Query processing over weighted data graphs often involves searching for a minimum weighted subgraph - a tree - which covers the nodes satisfying the given query criteria (such as a given set of keywords). Existing works often focus on graphs where the edges have scalar valued weights. In many applications, however, edge weights need to be represented as ranges (or intervals) of possible values. In this paper, we introduce the problem of skynets, for searching minimum weighted subgraphs, covering the nodes satisfying given query criteria, over interval-weighted graphs. The key challenge is that, unlike scalars which are often totally ordered, depending on the application specific semantics of the ≤ operator, intervals may be partially ordered. Naturally, the need to maintain alternative, incomparable solutions can push the computational complexity of the problem (which is already high for the case with totally ordered scalar edge weights) even higher. In this paper, we first provide alternative definitions of the ≤ operator for intervals and show that some of these lend themselves to efficient solutions. To tackle the complexity challenge in the remaining cases, we propose two optimization criteria that can be used to constrain the solution space. We also discuss how to extend existing approximation algorithms for Steiner trees to discover solutions to the skynet problem. For efficient calculation of the results, we introduce a novel skyline union operator. Experiments show that the proposed approach achieves significant gains in efficiency, while providing close to optimal results.