Refining the Semantics of Social Influence

Abstract: With the proliferation of network data, researchers are increasingly focusing on questions investigating phenomena occurring on networks. This often includes analysis of peer-effects, i.e., how the connections of an individual affect that individual's behavior. This type of influence is not limited to direct connections of an individual (such as friends), but also to individuals that are connected through longer paths (for example, friends of friends, or friends of friends of friends). In this work, we identify an ambiguity in the definition of what constitutes the extended neighborhood of an individual. This ambiguity gives rise to different semantics and supports different types of underlying phenomena. We present experimental results, both on synthetic and real networks, that quantify differences among the sets of extended neighbors under different semantics. Finally, we provide experimental evidence that demonstrates how the use of different semantics affects model selection.