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Zipf's Law across social media

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Abstract

Zipf's Law describes an empirical regularity that appears across many human and physical domains, and states that ranked data exhibits a power law distribution. Although there are various extant studies illustrating power law relationships using social media data, we significantly extend these previous studies by looking at eight popular online social media networks: (1) Twitter; (2) YouTube; (3) Instagram; (4) Twitch; (5) DLive; (6) TikTok; (7) Daily Motion; and (8) Facebook. Specifically, we test whether the distribution of connections (followers, subscribers, or likes) follows a power law distribution for the top 5000 members of each social network. We find strong evidence that a power law relationship exists for every one of the social networks that we study, although this relationship breaks down for users at the top of the connections distribution. Despite the finding of a power law relationship for all of these social networks, the degree of inequality in social media connections differs substantially across the different networks, with the highest degree of inequality in DLive, and the lowest degree in TikTok and YouTube.

Suggested Citation

  • Michael P Cameron, 2022. "Zipf's Law across social media," Working Papers in Economics 22/07, University of Waikato.
    • Handle: RePEc:wai:econwp:22/07
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    References listed on IDEAS

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    1. Krawczyk, Malgorzata J. & Libirt, Mateusz & Malarz, Krzysztof, 2025. "Rank-based distributions in scientific papers affiliations: Different forms of Zipf's law with and without higher order inverse participation ratios," Journal of Informetrics, Elsevier, vol. 19(3).

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    Keywords

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    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • L86 - Industrial Organization - - Industry Studies: Services - - - Information and Internet Services; Computer Software

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