The Influence of Indirect Ties on Social Network Dynamics Xiang Zuo 1, Jeremy Blackburn 2, Nicolas Kourtellis 3, John Skvoretz 1 and Adriana Iamnitchi 1 1 University of South Florida – Florida, USA 2 Telefonica Research – Barcelona, Spain 3 Yahoo Labs – Barcelona, Spain

Network Dynamics 2

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. 3

Why Study Indirect Ties? 4  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 5  Datasets and indirect tie measurements  Indirect ties and link prediction  Timing of link formation  Indirect ties and information diffusion paths

Datasets 6 NetworksNodesEdgesAPLEdge weightsDOT TF22,4069,7204.2[1-21,767]12300 days IE4102,7653.6[1-191]990 days CA-I [1-52]14N/A CA-II1,1276,6903.4[1-127]11N/A Datasets vary from online gaming networks to face-to- face interaction networks and co-authorship networks

Indirect Tie Measurements 7 Jaccard Coefficient (J) Adamic- Adar (AA) Social Strength (SS)

Outline 8  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 9 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 10 NetworksnClassifier MetricPrecision Recall F-Measure AUC TF22 Decision Tree (J48) SS0.75± ± ±0.009 AA0.71± ±0.006 J0.51± ± ± ±0.008 IE2 SS0.84± ± ±0.001 AA0.69± ± ±0.003 J0.69± ± ± ±0.004 TF23SS0.63± ± ± ±0.030 IE3SS0.64± ± ±0.010 Indirect ties are able to predict the formation of links even when the social path is longer than 2.

Outline 11  Datasets and indirect tie measurements  Indirect ties and link prediction  Timing of link formation  Indirect ties and information diffusion paths

Timing of Link Formation 12 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 13

Tie Classification 14 Classify indirect ties into strong and weak with three criteria:

Tie Strength vs. Link Delay 15 33% (strong) vs. 7% (weak) Strong indirect ties form direct links quicker both in 2 and 3 hops.

Outline 16  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? 17 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 18 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) 19

Prediction Evaluation (3-hop paths) 20 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

22 Thanks! Distributed Systems Group

Social Strength Metrics (Cntd…) 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 SS 2 (i,m)= i j k m 7 3 i j k m SS 2 (m,i)=0.44 Backup Slides 0.7

Indirect Ties Infer Diffusion Paths 24 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.