The Key Player Problem

The key player problem (KPP) consists of two separate sub-problems, which can be described at a general level as follows: 1. (KPP-1) Given a social network, find a set of k nodes (called a kp-set of order k) which, if removed, would maximally disrupt communication among the remaining nodes. 2. (KPP-2) Given a social network, find a kp-set of order k that is maximally connected to all other nodes.