The friendship paradox states that your friends have on average more friends than you have. Does the paradox “hold” for other individual characteristics like income or happiness? To address this question, we generalize the friendship paradox for arbitrary node characteristics in complex networks. By analyzing two coauthorship networks of Physical Review journals and Google Scholar profiles, we find that the generalized friendship paradox (GFP) holds at the individual and network levels for various characteristics, including the number of coauthors, the number of citations, and the number of publications. The origin of the GFP is shown to be rooted in positive correlations between degree and characteristics. As a fruitful application of the GFP, we suggest effective and efficient sampling methods for identifying high characteristic nodes in large-scale networks. Our study on the GFP can shed lights on understanding the interplay between network structure and node characteristics in complex networks.

Understanding the patterns of mobility of individuals is crucial for a number of reasons, from city planning to disaster management. There are two common ways of quantifying the amount of travel between locations: by direct observations that often involve privacy issues, e.g., tracking mobile phone locations, or by estimations from models. Typically, such models build on accurate knowledge of the population size at each location. However, when this information is not readily available, their applicability is rather limited. As mobile phones are ubiquitous, our aim is to investigate if mobility patterns can be inferred from aggregated mobile phone call data alone. Using data released by Orange for Ivory Coast, we show that human mobility is well predicted by a simple model based on the frequency of mobile phone calls between two locations and their geographical distance. We argue that the strength of the model comes from directly incorporating the social dimension of mobility. Furthermore, as only aggregated call data is required, the model helps to avoid potential privacy problems.

Information, ideas, or diseases spread through interactions between individuals. The temporal pattern of such interactions is known to show ``burstiness,'' but little is known about how it affects large-scale spreading dynamics. Analytic results on a simple model of bursty spreading dynamics provide a rare, but much needed reference point for numerical simulations and empirical data analysis.

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.