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More and more social interactions happen online. On online social networks such as Instagram, millions of users share, like, and comment on photos and videos every day, interacting with other users world wide, at large scale and at a high rate. These networks do not only introduce new user experiences, but they also enable new insights into human behavior. Here, we use these new possibilities to study homophilic behavior—the tendency of individuals to bond with people similar to themselves. While homophilic behavior has been observed in many contexts, little is known about gender-specific differences and the extent of homophilic behavior of female and male users in online social networks. Based on a unique and extensive data set, covering over 800,000 (directed) Instagram interactions and a time span of three years, we shed light on differences between genders and uncover an intriguing asymmetry of homophily. In particular, we show that female users exhibit homophily to a larger extent than male users. The magnitude of this asymmetry depends on the type of interaction, as differences are more pronounced for 'comment'-interactions than for 'like'-interactions. Given these empirical observations, we further study the implications of such gender differences on the spread of information in social networks in a basic model. We find that on average, a piece of information that originates from a female group reaches significantly more female users than male users. [ABSTRACT FROM AUTHOR]

Blockchains, in general, and cryptocurrencies such as Bitcoin, in particular, are realized using distributed systems and hence critically rely on the performance and security of the interconnecting network. The requirements on these networks and their usage, however, can differ significantly from traditional communication networks, with implications on all layers of the protocol stack. This article is motivated by these differences and, in particular, by the observation that many fundamental design aspects of these networks are not well-understood today. To support the networking community to contribute to this emerging application domain, we present a structured overview of the field, from topology and neighbor discovery, over block and transaction propagation, to sharding and off-chain networks, also reviewing existing empirical results from different measurement studies. In particular, for each of these domains, we provide the context, highlighting differences and commonalities with traditional networks, review the state-of-the-art, and identify open research challenges. Our article can hence also be seen as a call-to-arms to improve the foundation on top of which blockchains are built. [ABSTRACT FROM AUTHOR]

A common two-tier structure for social networks is based on partitioning society into two parts, referred to as the elite and the periphery, where the “elite” is the relatively small but well-connected and highly influential group of powerful individuals around which the society is centered, and the “periphery” consists of the rest of society. It is observed that the relative sizes of economic and social elites in various societies appear to be continually declining. One possible explanation is that this is a natural social phenomenon, resembling Price’s “square root” law for the fraction of good scientists in the scientific community. We try to assess the validity of this explanation by studying the elite-periphery structure via introducing a novel axiom-based model for representing and measuring the influence between the elite and the periphery. The model is accompanied by a set of axioms that capture the elite’s dominance, robustness and density, as well as a compactness property. Relying on the model and the accompanying axioms, we are able to draw a number of insightful conclusions about the elite-periphery structure. In particular, we show that in social networks that respect our axioms, the size of a compact elite is sublinear in the network size. This agrees with Price’s principle but appears to contradict the common belief that the elite size tends to a linear fraction of society (recently claimed to be around 1%). We propose a natural method to create partitions with nice properties, based on the key observation that an elite-periphery partition is at what we call a ‘balance point’, where the elite and the periphery maintain a balance of powers. Our method is based on setting the elite to be the k most influential nodes in the network and suggest the balance point as a tool for choosing k and therefore the size of the elite. When using nodes degrees to order the nodes, the resulting k-rich club at the balance point is the elite of a partition we refer to as the balanced edge-based partition. We accompany these findings with an empirical study on 32 real-world social networks, which provides evidence that balanced edge-based partitions which satisfying our axioms commonly exist. [ABSTRACT FROM AUTHOR]

Individuals in social networks tend to exhibit homophily in their social ties, namely, they prefer bonding with others of the same social group (e.g., the same nationality, gender, socio-economic background, etc.). To formalize this phenomenon in the context of an evolving social network, we consider a mixed preferential attachment (MPA), bi-populated, network model. In this model each of the two social groups has a certain level of bias applied by its members toward other group members, ranging form homophily (affinity toward the same) to heterophily (affinity toward the different). Thus, the MPA model supports the following three simple and well-accepted observations on human behavior related to forming networks: (i) the "rich get richer" mechanism, (ii) heterogeneity and a resulting minority–majority partition, and (iii) selection bias between groups. The main contribution of this paper is to propose a model for the evolution of a social network under these three assumptions and analyze its behavior. We show that the suggested mixed preferential attachment model exhibits, for each population, a (possibly different) power law degree distribution, i.e., a distribution where the fraction of nodes with degree k is proportional to k − β (note that β may be different for each group, as a function of the bias level and the minority–majority partition). We believe that this model may contribute to a better understanding of the forces that shape the groups and communities of our society. • Extending the preferential attachment model for mixed-population. • Model the homophily behavior of heterogeneous groups. • Proving the model exhibits, for each population, a power law degree distribution. • The power law exponents depend on the homophily level and the rate in society. [ABSTRACT FROM AUTHOR]