  We propose a method for constructing optimal block designs for experiments on
networks. The response model for a given network interference structure extends
the linear network effects model to incorporate blocks. The optimality criteria
are chosen to reflect the experimental objectives and an exchange algorithm is
used to search across the design space for obtaining an efficient design when
an exhaustive search is not possible. Our interest lies in estimating the
direct comparisons among treatments, in the presence of nuisance network
effects that stem from the underlying network interference structure governing
the experimental units, or in the network effects themselves. Comparisons of
optimal designs under different models, including the standard treatment
models, are examined by comparing the variance and bias of treatment effect
estimators. We also suggest a way of defining blocks, while taking into account
the interrelations of groups of experimental units within a network, using
spectral clustering techniques to achieve optimal modularity. We expect
connected units within closed-form communities to behave similarly to an
external stimulus. We provide evidence that our approach can lead to efficiency
gains over conventional designs such as randomized designs that ignore the
network structure and we illustrate its usefulness for experiments on networks.
