Before revision: We present a methodology to extract the backbone of complex networks in which the weight and direction of links, as well as non-topological state variables associated with nodesplay a crucial role. This methodology can be applied in general to networks in which mass or energy is flowing along the links.
After revision: We present a methodology to extract the backbone of complex networks in which the weight and direction of links, as well as on nontopological properties of nodes. We show how the methodology can be applied in general to networks in which mass or energy is flowing along the links.