University of California at Santa Barbara

Christo Wilson, Bryce Boe, Alessandra Sala, Krishna P. N. Puttaswamy, and Ben Zhao

Social Networks

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Social Applications

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Enables new ways to solve problems for distributed systems Social web search Social bookmarking Social marketplaces Collaborative spam filtering (RE: Reliable

Email) How popular are social applications?

Facebook Platform – 50,000 applications Popular ones have >10 million users

each3

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Social Graphs and User Interactions Social applications rely on

1. Social graph topology2. User interactions

Currently, social applications evaluated just using social graph Assume all social links are equally

important/interactive Is this true in reality? Milgram’s familiar stranger Connections for ‘status’ rather than ‘friendship’

Incorrect assumptions lead to faulty application design and evaluation

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Goals

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Question: Are social links valid indicators of real user interaction? First large scale study of Facebook

10 million users (15% of total users) / 24 million interactions

Use data to show highly skewed distribution of interactions <1% of people on Facebook talk to >50% of their friends

Propose new model for social graphs that includes interaction information Interaction Graph Reevaluate existing social application using new

model In some cases, break entirely

• Characterizing Facebook• Analyzing User Interactions• Interaction Graphs• Effects on Social Applications

Outline

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Crawling Facebook for Data

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Facebook is the most popular social network Crawling social networks is difficult

Too large to crawl completely, must be sampled Privacy settings may prevent crawling

Thankfully, Facebook is divided into ‘networks’ Represent geographic regions, schools,

companies Regional networks are not authenticated

Crawling for Data, cont.

Crawled Facebook regional networks 22 largest networks: London, Australia, New York, etc Timeframe: March – May 2008 Start with 50 random ‘seed’ users, perform BFS search

Data recorded for each user: Friends list History of wall posts and photo comments

Collectively referred to as interactions Most popular publicly accessible Facebook

applications

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Facebook Orkut1

Number of Users Crawled 10,697,000 1,846,000

Percentage of Total Users 15% 26.9%

Number of Social Links Crawled

408,265,000 22,613,000

Radius 9.8 6

Diameter 13.4 9

Average Path Length 4.8 4.25

Clustering Coefficient 0.164 0.171

Power-law Coefficient α=1.5, D=0.55

α=1.5, D=0.6

High Level Graph Statistics

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1. A. Mislove, M. Marcon, K. P. Gummadi, P. Druschel, and B. Bhattacharjee. Measurement and analysis of online social networks. In Proc. of IMC, October 2007.

•Based on Facebook’s total size of 66 million users in early 2008

•Represents ~50% of all users in the crawled regions

•~49% of links were crawlable

•This provides a lower bound on the average number of in-network friends

•Avg. social degree = ~77

•Low average path length and high clustering coefficient indicate Facebook is small-world

• Characterizing Facebook• Analyzing User Interactions• Interaction Graphs• Effects on Social Applications

Outline

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Analyzing User Interactions

Having established that Facebook has the expected social graph properties…

Question: Are social links valid indicators of real user interaction?

Examine distribution of interactions among friends

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Distribution Among Friends

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For 50% of users, 70% of interaction comes from 7% of

friends.

Almost nobody interacts with more than 50% of their friends!

For 50% of users, 100% of interaction comes from 20% of

friends.

•Social degree does not accurately predict human behavior

•Initial Question: Are social links valid indicators of real user interaction?

Answer: NO

•Social degree does not accurately predict human behavior

•Initial Question: Are social links valid indicators of real user interaction?

Answer: NO

• Characterizing Facebook• Analyzing User Interactions• Interaction Graphs• Effects on Social Applications

Outline

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A Better Model of Social Graphs

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Answer to our initial question: Not all social links are created equal Implication: can not be used to evaluate

social applications What is the right way to model social

networks? More accurately approximate reality by

taking user interactivity into account Interaction Graphs

Chun et. al. IMC 2008

Interaction Graphs

Definition: a social graph parameterized by… n : minimum number of interactions per

edge t : some window of time for interactions

n = 1 and t = {2004 to the present}

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Social vs. Interaction Degree

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1:1 Degree Ratio

Dunbar’s Number (150)

99% of Facebook Users

•Interaction graph prunes useless edges

•Results agree with theoretical limits on human social cognition

•Interaction graph prunes useless edges

•Results agree with theoretical limits on human social cognition

Interaction Graph Analysis

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Do Interaction Graphs maintain expected social network graph properties?

