Inference for influence over multiple degrees of separation on a social network.

States and behaviors of different individuals are expected to be correlated across a social network. Christakis and Fowler have proposed a 'three degrees of influence rule' to characterize the extent of such dependence. In this paper, we discuss three distinct interpretations of such a rule, one involving only associations (which is the interpretation for which Christakis and Fowler give evidence), one involving actual causation, generally referred to as contagion or social influence, and one involving direct effects. We discuss analytic procedures appropriate for assessing evidence for each possible interpretation and the increasingly difficult methodological challenges present in each interpretation.