Abstract:
This work investigates the friendship paradox in complex networks and introduces a new metric — the friendship rank of a node, designed to quantify the paradox. The study examines the limiting distribution of friendship rank in networks generated via the configuration model, where node degrees are produced by independent realizations of a random variable. A convergence theorem for friendship rank is proven for networks with finite moments of degree distribution. Empirical results confirm that, unlike the friendship index, the friendship rank is a more stable characteristic when comparing networks of different sizes, especially for degree distributions with heavy tails. The proposed method can be useful for comparing networks of varying scales, such as social networks.
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