  This paper studies how a centralized planner can modify the structure of a
social or information network to reduce polarization. First, polarization is
found to be highly dependent on degree and structural properties of the network
-- including the well-known isoperimetric number (i.e., Cheeger constant). We
then formulate the planner's problem under full information, and motivate
disagreement-seeking and coordinate descent heuristics. A novel setting for the
planner in which the population's innate opinions are adversarially chosen is
introduced, and shown to be equivalent to maximization of the Laplacian's
spectral gap. We prove bounds for the effectiveness of a strategy that adds
edges between vertices on opposite sides of the cut induced by the spectral
gap's eigenvector. Finally, these strategies are evaluated on six real-world
and synthetic networks. In several networks, we find that polarization can be
significantly reduced through the addition of a small number of edges.
