  Designing networks with specified collective properties is useful in a
variety of application areas, enabling the study of how given properties affect
the behavior of network models, the downscaling of empirical networks to
workable sizes, and the analysis of network evolution. Despite the importance
of the task, there currently exists a gap in our ability to systematically
generate networks that adhere to theoretical guarantees for the given property
specifications. In this paper, we propose the use of Mixed-Integer Linear
Optimization modeling and solution methodologies to address this Network
Generation Problem. We present a number of useful modeling techniques and apply
them to mathematically express and constrain network properties in the context
of an optimization formulation. We then develop complete formulations for the
generation of networks that attain specified levels of connectivity, spread,
assortativity and robustness, and we illustrate these via a number of
computational case studies.
