Growing connected networks under privacy constraint: Achieving trade-off between performance and security

In this paper, we consider the problem of adding links into an undirected connected network. The objective is to achieve a trade-off between maximizing the algebraic connectivity of the resulting network (which defines the convergence speed of the consensus protocol) and minimizing the increase of the largest eigenvalue of its adjacency matrix, namely, maintaining the network to be secured against infection. In addition, the problem needs to be solved under privacy constraint on the network corresponding to the unavailability of the global network topology. To this end, a distributed strategy performed by each nodes and based solely upon their local neighbors information is proposed. The approach is composed of eigenvalue sensitivity analysis and distributed estimation of eigenvectors corresponding to both performance and security metrics. A numerical example is presented to demonstrate and evaluate the proposed strategy.