Understanding social network structure and evolution has important implications for many aspects of network and system design including provisioning, bootstrapping trust and reputation systems via social networks, and defenses against Sybil attacks. Several recent results suggest that augmenting the social network structure with user attributes (e.g., location, employer, communities of interest) can provide a more fine-grained understanding of social networks. However, there have been few studies to provide a systematic understanding of these effects at scale. We bridge this gap using a unique dataset collected as the Google+ social network grew over time since its release in late June 2011. We observe novel phenomena with respect to both standard social network metrics and new attribute-related metrics (that we define). We also observe interesting evolutionary patterns as Google+ went from a bootstrap phase to a steady invitation-only stage before a public release. Based on our empirical observations, we develop a new generative model to jointly reproduce the social structure and the node attributes. Using theoretical analysis and empirical evaluations, we show that our model can accurately reproduce the social and attribute structure of real social networks. We also demonstrate that our model provides more accurate predictions for practical application contexts.
Modeling social-attribute networks There has been relatively little work on generating , though a few recent work jointly generating both social structure and node attributes can be viewed as models; the most relevant work is from @cite_57 and Kim and Leskovec @cite_2 . @cite_57 focus on dynamic attributes; their model generates undirected networks with power-law distribution for social degree and non-lognormal distribution for attribute degree (see Figure ). Kim and Leskovec model the social and attribute structure simultaneously @cite_2 . Here, both the social degree of attribute nodes and attribute degrees of social nodes follow binomial distribution, which differs from empirically observed . Our model can generate that we confirm through both analysis and simulations to be consistent with real .
@cite_57 @cite_2
2047443612 2015326995
Social networks are popular platforms for interaction, communication and collaboration between friends. Researchers have recently proposed an emerging class of applications that leverage relationships from social networks to improve security and performance in applications such as email, web browsing and overlay routing. While these applications often cite social network connectivity statistics to support their designs, researchers in psychology and sociology have repeatedly cast doubt on the practice of inferring meaningful relationships from social network connections alone. This leads to the question: Are social links valid indicators of real user interaction? If not, then how can we quantify these factors to form a more accurate model for evaluating socially-enhanced applications? In this paper, we address this question through a detailed study of user interactions in the Facebook social network. We propose the use of interaction graphs to impart meaning to online social links by quantifying user interactions. We analyze interaction graphs derived from Facebook user traces and show that they exhibit significantly lower levels of the "small-world" properties shown in their social graph counterparts. This means that these graphs have fewer "supernodes" with extremely high degree, and overall network diameter increases significantly as a result. To quantify the impact of our observations, we use both types of graphs to validate two well-known social-based applications (RE and SybilGuard). The results reveal new insights into both systems, and confirm our hypothesis that studies of social applications should use real indicators of user interactions in lieu of social graphs. Large scale real-world network data such as social and information networks are ubiquitous. The study of such networks seeks to find patterns and explain their emergence through tractable models. In most networks, and especially in social networks, nodes have a rich set of attributes associated with them. We present the Multiplicative Attribute Graphs (MAG) model, which naturally captures the interactions between the network structure and the node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes depends on the product of individual attribute-attribute similarities. The model yields itself to mathematical analysis. We derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to networks with a constant diameter. We also show that MAG model can produce networks with either log-normal or power-law degree distributions.