  Designing reliable networks consists in finding topological structures, which
are able to successfully carry out desired processes and operations. When this
set of activities performed within a network are unknown and the only available
information is a probabilistic model reflecting topological network features,
highly probable networks are regarded as "reliable", in the sense of being
consistent with those probabilistic model. In this paper we are studying the
reliability maximization, based on the Exponential Random Graph Model (ERGM),
whose statistical properties has been widely used to capture complex
topological feature of real-world networks. Under such models the probability
of a network is maximized when specified structural properties appear in the
network. However, the search of maximally reliable (highly probable) networks
might result in difficult combinatorial optimization problems and an important
goal of this work is to translate them into solvable systems of linear
constraints. Analytical and numerical results are provided, using exact
optimization techniques and efficient computer implementation.
