Generalized friendship paradox in networks with tunable degree-attribute correlation

Abstract

One of interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.

arXiv comment7 pages, 5 figures

References in corpus (15)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Community detection in graphs
• Assortative mixing in networks
• Statistical physics of social dynamics
• Specificity and stability in topology of protein networks
• Temporal Networks
• Efficient Immunization Strategies for Computer Networks and Populations
• The Anatomy of the Facebook Social Graph
• Generation of uncorrelated random scale-free networks
• Social Network Sensors for Early Detection of Contagious Outbreaks
• Model of Genetic Variation in Human Social Networks
• Characterizing and modeling citation dynamics
• Performance of Social Network Sensors During Hurricane Sandy
• Generalized friendship paradox in complex networks: The case of scientific collaboration

Cited by in corpus (10)

• The Majority Illusion in Social Networks
• Tail-scope: Using friends to estimate heavy tails of degree distributions in large-scale complex networks
• Qualities and Inequalities in Online Social Networks through the Lens of the Generalized Friendship Paradox
• Friendship Paradox Biases Perceptions in Directed Networks
• Impact of perception models on friendship paradox and opinion formation
• Modeling the dynamics of dissent
• Concurrency and reachability in tree-like temporal networks
• Copula-based analysis of the generalized friendship paradox in clustered networks
• Analytical approach to the generalized friendship paradox in networks with correlated attributes
• Interventions with Inversity in Unknown Networks Can Help Regulate Contagion