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 Web today offers a tremendous number of sites and services that can provide useful data for researchers. Websites ranging from online social networks (e.g., Facebook, Twitter), to online marketplaces (e.g., eBay, Craigslist), to recommendation services (e.g., Yelp, TripAdvisor) can be used to examine human behavior at scale. However, collecting data from these services brings up a host of technical, legal, and ethical issues for researchers, and many research communities are still grappling with the challenges that obtaining data from these services presents. This chapter provides an overview of many such issues, aiming to provide practitioners with specific examples of how various services can be accessed and how different communities have dealt with the ethical and legal challenges that they present.

A Practitioner’s Guide to Ethical Web Data Collection

This chapter is focused towards the empirical validation of generation of powerlaw networks. Empirical growth data from four different networks (the Flickr and the YouTube online social networks, Wikipedia’s content graph, and the Internet’s AS-level graph) are used to show this growth. This study makes two contributions: First, the gathering of detailed measurements of the growth of four large-scale networks and make the data available to the research community. Second, the thorough investigation of the link creation processes in datasets. The inadequacy of preferential attachment (i.e., “the rich get richer”), a popular growth model, to explain growth has been revealed in this chapter.

https://www.springer.com/cda/content/document/cda_downloaddocument/9781461467281-c1.pdf?SGWID=0-0-45-1395606-p174894407

An Empirical Validation of Growth Models for Complex Networks

In the past couple of years, websites such as Facebook, MySpace, and YouTube have rocketed to the top of web popularity. These sites are instances of what is known as "Web 2.0". Notably, and in contrast to the more traditional popular sites such as portals, search engines, or news aggregators, these sites are organized around user identities and a social network (or graph) of links between identities.

The social network gives users a new basis for forming and maintaining relationships and locating, consuming, filtering, and publishing content. Since the social network is expressed in a formal way, it can also be used by non-user system components to improve performance, security, or other objectives based on assumptions about trust or shared interests. A social network system is a software system organized around a dynamic social network core. The study and understanding of these systems is highly relevant to the systems community.

Surprisingly, despite both their exciting possibilities and their amazing popularity growth, social network systems have been largely neglected by researchers. To begin to remedy this, we have organized this workshop; the First Workshop on Social Network Systems (SocialNets'08).

As a first-year workshop, we were pleasantly surprised to receive sixteen high-quality submissions. We accepted eight into the workshop, for an acceptance rate of exactly 50 percent. A tight reviewing schedule gave the program committee just over one week to complete and submit reviews. However, we are happy to report that all papers received at least three reviews from program committee members.

The workshop papers cover a range of topics on social network systems. The presentations are organized into three broad sessions; the measurement and analysis of existing social networks, issues of security and privacy in social network systems, and new applications that leverage social networks. Many of the papers are likely to spark lively discussion at the workshop.

Proceedings of the 1st Workshop on Social Network Systems

The Transport Layer Security (TLS) Public Key Infrastructure (PKI) is essential to the security and privacy of users on the Internet. Despite its importance, prior work from the mid-2010s has shown that mismanagement of the TLS PKI often led to weakened security guarantees, such as compromised certificates going unrevoked and many internet devices generating self-signed certificates. Many of these problems can be traced to manual processes that were the only option at the time. However, in the intervening years, the TLS PKI has undergone several changes: once-expensive TLS certificates are now freely available, and they can be obtained and reissued via automated programs.

Measurement and Analysis of Automated Certificate Reissuance

The success of platforms such as Facebook and Google has been due in no small part to features that allow advertisers to target ads in a fine-grained manner. However, these features open up the potential for discriminatory advertising when advertisers include or exclude users of protected classes---either directly or indirectly---in a discriminatory fashion. Despite the fact that advertisers are able to compose various targeting features together, the existing mitigations to discriminatory targeting have focused only on individual features; there are concerns that such composition could result in targeting that is more discriminatory than the features individually.In this paper, we first demonstrate how compositions of individual targeting features can yield discriminatory ad targeting even for Facebook's restricted targeting features for ads in special categories (meant to protect against discriminatory advertising). We then conduct the first study of the potential for discrimination that spans across three major advertising platforms (Facebook, Google, and LinkedIn), showing how the potential for discriminatory advertising is pervasive across these platforms. Our work further points to the need for more careful mitigations to address the issue of discriminatory ad targeting.

Alan Mislove

Papers

A Practitioner’s Guide to Ethical Web Data Collection

An Empirical Validation of Growth Models for Complex Networks

Proceedings of the 1st Workshop on Social Network Systems

Measurement and Analysis of Automated Certificate Reissuance

On the Potential for Discrimination via Composition