the influence of indirect ties on social network dynamics

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, USA2Telefonica Research – Barcelona, Spain

3Yahoo Labs – Barcelona, Spain

Network Dynamics

2The spread of cheating behavior in an

online game social network

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 forceshaping the network dynamics.

We lack quantitative studies of theinfluence of indirect ties on networkdynamics, especially for social distanceslonger 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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JaccardCoefficient

(J)

Adamic-Adar (AA)

Social Strength

(SS)

J(a,b) =G(a)Ç G(b)

G(a)È G(b)

AA(a,b) =

1

log G(Z)ZÎG(a)∩G(b)

å

AA(a,b) =1

log(2)+

1

log(3)= 5.42

SSn(a,b) = 1- PpÎRa ,b

n(1-

minc,...kÎN ( p)

[NW (a,c),...NW (k,b)]

n)

NW (a,k) =

w (a,k,l)"lÎLi ,k

å

w (i,u,l)"lÎLi ,u

å"uÎNi

å

Outline

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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

DecisionTree(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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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:

J(a,b) > mean

AA(a,b) > mean

SS(a,b) > mean [C-mean]:

[C-max]:J(a,b) > max

AA(a,b) > max

SS(a,b) > max

J(a,b) > min

AA(a,b) > min

SS(a,b) > min

[C-min]:

Tie (a,b) is a strong

indirect tie

Tie Strength vs. Link Delay

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2−hop ties with C−max cr iterion in TF2 2−hop ties with C−mean cr iterion in TF2 2−hop ties with C−min cr iterion in TF2

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0.1

0.2

0.3

0.4

0−1 1−7 7−14 14−30 30−60 60+ 0−1 1−7 7−14 14−30 30−60 60+ 0−1 1−7 7−14 14−30 30−60 60+

Fra

ction ● strong tie

weak tie

3−hop ties with C−max cr iterion in TF2 3−hop ties with C−mean cr iterion in TF2 3−hop ties with C−min cr iterion in TF2

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0.0

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0−1 1−7 7−14 14−30 30−60 60+ 0−1 1−7 7−14 14−30 30−60 60+ 0−1 1−7 7−14 14−30 30−60 60+

Delay in Days

Fra

ction

2−hop ties with C−max criterion in IE 2−hop ties with C−mean criterion in IE 2−hop ties with C−min criterion in IE●

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0.2

0.4

0.6

0.8

0−5 5−10 10−15 15−20 20−25 25+ 0−5 5−10 10−15 15−20 20−25 25+ 0−5 5−10 10−15 15−20 20−25 25+

Fra

ction

3−hop ties with C−max criterion in IE 3−hop ties with C−mean criterion in IE 3−hop ties with C−min criterion in IE●

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0.0

0.2

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0−5 5−10 10−15 15−20 20−25 25+ 0−5 5−10 10−15 15−20 20−25 25+ 0−5 5−10 10−15 15−20 20−25 25+

Delay in Minutes

Fra

ction

3−hop ties with C−max cr iterion in TF2

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0.1

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0−1 1−7 7−14 14−30 30−60 60+

Delay in Days

Fra

ctio

n33% (strong)

vs. 7% (weak)

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

Outline

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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 topNindirect neighbors

Î

Î

Î

q

random(0,1) /wq pred

Compare

q = random(0,1)

Prediction Evaluation (2-hop paths)

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CA−I CA−II TF2

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0.50.60.70.80.9

2.5 5.0 7.5 10.0 10 20 30 25 50 75 100

Accura

cy

● Adamic−Adar Baseline Jaccard Social Strength

CA−I CA−II TF2●

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0.2

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2.5 5.0 7.5 10.0 10 20 30 25 50 75 100

Sensitiv

ity

CA−I CA−II TF2

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0.4

0.6

0.8

1.0

2.5 5.0 7.5 10.0 10 20 30 25 50 75 100Diffusion Parameter w

Spe

cific

ity

Prediction Evaluation (3-hop paths)

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CA−I CA−II TF2

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0.5

0.6

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2.5 5.0 7.5 10.00 10 20 30 25 50 75 100

Accu

racy

● Baseline Social Strength

CA−I CA−II TF2

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2.5 5.0 7.5 10.00 10 20 30 25 50 75 100

Se

nsitiv

ity

CA−I CA−II TF2

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0.4

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2.5 5.0 7.5 10.00 10 20 30 25 50 75 100

Diffusion Parameter w

Sp

ecific

ity

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/

the influence of indirect ties on social network dynamics

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