  Networks are largely used for modelling and analysing data and relations
among them. Recently, it has been shown that the use of a single network may
not be the optimal choice, since a single network may misses some aspects.
Consequently, it has been proposed to use a pair of networks to better model
all the aspects, and the main approach is referred to as dual networks (DNs).
DNs are two related graphs (one weighted, the other unweighted) that share the
same set of vertices and two different edge sets. In DNs is often interesting
to extract common subgraphs among the two networks that are maximally dense in
the conceptual network and connected in the physical one. The simplest instance
of this problem is finding a common densest connected subgraph (DCS), while we
here focus on the detection of the Top-k Densest Connected subgraphs, i.e. a
set k subgraphs having the largest density in the conceptual network which are
also connected in the physical network. We formalise the problem and then we
propose a heuristic to find a solution, since the problem is computationally
hard. A set of experiments on synthetic and real networks is also presented to
support our approach.
