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

The microblogging site Twitter is now one of the most popular Web destinations. Due to the relative ease of data access, there has been significant research based on Twitter data, ranging from measuring the spread of ideas through society to predicting the behavior of real-world phenomena such as the stock market. Unfortunately, relatively little work has studied the changes in the Twitter ecosystem itself; most research that uses Twitter data is typically based on a small time-window of data, generally ranging from a few weeks to a few months.  Twitter is known to have evolved significantly since its founding, and it remains unclear whether prior results still hold, and whether the (often implicit) assumptions of proposed systems are still valid. In this paper, we take a first step towards answering these question by focusing on the evolution of Twitter's users and their behavior.  Using a set of over 37 billion tweets spanning over seven years, we quantify how the users, their behavior, and the site as a whole have evolved.  We observe and quantify a number of trends including the spread of Twitter across the globe, the rise of spam and malicious behavior, the rapid adoption of tweeting conventions, and the shift from desktop to mobile usage.  Our results can be used to interpret and calibrate previous Twitter work, as well as to make future projections of the site as a whole.

/pdf/the-tweets-they-are-a-changin-evolution-of-twitter-users-and-ps8pwofcak.pdf

The Tweets They Are a-Changin’: Evolution of Twitter Users and Behavior

The rise of e-commerce has unlocked practical applications for algorithmic pricing (also called dynamic pricing algorithms), where sellers set prices using computer algorithms. Travel websites and large, well known e-retailers have already adopted algorithmic pricing strategies, but the tools and techniques are now available to small-scale sellers as well. While algorithmic pricing can make merchants more competitive, it also creates new challenges. Examples have emerged of cases where competing pieces of algorithmic pricing software interacted in unexpected ways and produced unpredictable prices, as well as cases where algorithms were intentionally designed to implement price fixing. Unfortunately, the public currently lack comprehensive knowledge about the prevalence and behavior of algorithmic pricing algorithms in-the-wild. In this study, we develop a methodology for detecting algorithmic pricing, and use it empirically to analyze their prevalence and behavior on Amazon Marketplace. We gather four months of data covering all merchants selling any of 1,641 best-seller products. Using this dataset, we are able to uncover the algorithmic pricing strategies adopted by over 500 sellers. We explore the characteristics of these sellers and characterize the impact of these strategies on the dynamics of the marketplace.

https://www.ccs.neu.edu/home/amislove/publications/Amazon-WWW.pdf

An Empirical Analysis of Algorithmic Pricing on Amazon Marketplace

Recently, online social networking sites have exploded in popularity Numerous sites are dedicated to finding and maintaining contacts and to locating and sharing different types of content Online social networks represent a new kind of information network that differs significantly from existing networks like the Web For example, in the Web, hyperlinks between content form a graph that is used to organize, navigate, and rank information The properties of the Web graph have been studied extensively, and have lead to useful algorithms such as PageRank In contrast, few links exist between content in online social networks and instead, the links exist between content and users, and between users themselves However, little is known in the research community about the properties of online social network graphs at scale, the factors that shape their structure, or the ways they can be leveraged in information systems 
In this thesis, we use novel measurement techniques to study online social networks at scale, and use the resulting insights to design innovative new information systems First, we examine the structure and growth patterns of online social networks, focusing on how users are connecting to one another We conduct the first large-scale measurement study of multiple online social networks at scale, capturing information about over 50 million users and 400 million links Our analysis identifies a common structure across multiple networks, characterizes the underlying processes that are shaping the network structure, and exposes the rich community structure 
Second, we leverage our understanding of the properties of online social networks to design new information systems Specifically, we build two distinct applications that leverage different properties of online social networks We present and evaluate Ostra, a novel system for preventing unwanted communication that leverages the difficulty in establishing and maintaining relationships in social networks We also present, deploy, and evaluate PeerSpective, a system for enhancing Web search using the natural community, structure in social networks Each of these systems has been evaluated on data from real online social networks or in a deployment with real users

/pdf/online-social-networks-measurement-analysis-and-applications-4nxtfj85tm.pdf

Online social networks: measurement, analysis, and applications to distributed information systems

The enormous financial success of online advertising platforms is partially due to the precise targeting features they offer. Although researchers and journalists have found many ways that advertisers can target---or exclude---particular groups of users seeing their ads, comparatively little attention has been paid to the implications of the platform's ad delivery process, comprised of the platform's choices about which users see which ads. It has been hypothesized that this process can "skew" ad delivery in ways that the advertisers do not intend, making some users less likely than others to see particular ads based on their demographic characteristics. In this paper, we demonstrate that such skewed delivery occurs on Facebook, due to market and financial optimization effects as well as the platform's own predictions about the "relevance" of ads to different groups of users. We find that both the advertiser's budget and the content of the ad each significantly contribute to the skew of Facebook's ad delivery. Critically, we observe significant skew in delivery along gender and racial lines for "real" ads for employment and housing opportunities despite neutral targeting parameters. Our results demonstrate previously unknown mechanisms that can lead to potentially discriminatory ad delivery, even when advertisers set their targeting parameters to be highly inclusive. This underscores the need for policymakers and platforms to carefully consider the role of the ad delivery optimization run by ad platforms themselves---and not just the targeting choices of advertisers---in preventing discrimination in digital advertising.

Discrimination through Optimization: How Facebook's Ad Delivery Can Lead to Biased Outcomes

This paper describes a cooperative overlay network that provides anonymous communication services for participating users. The Anonymizing Peer-to-Peer Proxy (AP3) system provides clients with three primitives: (i) anonymous message delivery, (ii) anonymous channels, and (iii) secure pseudonyms. AP3 is designed to be lightweight, low-cost and provides "probable innocence" anonymity to participating users, even under a large-scale coordinated attack by a limited fraction of malicious overlay nodes. Additionally, we use AP3's primitives to build novel anonymous group communication facilities (multicast and anycast), which shield the identity of both publishers and subscribers.

/pdf/ap3-cooperative-decentralized-anonymous-communication-z2hpdlxe5r.pdf

Alan Mislove

Papers

The Tweets They Are a-Changin’: Evolution of Twitter Users and Behavior

An Empirical Analysis of Algorithmic Pricing on Amazon Marketplace

Online social networks: measurement, analysis, and applications to distributed information systems

Discrimination through Optimization: How Facebook's Ad Delivery Can Lead to Biased Outcomes

AP3: cooperative, decentralized anonymous communication