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Brian Karrer

Bio: Brian Karrer is an academic researcher from Facebook. The author has contributed to research in topics: Clustering coefficient & Bayesian optimization. The author has an hindex of 25, co-authored 38 publications receiving 6086 citations. Previous affiliations of Brian Karrer include University of Michigan & Santa Fe Institute.

Papers
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Journal ArticleDOI
TL;DR: This work demonstrates how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks and proposes a heuristic algorithm forcommunity detection using this objective function or its non-degree-corrected counterpart.
Abstract: Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them unsuitable for applications to real-world networks, which typically display broad degree distributions that can significantly affect the results. Here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks. We also propose a heuristic algorithm for community detection using this objective function or its non-degree-corrected counterpart and show that the degree-corrected version dramatically outperforms the uncorrected one in both real-world and synthetic networks.

2,024 citations

Posted Content
TL;DR: A strong effect of age on friendship preferences as well as a globally modular community structure driven by nationality are observed, but it is shown that while the Facebook graph as a whole is clearly sparse, the graph neighborhoods of users contain surprisingly dense structure.
Abstract: 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 structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component, and we confirm the "six degrees of separation" phenomenon on a global scale. Second, by studying the average local clustering coefficient and degeneracy of graph neighborhoods, we show that while the Facebook graph as a whole is clearly sparse, the graph neighborhoods of users contain surprisingly dense structure. Third, we characterize the assortativity patterns present in the graph by studying the basic demographic and network properties of users. We observe clear degree assortativity and characterize the extent to which "your friends have more friends than you". Furthermore, we observe a strong effect of age on friendship preferences as well as a globally modular community structure driven by nationality, but we do not find any strong gender homophily. We compare our results with those from smaller social networks and find mostly, but not entirely, agreement on common structural network characteristics.

938 citations

Journal ArticleDOI
TL;DR: This work describes a method for finding overlapping communities based on a principled statistical approach using generative network models and shows how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times.
Abstract: A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times. We test the method both on real-world networks and on synthetic benchmarks and find that it gives results competitive with previous methods. We also show that the same approach can be used to extract nonoverlapping community divisions via a relaxation method, and demonstrate that the algorithm is competitively fast and accurate for the nonoverlapping problem.

412 citations

Journal ArticleDOI
TL;DR: It is shown that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure.
Abstract: The discovery of community structure is a common challenge in the analysis of network data Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is statistically significant or whether, conversely, it could have arisen purely as a result of chance In this paper we show that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure We propose a suitable method for perturbing networks and a measure of the resulting change in community structure and use them to assess the significance of community structure in a variety of networks, both real and computer generated

362 citations

Proceedings ArticleDOI
27 Apr 2013
TL;DR: This paper combines survey and large-scale log data to examine how well users' perceptions of their audience match their actual audience on Facebook, and finds that social media users consistently underestimate their audience size for their posts.
Abstract: When you share content in an online social network, who is listening? Users have scarce information about who actually sees their content, making their audience seem invisible and difficult to estimate. However, understanding this invisible audience can impact both science and design, since perceived audiences influence content production and self-presentation online. In this paper, we combine survey and large-scale log data to examine how well users' perceptions of their audience match their actual audience on Facebook. We find that social media users consistently underestimate their audience size for their posts, guessing that their audience is just 27% of its true size. Qualitative coding of survey responses reveals folk theories that attempt to reverse-engineer audience size using feedback and friend count, though none of these approaches are particularly accurate. We analyze audience logs for 222,000 Facebook users' posts over the course of one month and find that publicly visible signals --- friend count, likes, and comments --- vary widely and do not strongly indicate the audience of a single post. Despite the variation, users typically reach 61% of their friends each month. Together, our results begin to reveal the invisible undercurrents of audience attention and behavior in online social networks.

343 citations


Cited by
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28 Jul 2005
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1(PfPMP1)与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员,通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

18,940 citations

Journal ArticleDOI
TL;DR: A thorough exposition of community structure, or clustering, is attempted, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists.
Abstract: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

9,057 citations

Journal ArticleDOI
TL;DR: A thorough exposition of the main elements of the clustering problem can be found in this paper, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

8,432 citations

Proceedings ArticleDOI
22 Jan 2006
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

7,116 citations

Journal ArticleDOI
09 Mar 2018-Science
TL;DR: A large-scale analysis of tweets reveals that false rumors spread further and faster than the truth, and false news was more novel than true news, which suggests that people were more likely to share novel information.
Abstract: We investigated the differential diffusion of all of the verified true and false news stories distributed on Twitter from 2006 to 2017. The data comprise ~126,000 stories tweeted by ~3 million people more than 4.5 million times. We classified news as true or false using information from six independent fact-checking organizations that exhibited 95 to 98% agreement on the classifications. Falsehood diffused significantly farther, faster, deeper, and more broadly than the truth in all categories of information, and the effects were more pronounced for false political news than for false news about terrorism, natural disasters, science, urban legends, or financial information. We found that false news was more novel than true news, which suggests that people were more likely to share novel information. Whereas false stories inspired fear, disgust, and surprise in replies, true stories inspired anticipation, sadness, joy, and trust. Contrary to conventional wisdom, robots accelerated the spread of true and false news at the same rate, implying that false news spreads more than the truth because humans, not robots, are more likely to spread it.

4,241 citations