Social Graph Interaction Graph

Number of Vertices 10,697,000 8,403,000

Number of Edges 408,265,000 94,665,000

Radius 9.8 12.4

Diameter 13.4 19.8

Average Path Length 4.8 7.3

Clustering Coefficient 0.164 0.078

Power-law Coefficient α=1.5, D=0.55 α=1.5, D=0.24

•Interaction Graphs still have

Power-law scaling

Scale-free behavior

Small-world clustering

•… But, exhibit less of these characteristics than the full social network

•Interaction Graphs still have

Power-law scaling

Scale-free behavior

Small-world clustering

•… But, exhibit less of these characteristics than the full social network

• Characterizing Facebook• Analyzing User Interactions• Interaction Graphs• Effects on Social

Applications

Outline

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Social Applications, Revisited

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Recap: Need a better model to evaluate social

applications Interaction Graphs augment social graphs

with interaction information How do these changes effect social

applications? Sybilguard Analysis of Reliable Email in the paper

Sybilguard

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Sybilguard is a system for detecting Sybil nodes in social graphs

Why do we care about detecting Sybils? Social network based games:

Social marketplaces:

How Sybilguard works Key insight: few edges between Sybils and

legitimate users (attack edges) Use persistent routing tables and random walks

to detect attack edges

Sybilguard Algorithm

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Step 1:

Bootstrap the network.

All users exchange signed keys.

Key exchange implies that both parties are human and trustworthy.

Step 2:

Choose a verifier (A) and a suspect (B).

A and B send out random walks of a certain length (2).

Look for intersections.

A knows B is not a Sybil because multiple paths intersect and they do so at different nodes.

A

B

Sybilguard Algorithm, cont.

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A

B

Sybilguard Caveats

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Bootstrapping requires human interaction Evaluating Sybilguard on the social graph is

overly optimistic because most friends never interact!

Better to evaluate using Interaction Graphs

Expected Impact

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Fewer of edges, lower clustering lead to reduced performance

Why? Self-loops

A

B

Sybilguard on Interaction Graphs

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•When evaluated under real world conditions, performance of social applications changes dramatically

•When evaluated under real world conditions, performance of social applications changes dramatically

Conclusion

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First large scale analysis of Facebook Answer the question: Are social links

valid indicators of real user interaction? Formulate new model of social networks:

Interaction Graphs Demonstrate the effect of Interaction

Graphs on social applications Final takeaway: when building social

applications, use interaction graphs!

Anonymized Facebook data (social graphs and interaction graphs) will be available for download soon at the Current Lab website!

http://current.cs.ucsb.edu/facebook

Questions?

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Social Networks

Social Networks are popular platforms for interaction, communication and collaboration > 110 million users

9th most trafficked site on the Internet

> 170 million users #1 photo sharing site 4th most trafficked site on the Internet 114% user growth in 2008

> 800 thousand users 1,689% user growth in 2008

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Facebook Orkut1

Number of Users Crawled 10,697,000 1,846,000

Percentage of Total Users 15% 26.9%

Number of Social Links Crawled

408,265,000 22,613,000

Radius 9.8 6

Diameter 13.4 9

Average Path Length 4.8 4.25

Clustering Coefficient 0.164 0.171

Power-law Coefficient α=1.5, D=0.55

α=1.5, D=0.6

High Level Graph Statistics

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1. A. Mislove, M. Marcon, K. P. Gummadi, P. Druschel, and B. Bhattacharjee. Measurement and analysis of online social networks. In Proc. of IMC, October 2007.

•Based on Facebook’s total size of 66 million users in early 2008

•Represents ~50% of all users in the crawled regions

•~49% of links were crawlable

•This provides a lower bound on the average number of in-network friends

•Avg. social degree = ~77

•Clustering Coefficient measures strength of local cliques

•Measured between zero (random graphs) and one (complete connectivity)

•Social networks display power law degree distribution

•Alpha is the curve of the power law

•D is the fitting error

Social Degree CDF

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Nodes vs. Total Interactions

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Top 10% of most well connected users are

responsible for 60% of total interactions

Top 10% of most interactive users are responsible for 85%

of total interactions•Social degree does not accurately predict human behavior

•Interactions are highly skewed towards a small percent of the Facebook population

•Social degree does not accurately predict human behavior

•Interactions are highly skewed towards a small percent of the Facebook population