The Influence of Indirect Ties on Social Network Dynamics

Xiang Zuo1, Jeremy Blackburn2, Nicolas Kourtellis3, John Skvoretz1 and Adriana Iamnitchi1

1University of South Florida – Florida, USA 2Telefonica Research – Barcelona, Spain 3Yahoo Labs – Barcelona, Spain

Network Dynamics

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http://not-ionic.tumblr.com/

What Is an Indirect Tie?

An indirect tie is defined as a relationship between two individuals who have no direct relation but are connected through other node(s) in the network.

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Why Study Indirect Ties?

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Indirect ties are known to be a strong force shaping the network dynamics.

We lack quantitative studies of the influence of indirect ties on network dynamics, especially for social distances longer than 2 hops.

Outline

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Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths

Datasets

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Networks Nodes Edges APL Edge weights D OT

TF2 2,406 9,720 4.2 [1-21,767] 12 300 days

IE 410 2,765 3.6 [1-191] 9 90 days

CA-I 348 595 6.1 [1-52] 14 N/A

CA-II 1,127 6,690 3.4 [1-127] 11 N/A

Datasets vary from online gaming networks to face-to-face interaction networks and co-authorship networks

Indirect Tie Measurements

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Jaccard Coefficient

(J)

Adamic-Adar (AA)

Social Strength

(SS)

Outline

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Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths

Using Indirect Ties for Link Prediction

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Can we use a 2-hop (or 3-hop) indirect tie between nodes that are not directly connected to predict whether a link will form between them?

Link Prediction Results

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Networks n Classifier Metric Precision Recall F-Measure AUC

TF2 2

Decision Tree (J48)

SS 0.75±0.012 0.74±0.008 0.74±0.008 0.77±0.009

AA 0.71±0.004 0.71±0.004 0.71±0.004 0.71±0.006

J 0.51±0.007 0.51±0.006 0.50±0.008 0.51±0.008

IE 2SS 0.84±0.013 0.84±0.002 0.84±0.002 0.87±0.001

AA 0.69±0.002 0.69±0.002 0.68±0.003 0.70±0.003

J 0.69±0.007 0.68±0.005 0.68±0.001 0.68±0.004

TF2 3 SS 0.63±0.020 0.63±0.010 0.62±0.010 0.64±0.030

IE 3 SS 0.64±0.010 0.63±0.010 0.63±0.010 0.66±0.010

Indirect ties are able to predict the formation of links even when the social path is longer than 2.

Outline

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Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths

Timing of Link Formation

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Link formation delay: the interval

between the time when the link

formation conditions are met and

the time when the link forms.

Is there any connection between the strength of an indirect tie and the delay of link formation?

Link Formation Delay Definition

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Tie Classification

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Classify indirect ties into strong and weak with

three criteria:

Tie Strength vs. Link Delay

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33% (strong) vs. 7% (weak)

Strong indirect ties form direct links quicker both in 2 and 3 hops.

Outline

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Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths

Can Indirect Ties Predict Diffusion Paths?

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Given that a user received a piece of information at time step t, can we predict which other users will receive this information at time step t+2 or t+3?

Experimental Setup

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Ground Truth Linear Threshold (LT)

model in LT Scale the value of as

ω [1-10] in CA-I ω [1-30] in CA-II ω [1-100] in TF2

Path Prediction Calculate strength of indirect

ties Rank a user’s 2(3)-hop

neighbors based on the calculated strength values

Define a cut-off threshold to select the user’s topN indirect neighbors

Compare

Prediction Evaluation (2-hop paths)

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Prediction Evaluation (3-hop paths)

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Indirect ties can serve as a predictor for information diffusion paths.

Summary

Indirect ties have the power to predict link

formation between people at social distances

greater than 2.

The strength of an indirect tie positively

correlates to the speed at which a direct link

forms between the two people.

Indirect ties can serve as a predictor for

diffusion paths in social networks. 21

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Thanks!

Distributed Systems Grouphttp://www.cse.usf.edu/dsg/

Social Strength Metrics (Cntd…)

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3 2

i

j

k

m

7 3

i

j

k

m

3/(7+3)=0.3

7/(3+7)=0.7

2/(2+3)=0.4

3/(3+7)=0.3

SS2(i,m)=0.2775

SS2(i,m)=0.2775

3 2i

j

k

m

7 3

i

j

k

m

0.3

0.3 0.4

SS2(m,i)=0.44

Backup Slides

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Indirect Ties Infer Diffusion Paths

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Rank indirect relationship according to the score

calculated by indirect tie measurements.

where q is inverse proportional to ω

User A’s 2-hop contacts’ rank:

Example

e.g., in CA-I.