  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.
