The Influence of Indirect Ties on Social Network

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

Network Dynamics http: //not-ionic. tumblr. com/ 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? Ø Indirect ties are known to be a strong force shaping the network dynamics. Ø We lack quantitative studies of the influence of indirect ties on network dynamics, especially for social distances longer than 2 hops. 4

Outline Ø Ø Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths 5

Datasets vary from online gaming networks to face-toface interaction networks and co-authorship networks Nodes Edges APL Edge weights D OT TF 2 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 6

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

Outline Ø Ø Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths 8

Using Indirect Ties for Link Prediction 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? 9

Link Prediction Results Networks TF 2 n Classifier 2 Metric Precision Recall F-Measure AUC SS 0. 75± 0. 012 0. 74± 0. 008 0. 77± 0. 009 AA 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 AA 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 Indirect ties are able to predict the formation of links Decision SS 0. 84± 0. 013 0. 84± 0. 002 0. 87± 0. 001 Treethe social even when path is longer than 2. IE 2 (J 48) TF 2 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. 66± 0. 010 10

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

Timing of Link Formation 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? 12

Link Formation Delay Definition 13

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

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

Outline Ø Ø Datasets and indirect tie measurements Indirect ties and link prediction Timing of link formation Indirect ties and information diffusion paths 16

Can Indirect Ties Predict Diffusion Paths? 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? 17

Experimental Setup Ground Truth Path Prediction Ø Linear Threshold (LT) model Ø in LT Ø Scale the value of as Ø ω [1 -10] in CA-I ω [1 -30] in CA-II ω [1 -100] in TF 2 Ø Calculate strength of indirect ties Ø Rank a user’s 2(3)-hop neighbors based on the calculated strength values Ø Define a cut-off threshold to select the user’s top. N indirect neighbors Compare 18

Prediction Evaluation (2 -hop paths) 19

Prediction Evaluation (3 -hop paths) Indirect ties can serve as a predictor for information diffusion paths. 20

Summary Ø Indirect ties have the power to predict link formation between people at social distances greater than 2. Ø The strength of an indirect tie positively correlates to the speed at which a direct link forms between the two people. Ø Indirect ties can serve as a predictor for diffusion paths in social networks. 21

Thanks! Distributed Systems Group http: //www. cse. usf. edu/dsg/ 22

Backup Slides Social Strength Metrics (Cntd…) j 0. 3 2 3 i 3 k j 3 i 7 3 i SS 2(m, i)=0. 44 k m 0. 3 2/(2 0 +3 )= + 7 0. 4 j ( 3/ m k SS 2(i, m)=0. 2775 0. 7 2 7 m 0. 4 j SS 2(i, m)=0. 2775 i 7/( 3+ 7)= 0. 7 k m 0. 3 )= 3/ 7 + 3 ( 23

Indirect Ties Infer Diffusion Paths Rank indirect relationship according to the score calculated by indirect tie measurements. Example User A’s 2 -hop contacts’ rank: where q is inverse proportional to ω e. g. , in CA-I. 24