Parameterized complexity of multi-node hubs

Hubs are high-degree nodes within a network, ubiquitous in complex networks such as telecommunication, biological, social and semantic networks. Here, we do not seek a hub that is a single node, but a hub consisting of k nodes. Formally, given a graph G=(V,E), we a seek a set A⊆V of size k that induces a connected subgraph from which at least p edges emanate. Thus, we identify k nodes which can act as a unit (due to the connectivity constraint) that is a hub (due to the cut constraint). This problem, which we call MULTI-NODE HUB (MNH), is a variant of the classic MAX CUT problem. While it is easy to see that MNH is W[1]-hard with respect to the parameter k, our main contribution is a parameterized algorithm that shows that MNH is FPT with respect to the parameter p.