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Understanding mechanisms driving link formation in dynamic social networks isa long-standing problem that has implications to understanding social structureas well as link prediction and recommendation. Social networks exhibit a highdegree of transitivity, which explains the successes of common neighbor-basedmethods for link prediction. In this paper, we examine mechanisms behind linkformation from the perspective of an ego node. We introduce the notion ofpersonalized degree for each neighbor node of the ego, which is the number ofother neighbors a particular neighbor is connected to. From empirical analyseson four on-line social network datasets, we find that neighbors with higherpersonalized degree are more likely to lead to new link formations when theyserve as common neighbors with other nodes, both in undirected and directedsettings. This is complementary to the finding of Adamic and Adar that neighbornodes with higher (global) degree are less likely to lead to new linkformations. Furthermore, on directed networks, we find that personalizedout-degree has a stronger effect on link formation than personalized in-degree,whereas global in-degree has a stronger effect than global out-degree. Wevalidate our empirical findings through several link recommendation experimentsand observe that incorporating both personalized and global degree into linkrecommendation greatly improves accuracy.

Personalized Degrees: Effects on Link Formation in Dynamic Networks from an Egocentric Perspective