Copula-based analysis of the generalized friendship paradox in clustered networks
arXiv:2208.07009 · doi:10.1063/5.0122351
Abstract
A heterogeneous structure of social networks induces various intriguing phenomena. One of them is the friendship paradox, which states that on average your friends have more friends than you do. Its generalization, called the generalized friendship paradox (GFP), states that on average your friends have higher attributes than yours. Despite successful demonstrations of the GFP by empirical analyses and numerical simulations, analytical, rigorous understanding of the GFP has been largely unexplored. Recently, an analytical solution for the probability that the GFP holds for an individual in a network with correlated attributes was obtained using the copula method but by assuming a locally tree structure of the underlying network [Jo~et~al., Physical Review E~\textbf{104}, 054301 (2021)]. Considering the abundant triangles in most social networks, we employ a vine copula method to incorporate the attribute correlation structure between neighbors of a focal individual in addition to the correlation between the focal individual and its neighbors. Our analytical approach helps us rigorously understand the GFP in more general networks such as clustered networks and other related interesting phenomena in social networks.
9 pages, 3 figures. arXiv admin note: text overlap with arXiv:2107.05838
References in corpus (7)
- Power-law distributions in empirical data
- Statistical physics of social dynamics
- Random graphs with clustering
- Generalized friendship paradox in networks with tunable degree-attribute correlation
- Constructing a multivariate distribution function with a vine copula: toward multivariate luminosity and mass functions
- Analytically solvable autocorrelation function for weakly correlated interevent times
- Analytical approach to the generalized friendship paradox in networks with correlated attributes