Choosing a leader on a complex network

In many real life applications a group of people interact through a communication network, mathematically modelled as a connected graph linking each element of the group. These participants may have diverse objectives and play very different roles depending on their knowledge and privileges. We focus on a particular scenario, in which a certain node is absolutely essential for completing the intended task. Moreover, if a technical failure results in disconnection of a participant to this leader node, this participant can no longer take part in the group's performance.In this setting a sound choice of the underlying network topology could minimize the damage caused by random or provoked technical failures. We study different criteria for choosing suitable communication networks, from the point of view of both efficiency and robustness.