randomization* [@ugander_graph_2013]. Since the counterfactual situations of interest involve all vertices being in the same condition, the intuition is that assigning a vertex and vertices near it in the network into the same condition, the vertex is “closer” to the counterfactual situation of interest. For analysis methods, we consider methods that define *effective treatments* such that only units that are effectively in global treatment or global control are used to estimate the ATE. For example, an estimator for the ATE might only compare units in treatment that are surrounded by units in treatment with units in control that are surrounded by units in control. The intuition is that a unit that meets one of these conditions is “closer” to a counterfactual situation of interest.

The rest of the paper is structured as follows. We briefly review some related work on experiments in networks. Section \[sec:model\] presents a model of the process of experimentation in networks, including initialization of the network, treatment assignment, outcome generation, and analysis. This formalization allows us to develop theorems giving sufficient conditions for bias reduction. To develop further understanding of the magnitude of the bias and error reduction in practice, Section \[sec:simulations\] presents simulations using networks 