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“…We consider canonical graphs and common graph models and find our aggregate measures produce well behaved functions that smoothly reflect small adjustments in the graphs where the function of network assortativity has a far less smooth curve. The present work is an extension of our previous work (Pal et al 2018); here we present complete and detailed proofs of results partially proven in Pal et al (2018) along with new theoretical findings on the proposed metrics in networks models, such as Erdos-Renyi and Barabasi-Albert graphs. Additionally, a more thorough simulation study on network models is presented here.…”

Section: Introductionmentioning

confidence: 59%

A study on the friendship paradox – quantitative analysis and relationship with assortative mixing

et al. 2019

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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 study local metrics to capture the strength of the paradox and the direction of the paradox from the perspective of individual nodes, i.e., an indication of whether the individual is more or less popular than its friends. These local metrics are aggregated, and global metrics are proposed to express the phenomenon on a network-wide level. Theoretical results show that the defined metrics are well-behaved enough to capture the friendship paradox. We also theoretically analyze the behavior of the friendship paradox for popular network models in order to understand regimes where friendship paradox occurs. These theoretical findings are complemented by experimental results on both network models and real-world networks. By conducting a correlation study between the proposed metrics and degree assortativity, we experimentally demonstrate that the phenomenon of the friendship paradox is related to the well-known phenomenon of assortative mixing.

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Section: Introductionmentioning

confidence: 59%