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.

Random graphs

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. Ranking by retweets differs from the previous two rankings, indicating a gap in influence inferred from the number of followers and that from the popularity of one's tweets. We have analyzed the tweets of top trending topics and reported on their temporal behavior and user participation. We have classified the trending topics based on the active period and the tweets and show that the majority (over 85%) of topics are headline news or persistent news in nature. A closer look at retweets reveals that any retweeted tweet is to reach an average of 1,000 users no matter what the number of followers is of the original tweet. Once retweeted, a tweet gets retweeted almost instantly on next hops, signifying fast diffusion of information after the 1st retweet.To the best of our knowledge this work is the first quantitative study on the entire Twittersphere and information diffusion on it.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=7104&context=sis_research

What is Twitter, a social network or a news media?

Online social networking sites like Orkut, YouTube, and Flickr are among the most popular sites on the Internet. Users of these sites form a social network, which provides a powerful means of sharing, organizing, and finding content and contacts. The popularity of these sites provides an opportunity to study the characteristics of online social network graphs at large scale. Understanding these graphs is important, both to improve current systems and to design new applications of online social networks.This paper presents a large-scale measurement study and analysis of the structure of multiple online social networks. We examine data gathered from four popular online social networks: Flickr, YouTube, LiveJournal, and Orkut. We crawled the publicly accessible user links on each site, obtaining a large portion of each social network's graph. Our data set contains over 11.3 million users and 328 million links. We believe that this is the first study to examine multiple online social networks at scale.Our results confirm the power-law, small-world, and scale-free properties of online social networks. We observe that the indegree of user nodes tends to match the outdegree; that the networks contain a densely connected core of high-degree nodes; and that this core links small groups of strongly clustered, low-degree nodes at the fringes of the network. Finally, we discuss the implications of these structural properties for the design of social network based systems.

/pdf/measurement-and-analysis-of-online-social-networks-1uw6gt0k3a.pdf

Measurement and analysis of online social networks

Directed links in social media could represent anything from intimate friendships to common interests, or even a passion for breaking news or celebrity gossip. Such directed links determine the flow of information and hence indicate a user's influence on others — a concept that is crucial in sociology and viral marketing. In this paper, using a large amount of data collected from Twitter, we present an in-depth comparison of three measures of influence: indegree, retweets, and mentions. Based on these measures, we investigate the dynamics of user influence across topics and time. We make several interesting observations. First, popular users who have high indegree are not necessarily influential in terms of spawning retweets or mentions. Second, most influential users can hold significant influence over a variety of topics. Third, influence is not gained spontaneously or accidentally, but through concerted effort such as limiting tweets to a single topic. We believe that these findings provide new insights for viral marketing and suggest that topological measures such as indegree alone reveals very little about the influence of a user.

/pdf/measuring-user-influence-in-twitter-the-million-follower-44v20fo7ym.pdf

Measuring User Influence in Twitter: The Million Follower Fallacy

The structure and dynamics of multilayer networks

Online social networks have become extremely popular; numerous sites allow users to interact and share content using social links. Users of these networks often establish hundreds to even thousands of social links with other users. Recently, researchers have suggested examining the activity network - a network that is based on the actual interaction between users, rather than mere friendship - to distinguish between strong and weak links. While initial studies have led to insights on how an activity network is structurally different from the social network itself, a natural and important aspect of the activity network has been disregarded: the fact that over time social links can grow stronger or weaker. In this paper, we study the evolution of activity between users in the Facebook social network to capture this notion. We find that links in the activity network tend to come and go rapidly over time, and the strength of ties exhibits a general decreasing trend of activity as the social network link ages. For example, only 30% of Facebook user pairs interact consistently from one month to the next. Interestingly, we also find that even though the links of the activity network change rapidly over time, many graph-theoretic properties of the activity network remain unchanged.

/pdf/on-the-evolution-of-user-interaction-in-facebook-360xojt210.pdf

On the evolution of user interaction in Facebook

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 favorite-markings, but with a significant delay at each hop.

/pdf/a-measurement-driven-analysis-of-information-propagation-in-25ow81shda.pdf

A measurement-driven analysis of information propagation in the flickr social network

Every second, the thoughts and feelings of millions of people across the world are recorded in the form of 140-character tweets using Twitter. However, despite the enormous potential presented by this remarkable data source, we still do not have an understanding of the Twitter population itself: Who are the Twitter users? How representative of the overall population are they? In this paper, we take the first steps towards answering these questions by analyzing data on a set of Twitter users representing over 1% of the U.S. population. We develop techniques that allow us to compare the Twitter population to the U.S. population along three axes (geography, gender, and race/ethnicity), and find that the Twitter population is a highly non-uniform sample of the population.

/pdf/understanding-the-demographics-of-twitter-users-47staar74l.pdf

Understanding the Demographics of Twitter Users

Online social networks are now a popular way for users to connect, express themselves, and share content. Users in today's online social networks often post a profile, consisting of attributes like geographic location, interests, and schools attended. Such profile information is used on the sites as a basis for grouping users, for sharing content, and for suggesting users who may benefit from interaction. However, in practice, not all users provide these attributes.In this paper, we ask the question: given attributes for some fraction of the users in an online social network, can we infer the attributes of the remaining users? In other words, can the attributes of users, in combination with the social network graph, be used to predict the attributes of another user in the network? To answer this question, we gather fine-grained data from two social networks and try to infer user profile attributes. We find that users with common attributes are more likely to be friends and often form dense communities, and we propose a method of inferring user attributes that is inspired by previous approaches to detecting communities in social networks. Our results show that certain user attributes can be inferred with high accuracy when given information on as little as 20% of the users.

/pdf/you-are-who-you-know-inferring-user-profiles-in-online-3rfivj91dh.pdf

Alan Mislove

Papers

Measurement and analysis of online social networks

On the evolution of user interaction in Facebook

A measurement-driven analysis of information propagation in the flickr social network

Understanding the Demographics of Twitter Users

You are who you know: inferring user profiles in online social networks