Improving network connectivity using trusted nodes and edges

Network connectivity is a primary attribute and a characteristic phenomenon of any networked system. A high connectivity is often desired within networks; for instance to increase robustness to failures, and resilience against attacks. A typical approach to increasing network connectivity is to strategically add links; however adding links is not always the most suitable option. In this paper, we propose an alternative approach to improving network connectivity, that is by making a small subset of nodes and edges "trusted," which means that such nodes and edges remain intact at all times and are insusceptible to failures. We then show that by controlling the number of trusted nodes and edges, any desired level of network connectivity can be obtained. Along with characterizing network connectivity with trusted nodes and edges, we present heuristics to compute a small number of such nodes and edges. Finally, we illustrate our results on various networks.