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We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and friendships, the degree distribution, path lengths, clustering, and mixing patterns. Our results center around three main observations. First, we characterize the global… (More)

Frigyes Karinthy, in his 1929 short story "Láncszemek" (in English, "Chains") suggested that any two persons are distanced by at most six friendship links.<sup>1</sup> Stanley Milgram in his famous experiments challenged people to route postcards to a fixed recipient by passing them only through direct acquaintances. Milgram found that the average… (More)

Partitioning graphs at scale is a key challenge for any application that involves distributing a graph across disks, machines, or data centers. Graph partitioning is a very well studied problem with a rich literature, but existing algorithms typically can not scale to billions of edges, or can not provide guarantees about partition sizes.
In this work we… (More)

The concept of contagion has steadily expanded from its original grounding in epidemic disease to describe a vast array of processes that spread across networks, notably social phenomena such as fads, political opinions, the adoption of new technologies, and financial decisions. Traditional models of social contagion have been based on physical analogies… (More)

A growing set of on-line applications are generating data that can be viewed as very large collections of small, dense social graphs --- these range from sets of social groups, events, or collaboration projects to the vast collection of graph neighborhoods in large social networks. A natural question is how to usefully define a domain-independent… (More)

People's interests and people's social relationships are intuitively connected, but understanding their interplay and whether they can help predict each other has remained an open question. We examine the interface of two decisive structures forming the backbone of online social media: the graph structure of social networks — who connects with whom — and… (More)

Partitioning large graphs is difficult, especially when performed in the limited models of computation afforded to modern large scale computing systems. In this work we introduce restreaming graph partitioning and develop algorithms that scale similarly to streaming partitioning algorithms yet empirically perform as well as fully offline algorithms. In… (More)

A/B testing is a standard approach for evaluating the effect of online experiments; the goal is to estimate the `average treatment effect' of a new feature or condition by exposing a sample of the overall population to it. A drawback with A/B testing is that it is poorly suited for experiments involving social interference, when the treatment of individuals… (More)

Estimating the effects of interventions in networks is complicated when the units are interacting, such that the outcomes for one unit may depend on the treatment assignment and behavior of many or all other units (i.e., there is interference). When most or all units are in a single connected component , it is impossible to directly experimentally compare… (More)

Latent variable mixture models are a powerful tool for exploring the structure in large datasets. A common challenge for interpreting such models is a desire to impose sparsity, the natural assumption that each data point only contains few latent features. Since mixture distributions are constrained in their L 1 norm, typical sparsity techniques based on L… (More)