  This paper aims to maximize algebraic connectivity of networks via topology
design under the presence of constraints and an adversary. We are concerned
with three problems. First, we formulate the concave maximization topology
design problem of adding edges to an initial graph, which introduces a
nonconvex binary decision variable, in addition to subjugation to general
convex constraints on the feasible edge set. Unlike previous methods, our
method is justifiably not greedy and capable of accommodating these additional
constraints. We also study a scenario in which a coordinator must selectively
protect edges of the network from a chance of failure due to a physical
disturbance or adversarial attack. The coordinator needs to strategically
respond to the adversary's action without presupposed knowledge of the
adversary's feasible attack actions. We propose three heuristic algorithms for
the coordinator to accomplish the objective and identify worst-case preventive
solutions. Each algorithm is shown to be effective in simulation and we provide
some discussion on their compared performance.
