Analysis of Topological Analysis of Topological Characteristics of Huge Characteristics of Huge

Online Social Networking Online Social Networking ServicesServices

Y.-Y. Ahn, S. Han, H. Kwak, S. Moon, H. JeongY.-Y. Ahn, S. Han, H. Kwak, S. Moon, H. JeongKAIST, Deajeon, South KoreaKAIST, Deajeon, South Korea

High-Level Questions in the High-Level Questions in the PaperPaper

Are online networks similar to offline Are online networks similar to offline networks?networks? What are online networks’ characteristics?What are online networks’ characteristics? Is sampling representative?Is sampling representative? How do online networks evolve?How do online networks evolve?

You should all know what they found You should all know what they found out…out…

1.1. Are these the right questions to ask?Are these the right questions to ask?

2.2. Is the evaluation sound?Is the evaluation sound?

3.3. Are the results surprising?Are the results surprising?

My High-Level QuestionsMy High-Level Questions

Question #1:Question #1:Are these the right questions to Are these the right questions to

ask?ask?

Why is it interestingWhy is it interesting

Map new phenomenonMap new phenomenon

One interesting study-case One interesting study-case

Why is it non-trivial?Why is it non-trivial?

Or is it…? Or is it…?

Data accessibilityData accessibility

Sampling analysisSampling analysis

Cyworld as a representative Cyworld as a representative online social network online social network

Question #2:Question #2:Is the evaluation sound?Is the evaluation sound?

number of triangles connected to vertex inumber of triples centered on vertex i

2 |{(v,w)|(i,v)(i,w)(v,w) Є E }|Ki (Ki -1)

Ci =

Ci =

(Newman ,SIAM Review 2003)

Aside 1: Calculating clustering Aside 1: Calculating clustering coeff. coeff.

Aside 2: Snowball SamplingAside 2: Snowball Sampling Under-sample low degree nodesUnder-sample low degree nodes

Over-sample high degree nodesOver-sample high degree nodes

Underestimate power law Underestimate power law coefficientcoefficient

Underestimating Underestimating αα

Estimated

K

P(K>k) = Fraction of

vertices with degree >=k

EvaluationEvaluation Snowball sampling method evaluationSnowball sampling method evaluation

More quantitative analysis…More quantitative analysis…

-3.2

Evaluation : Power lawEvaluation : Power law ““Clear power-law” :Clear power-law” :

Historical AnalysisHistorical Analysis

http://www.internetworldstats.com

Internet hosts in Europehttp://gandalf.it/data/data2.htm

Can the path length be Can the path length be calculated? calculated?

Question #3:Question #3:Are the results surprising?Are the results surprising?

Interesting findingsInteresting findings

Huge social networks are not ‘clean’. Huge social networks are not ‘clean’.

Different scaling (= user types?)Different scaling (= user types?)

Sampling – some rules of thumb for Sampling – some rules of thumb for rationsrations

Assortative mixing pattern in Assortative mixing pattern in social networkssocial networks

Intuitive for race examples in SF, Intuitive for race examples in SF, 58’58’

Found to be true even for degree Found to be true even for degree correlation correlation

Is it? Is it? Online networksOnline networks Other networksOther networks

Implications?Implications?Cyworld paper:6-9/2006100k users of 33M0.3%

Flicker paper:10-11/2006 3M users out of 27M 11.3%

Questions for discussionQuestions for discussion Is SK the model representative? Is SK the model representative?

Do social networks really display assortative Do social networks really display assortative mixing w.r.t degree correlation? Implications mixing w.r.t degree correlation? Implications

How should we analyze networks with multiple How should we analyze networks with multiple user types? Implications? user types? Implications?

How do we use findings to leverage How do we use findings to leverage Security (degree of shared interest, reliability)Security (degree of shared interest, reliability) Robustness Robustness Recommendations (beyond friends?)Recommendations (beyond friends?)