  Adding edges between layers of interconnected networks is an important way to
optimize the spreading dynamics. While previous studies mostly focus on the
case of adding a single edge, the theoretical optimal strategy for adding
multiple edges still need to be studied. In this study, based on the
susceptible-infected-susceptible (SIS) model, we investigate the problem of
maximizing the stationary spreading prevalence in interconnected networks. For
two isolated networks, we maximize the spreading prevalence near the critical
point by choosing multiple interconnecting edges. We present a theoretical
analysis based on the discrete-time Markov chain approach to derive the
approximate optimal strategy. The optimal inter-layer structure predicted by
the strategy maximizes the spreading prevalence, meanwhile minimizes the
spreading outbreak threshold for the interconnected network simultaneously.
Numerical simulations on synthetic and real-world networks show that near the
critical point, the proposed strategy gives better performance than connecting
large degree nodes and randomly connecting.
