In this paper, we consider a model of relativistic networks, a topological extension of the model of relativistic particles. Numerical experiments are performed to study thermodynamical properties of the model and their relationship with explicit symmetry of solutions under time reversal. An efficient algorithm is constructed, allowing to generate numerical solutions of high complexity in the given model. The algorithm includes a generator of random topology, an optimal choice of stiffness coefficients for the network and a solver for constrained optimization problem, describing an equilibrium of the network. A system, studied in the given paper, contains about 100 thousands of equations and inequalities. Possible extensions of the algorithm are discussed, necessary for processing of relativistic networks of higher complexity, containing millions of equations.