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Friendship Paradox Redux: Your Friends Are More Interesting Than You

Nathan O. Hodas, Farshad Kooti, Kristina Lerman

arXiv:1304.3480v1cs.SIcs.CYnlin.AOphysics.soc-phstat.AP

TL;DR

The paper asks how the friendship paradox and its consequences for online information flow appear on Twitter. It analyzes Twitter activity and network data and compares users with different information loads. The results include the friendship paradox for over 98% of users, new activity and virality paradoxes, and lower sensitivity to smaller URL outbreaks among overloaded users.

  • Problem

    The friendship paradox’s consequences for cognitive limits and online information flow are not well examined, even though following more users can sharply increase incoming information.

    Source: Introduction · p. 1

  • Method

    The paper analyzes Twitter tweets and social links, validates friendship-paradox claims, and compares overloaded and underloaded users’ activity and cascade behavior.

    Source: Data · p. 2, Friendship Paradox · p. 2, Information Overload · p. 6

  • Results

    The friendship paradox holds for over 98% of Twitter users, and friends are more active and receive more viral content; overloaded users are less sensitive to smaller URL outbreaks.

    Source: Introduction · p. 2, Conclusion · p. 7

  • Takeaways & Limitations

    Following additional users can produce a super-linear increase in incoming information, which may impose significant cognitive load and prompt users to adjust their networks.

    Source: Conclusion · p. 8

Abstract

from arXiv · show

Feld's friendship paradox states that "your friends have more friends than you, on average." This paradox arises because extremely popular people, despite being rare, are overrepresented when averaging over friends. Using a sample of the Twitter firehose, we confirm that the friendship paradox holds for >98% of Twitter users. Because of the directed nature of the follower graph on Twitter, we are further able to confirm more detailed forms of the friendship paradox: everyone you follow or who follows you has more friends and followers than you. This is likely caused by a correlation we demonstrate between Twitter activity, number of friends, and number of followers. In addition, we discover two new paradoxes: the virality paradox that states "your friends receive more viral content than you, on average," and the activity paradox, which states "your friends are more active than you, on average." The latter paradox is important in regulating online communication. It may result in users having difficulty maintaining optimal incoming information rates, because following additional users causes the volume of incoming tweets to increase super-linearly. While users may compensate for increased information flow by increasing their own activity, users become information overloaded when they receive more information than they are able or willing to process. We compare the average size of cascades that are sent and received by overloaded and underloaded users. And we show that overloaded users post and receive larger cascades and they are poor detector of small cascades.

Introduction

The friendship paradox can bias how people assess themselves and their social worlds, while online networks add an information-flow consequence: friends may be more active than users can keep up with. The paper examines these effects on Twitter, including new activity and virality paradoxes and how information load relates to user behavior.

Introduction

  • The friendship paradox can bias self-perception because people use local networks to assess themselves and learn about the wider world.Friends’ greater connectivity also means greater aggregate exposure to biological pathogens, a principle used in epidemiological early-warning networks.Source: Introduction · p. 1
  • Following more users can sharply increase incoming information because those users tend to be more active than users are willing to consume.The resulting information flow may collide with cognitive limits and dilute attention to individual tweets.Source: Introduction · p. 1
  • The paper studies the evidence and consequences of the friendship paradox on Twitter, whose directed network enables a more detailed analysis.It also compares overloaded and underloaded users’ viral-content behavior, finding that overloaded users are less sensitive to smaller outbreaks of less popular URLs.Source: Introduction · pp. 1–2
  • The paper reports that the friendship paradox holds on Twitter and that friends and followers have more friends and followers than the user.It also introduces activity and virality paradoxes, and compares overloaded with underloaded users.Source: Introduction · p. 2

A Variety of Paradoxes on Twitter

Twitter’s directed follower graph allows the friendship paradox to be tested across friends and followers, including connectivity, popularity, activity, and URL virality. The analysis also checks whether spam accounts explain the observed paradoxes.

A Variety of Paradoxes on Twitter

  • Twitter’s directed ties distinguish users who receive posts from friends they follow from users who receive their broadcasts as followers.The paper uses “friend” to mean a followee, making the direction of the relationship central to its paradox variants.Source: A Variety of Paradoxes on Twitter · p. 2

Data

  • The study combines 476 million tweets (20–30% of all tweets posted June–December 2009) with Twitter social links, analyzing the subgraph of users who had tweeted: 5.8 million users and 193.9 million links.Source: Data · p. 2

Friendship Paradox

  • 98% of users’ friends and 98% of users’ followers are better connected; 99% and 98% of users are less popular than their friends and followers, respectively.A typical friend is ten times better connected, while a typical follower is almost 20 times better connected; Figure 2 summarizes the four comparisons.Source: Friendship Paradox · pp. 2–3, Figure 2 · p. 3

