Friendship Paradox and Attention Economics

The friendship paradox is revisited by considering both local and global averages of friends. How the economics of attention affects the recruitment of friends is examined. Statistical implications of varying individual attentions are investigated and it is argued that this is one reason why the mean of friends is higher than the median in social networks. The distribution of friends skews to the right for two other reasons: (i) the presence of institutional nodes that increase the mean; and (ii) the dormancy of many of the nodes. The difference between friends and friends of friends is a measure of the structural information about the network.

💡 Research Summary

The paper revisits the classic “friendship paradox” – the observation that most people have fewer friends than the average of their friends – by incorporating two novel perspectives: (1) a distinction between local (neighbour‑averaged) and global (network‑wide) degree averages, and (2) an “attention economics” framework that treats each individual’s capacity to maintain social ties as a limited resource.
The authors begin by formalising the paradox. For a node i with degree k_i, the global average degree is ⟨k⟩ = (1/|V|) Σ_j k_j, while the local average seen by i is ⟨k⟩i^nbr = (1/k_i) Σ{j∈N(i)} k_j. The paradox holds when ⟨k⟩_i^nbr > k_i for the majority of nodes. Traditional explanations attribute this to the right‑skewed degree distribution of social networks, often modelled by power‑law or log‑normal forms.
The paper then introduces attention economics. Each person i possesses a finite amount of “social attention” A_i (measured in units of time, cognitive load, or digital bandwidth). Maintaining a single relationship requires a minimum attention cost c, so the maximum feasible number of friends for i is floor(A_i / c). The distribution of A_i across a population is assumed exponential, reflecting the empirical observation that most people allocate modest attention while a few allocate substantially more (e.g., influencers, community leaders).
Two additional structural factors are modelled: (a) institutional nodes (corporate accounts, media outlets, government pages) that have effectively unlimited attention and therefore acquire extremely high degrees, and (b) dormant nodes (inactive accounts that remain in the data set). Institutional nodes contribute a heavy tail to the degree distribution, inflating the mean, while dormant nodes increase the total node count and depress the median.
A combined analytical model is derived. The expected degree E