Measuring the Generalized Friendship Paradox in Networks with Quality-dependent Connectivity

The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment-like network growth mechanism governed by both node degrees and `qualities'. We introduce measures to quantify paradoxes, and contrast the results obtained in our model to those obtained for an uncorrelated network, where the degrees and qualities of adjacent nodes are uncorrelated. We shed light on the effect of the distribution of node qualities on the friendship paradox. We consider both the mean and the median to measure paradoxes, and compare the results obtained by using these two statistics

Tail-scope: Using friends to estimate heavy tails of degree distributions in large-scale complex networks

Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes more difficult to analyze complete data sets. Thus, it is crucial to devise effective and efficient estimation methods for heavy tails of degree distributions in large-scale networks only using local information of a small fraction of sampled nodes. Here we propose a tail-scope method based on local observational bias of the friendship paradox. We show that the tail-scope method outperforms the uniform node sampling for estimating heavy tails of degree distributions, while the opposite tendency is observed in the range of small degrees. In order to take advantages of both sampling methods, we devise the hybrid method that successfully recovers the whole range of degree distributions. Our tail-scope method shows how structural heterogeneities of large-scale complex networks can be used to effectively reveal the network structure only with limited local information.Comment: 9 pages, 6 figure

A study on the friendship paradox – quantitative analysis and relationship with assortative mixing

The friendship paradox is the observation that friends of individuals tend to have more friends or be more popular than the individuals themselves. In this work, we first study local metrics to capture the strength of the paradox and the direction of the paradox from the perspective of individual nodes, i.e., an indication of whether the individual is more or less popular than its friends. These local metrics are aggregated, and global metrics are proposed to express the phenomenon on a network-wide level. Theoretical results show that the defined metrics are well-behaved enough to capture the friendship paradox. We also theoretically analyze the behavior of the friendship paradox for popular network models in order to understand regimes where friendship paradox occurs. These theoretical findings are complemented by experimental results on both network models and real-world networks. By conducting a correlation study between the proposed metrics and degree assortativity, we experimentally demonstrate that the phenomenon of the friendship paradox is related to the well-known phenomenon of assortative mixing

Three Essays on Network Dynamics and Liminality

This dissertation focuses on the emergence and evolution of social networks by paying particular attention to the spanning of cultural boundaries that segregate actors in the context of specific societies. In particular, I use systems science methods to study the bridging of cultural holes in small and relatively dense artificial societies, as well as in an American high school. I also study the significance of local triadic configurations in giving rise to the highly hierarchical system of aggregate-level migration flows in place in the Americas during the late 20th century. I use the concept of liminality as a way to analyze these disparate social systems. More precisely, I focus on the role of cultural brokers seen as actors at the limen – i.e. at the border – of symbolic boundaries, actors that can act as bridges between culturally disconnected worlds. In this context, this dissertation explains key network dynamics behind two emergent phenomena that are the direct result of liminal agents’ behaviors: the diffusion of innovations (Chapters 1 and 2) and a system of international migration flows (Chapter 3). Finally, I also put forward a critical view on brokerage based on different cases mentioned in the literature (e.g. 1.5 generation migrants or multiracial individuals) that show how the spanning of cultural holes can put brokers at an increased risk of being socially and/or psychologically harmed