Friend Activity Paradox

  • 88% of users are less active than their average friend, rising to 99% in the one-week check.Activity is measured by tweets posted; the one-week check addresses the possibility that users became inactive over the longer period.Source: Friend Activity Paradox · p. 3, Figure 3 · p. 4

Virality Paradox

  • 86% of users posted less viral content than their friends, and 76% received smaller cascades than their friends.Among users who posted URLs, 79% had a lower average posted cascade size than their friends; 32% posted no URLs.Source: Virality Paradox · p. 4, Figure 4 · p. 4

Spam Filtering

  • After either spam-removal approach, all paradoxes still held; content- and activity-entropy filtering raised the less-active-than-friends share from 88% to 93%.The two approaches use a suspended-user/blacklisted-URL set and entropy-based classification.Source: Spam Filtering · pp. 4–5

Friend Paradox and Information Overload

Following more friends brings a super-linear increase in incoming information, while friends’ activity and connectivity are correlated. The section examines how overloaded users’ cascade activity and exposure differ from those of underloaded users.

Friend Paradox and Information Overload

User Activity and Incoming Information Volume

  • The average volume of information received by a user grows super-linearly with the number of friends, increasing quickly with connectivity; each new friend brings hundreds of new posts into the stream.Source: User Activity and Incoming Information… · p. 6
  • Users receiving more information are also more active, though the relationship becomes very noisy after about 500 posted tweets in two months.The authors include extremely active users, who could be spammers, because their activity affects the information load of their followers.Source: User Activity and Incoming Information… · p. 6
  • User activity correlates significantly with both friend and follower counts (p-value < 0.01), especially follower count; the detailed mechanism remains unclear.The authors suggest that activity could help users acquire followers, but leave the mechanism for future research.Source: Figure 6 · p. 5, User Activity and Incoming Information… · p. 6

Information Overload

  • The analysis groups users by tweets posted over two months, then classifies the top and bottom thirds by received tweets as overloaded and underloaded, respectively.It includes users who joined before June 2009 so their potential activity duration is identical.Source: Information Overload · p. 6
  • Across all four activity groups, overloaded users post cascades with larger mean size than underloaded users.Cascade size counts postings or retweets of a URL in the sample during the two-month period.Source: Information Overload · p. 6, Figure 7 · p. 7
  • Overloaded users receive larger cascades across all four activity groups, but see fewer small cascades and are poor detectors of developing cascades.They may learn about a cascade only once it is widely known in their network.Source: Information Overload · p. 6, Table 1 · p. 6

Related Work

Prior work uses the friendship paradox for early detection of outbreaks, but Twitter contagion also depends on whether users actively propagate content. The paper connects this issue to activity and connectivity, and discusses implications for overload and user recommendations.

Related Work

  • The friendship paradox arises because highly connected people are overrepresented among others’ friends, despite most people believing they have more friends than their friends do (Feld 1991; Zuckerman and Jost 2001).Prior work applied the paradox to early detection of virtual and pathogenic outbreaks (Christakis and Fowler 2010; Garcia-Herranz et al. 2012).Source: Related Work · p. 7
  • On Twitter, the paper reports that activity and connectivity are highly correlated, identifying this as a missing connection for understanding early detection of social contagion.Unlike pathogens, tweets must be actively propagated to become viral memes.Source: Related Work · p. 7
  • The activity paradox holds when activity and connectivity are highly correlated, as the paper reports for Twitter.Friends’ greater activity can make incoming information grow super-linearly as users add friends, reducing tweet visibility and dividing attention across topics.Source: Related Work · p. 7
  • Understanding how users discover and manage friendships may help networks recommend interesting users while accounting for information overload.The authors also point to possible influence of popular children on peers’ perceptions of alcohol and drug abuse.Source: Related Work · p. 7

Conclusion

The friendship paradox holds for over 98% of Twitter users, and friends are also more active and receive and send more viral content. These patterns connect activity with network connectivity and may contribute to information overload as users follow more people.

Conclusion

  • Over 98% of Twitter users exhibit the friendship paradox; friends also tend to be more active and receive and send more viral content.The authors report a large correlation between activity and both in- and out-degree in Twitter’s follower graph.Source: Conclusion · p. 7
  • Activity correlates with in- and out-degree, and the authors hypothesize that activity drives connectivity, producing the more detailed friendship paradox.Active users may gain visibility and followers, while more active users are also more interested in consuming content and follow more users.Source: Conclusion · pp. 7–8
  • Following additional users can increase incoming information super-linearly, potentially creating cognitive load against a finite communication budget.The authors suggest users may receive more incoming information than they prefer.Source: Conclusion · p. 8
  • Overloaded users are more likely to participate in viral cascades after controlling for activity, while each tweet’s visibility is diluted by their larger incoming volume.The authors suggest users may dynamically adjust their social networks to maintain an optimal level of information flux.Source: Conclusion · p. 8

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