Weighted degrees and truncated derived bibliographic networks

Large bibliographic networks are sparse—the average node degree is small. This does not necessarily apply to their product—in some cases, it can “explode” (not sparse, increasing in temporal and spatial complexity). An approach in such cases is to reduce the complexity of the problem by restricting our attention to a selected subset of important nodes and computing with corresponding truncated networks. Nodes can be selected based on various criteria. An option is to consider the most important nodes in the derived network—the nodes with the largest weighted degree. We show that the weighted degrees in a derived network can be efficiently computed without computing the derived network itself, and elaborate on this scheme in detail for some typical cases.