A null model for Dunbar’s circles

Manuel Jiménez-Martín, Silvia N. Santalla, Javier Rodríguez-Laguna and Elka Korutcheva

Physica A: Statistical Mechanics and its Applications, 2020, vol. 545, issue C

Abstract: An individual’s social group may be represented by their ego-network, formed by the links between the individual and their acquaintances. Ego-networks present an internal structure of increasingly large nested layers (or circles) of decreasing relationship intensity, whose size exhibits a precise scaling ratio. Starting from the notion of limited social bandwidth, and assuming fixed costs for the links in each layer, we propose a null model built on a grand-canonical ensemble that generates the observed hierarchical social structure. The observed internal structure of ego-networks becomes a natural outcome to expect when we assume the existence of layers demanding different amounts of resources. In the thermodynamic limit, reached when the number of ego-network copies is large, the specific layer degrees follow a Poisson distribution. We also find that, under certain conditions, equispaced layer costs are necessary to obtain a constant group size scaling. Our model presents interesting analogies to a Bose–Einstein gas, that we briefly discuss. Finally, we fit and compare the model with an empirical social network.

Keywords: Social networks; Null model; Dunbar circles (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320989

DOI: 10.1016/j.physa.2019.123767

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