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.
arXiv comment9 pages, 3 figures. arXiv admin note: text overlap with arXiv:2107.05838
References in corpus (24)
- Emergence of scaling in random networks
- Statistical mechanics of complex networks
- Community detection in graphs
- Power-law distributions in empirical data
- Assortative mixing in networks
- Statistical physics of social dynamics
- Epidemic processes in complex networks
- Why social networks are different from other types of networks
- Scale-free networks are rare
- The Majority Illusion in Social Networks
- Random walks and diffusion on networks
- Random graphs with clustering
- Homophily and minority size explain perception biases in social networks
- Generalized friendship paradox in complex networks: The case of scientific collaboration
- Qualities and Inequalities in Online Social Networks through the Lens of the Generalized Friendship Paradox
- Friendship Paradox Biases Perceptions in Directed Networks
- Constructing a bivariate distribution function with given marginals and correlation: application to the galaxy luminosity function
- Generalized friendship paradox in networks with tunable degree-attribute correlation
- Impact of perception models on friendship paradox and opinion formation
- Copula-based algorithm for generating bursty time series
- Constructing a multivariate distribution function with a vine copula: toward multivariate luminosity and mass functions
- Stylized facts in social networks: Community-based static modeling
- Analytically solvable autocorrelation function for weakly correlated interevent times
- Analytical approach to the generalized friendship paradox in networks with correlated attributes