Twitter, a microblogging service less than three years old, commands more than 41 million users as of July 2009 and is growing fast. Twitter users tweet about any topic within the 140-character limit and follow others to receive their tweets. The goal of this paper is to study the topological characteristics of Twitter and its power as a new medium of information sharing. We have crawled the entire Twitter site and obtained 41.7 million user profiles, 1.47 billion social relations, 4, 262 trending topics, and 106 million tweets. In its follower-following topology analysis we have found a non-power-law follower distribution, a short effective diameter, and low reciprocity, which all mark a deviation from known characteristics of human social networks [28]. In order to identify influentials on Twitter, we have ranked users by the number of followers and by PageRank and found two rankings to be similar.

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Online social networking sites like MySpace, Facebook, and Flickr have become a popular way to share and disseminate content. Their massive popularity has led to viral marketing techniques that attempt to spread content, products, and ideas on these sites. However, there is little data publicly available on viral propagation in the real world and few studies have characterized how information spreads over current online social networks. In this paper, we collect and analyze large-scale traces of information dissemination in the Flickr social network. Our analysis, based on crawls of the favorite markings of 2.5 million users on 11 million photos, aims at answering three key questions: (a) how widely does information propagate in the social network? (b) how quickly does information propagate? and (c) what is the role of word-of-mouth exchanges between friends in the overall propagation of information in the network? Contrary to viral marketing “intuition, ” we find that (a) even popular photos do not spread widely throughout the network, (b) even popular photos spread slowly through the network, and (c) information exchanged between friends is likely to account for over 50 % of all favoritemarkings, but with a significant delay at each hop.

Social networks are of interest to researchers in part because they are thought to mediate the flow of information in communities and organizations. Here we study the temporal dynamics of communication using on-line data, including e-mail communication among the faculty and staff of a large university over a two-year period. We formulate a temporal notion of “distance ” in the underlying social network by measuring the minimum time required for information to spread from one node to another — a concept that draws on the notion of vector-clocks from the study of distributed computing systems. We find that such temporal measures provide structural insights that are not apparent from analyses of the pure social network topology. In particular, we define the network backbone to be the subgraph consisting of edges on which information has the potential to flow the quickest. We find that the backbone is a sparse graph with a concentration of both highly embedded edges and long-range bridges — a finding that sheds new light on the relationship between tie strength and connectivity in social networks.

There is a widespread intuitive sense that different kinds of information spread differently on-line, but it has been difficult to evaluate this question quantitatively since it requires a setting where many different kinds of information spread in a shared environment. Here we study this issue on Twitter, analyzing the ways in which tokens known as hashtags spread on a network defined by the interactions among Twitter users. We find significant variation in the ways that widely-used hashtags on different topics spread. Our results show that this variation is not attributable simply to differences in “stickiness, ” the probability of adoption based on one or more exposures, but also to a quantity that could be viewed as a kind of “persistence ” — the relative extent to which repeated exposures to a hashtag continue to have significant marginal effects. We find that hashtags on politically controversial topics are particularly persistent, with repeated exposures continuing to have unusually large marginal effects on adoption; this provides, to our knowledge, the first large-scale validation of the “complex contagion” principle from sociology, which posits that repeated exposures to an idea are particularly crucial when the idea is in some way controversial or contentious. Among other findings, we discover that hashtags representing the natural analogues of Twitter idioms and neologisms are particularly non-persistent, with the effect of multiple exposures decaying rapidly relative to the first exposure. We also study the subgraph structure of the initial adopters for different widely-adopted hashtags, again finding structural differences across topics. We develop simulation-based and generative models to analyze how the adoption dynamics interact with the network structure of the early adopters on which a hashtag spreads.

Abstract—Social media forms a central domain for the production and dissemination of real-time information. Even though such flows of information have traditionally been thought of as diffusion processes over social networks, the underlying phenomena are the result of a complex web of interactions among numerous participants. Here we develop a Linear Influence Model where rather than requiring the knowledge of the social network and then modeling the diffusion by predicting which node will influence which other nodes in the network, we focus on modeling the global influence of a node on the rate of diffusion through the (implicit) network. We model the number of newly infected nodes as a function of which other nodes got infected in the past. For each node we estimate an influence function that quantifies how many subsequent infections can be attributed to the influence of that node over time. A nonparametric formulation of the model leads to a simple least squares problem that can be solved on large datasets. We validate our model on a set of 500 million tweets and a set of 170 million news articles and blog posts. We show that the Linear Influence Model accurately models influences of nodes and reliably predicts the temporal dynamics of information diffusion. We find that patterns of influence of individual participants differ significantly depending on the type of the node and the topic of the information. I.

Transmission of infectious diseases, propagation of information, and spread of ideas and influence through social networks are all examples of diffusion. In such cases we say that a contagion spreads through the network, a process that can be modeled by a cascade graph. Studying cascades and network diffusion is challenging due to missing data. Even a single missing observation in a sequence of propagation events can significantly alter our inferences about the diffusion process. We address the problem of missing data in information cascades. Specifically, given only a fraction C ′ of the complete cascade C, our goal is to estimate the properties of the complete cascade C, such as its size or depth. To estimate the properties of C, we first formulate k-tree model of cascades and analytically study its properties in the face of missing data. We then propose a numerical method that given a cascade model and observed cascade C ′ can estimate properties ofthecomplete cascade C. Weevaluate our methodology usinginformation propagation cascades in the Twitter network (70 million nodes and 2 billion edges), as well as information cascades arising in the blogosphere. Our experiments show that the k-tree model is an effective tool to study the effects of missing data in cascades. Most importantly, we show that our method (and the k-tree model) can accurately estimate properties of the complete cascade C even when 90 % of the data is missing. 1

Information spreading processes are central to human interactions. Despite recent studies in online domains, little is known about factors that could affect the dissemination of a single piece of information. In this paper, we address this challenge by combining two related but distinct datasets, collected from a large scale privacy-preserving distributed social sensor system. We find that the social and organizational context significantly impacts to whom and how fast people forward information. Yet the structures within spreading processes can be well captured by a simple stochastic branching model, indicating surprising independence of context. Our results build the foundation of future predictive models of information flow and provide significant insights towards design of communication platforms.

Motivated by the observation that the sparse tree-like subgraphs in a small world graph have large diameter, we analyze random spanning trees in a given host graph. We show that the diameter of a random spanning tree of a given host graph G is between c √ n and c ′ √ n log n with high probability., where c and c ′ depend on the spectral gap of G and the ratio of the moments of the degree sequence. For the special case of regular graphs, this result improves the previous lower bound by Aldous by a factor of log n. 1

The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling and analyzing social networks? We argue that unlike a random walk, which conserves the quantity diffusing on a network, many interesting social phenomena, such as the spread of information or disease on a social network, are fundamentally non-conservative. When an individual infects her neighbor with a virus, the total amount of infection increases. We classify diffusion processes as conservative and non-conservative and show how these differences impact the choice of metrics used for network analysis, as well as our understanding of network structure and behavior. We show that Alpha-Centrality, which mathematically describes non-conservative diffusion, leads to new insights into the behavior of spreading processes on networks. We give a scalable approximate algorithm for computing the Alpha-Centrality in a massive graph. We validate our approach on real-world online social networks of Digg. We show that a non-conservative metric, such as Alpha-Centrality, produces better agreement with empirical measure of influence than conservative metrics, such as PageRank. We hope that our investigation will inspire further exploration into the realms of conservative and non-conservative metrics in social network analysis. 1.