Cycling and reciprocity in weighted food webs and economic networks

Networks of mass flows describe the basic structure of ecosystems as food webs, and of economy as input–output tables. Matter leaving a node in these networks can return to it immediately as part of a reciprocal flow, or completing a longer, multi‐node cycle. Previous research comparing cycling of matter in ecosystems and economy was limited by relying on unweighted or few networks. Overcoming this limitation, we study mass cycling in large datasets of weighted real‐world networks: 169 mostly aquatic food webs and 155 economic networks. We quantify cycling as the portion of all flows that is due to cycles, known as the Finn Cycling Index (FCI). We find no correlation between FCI and the largest eigenvalues of unweighted adjacency matrices used as a cycling proxy in the past. Unweighted networks ignore the actual flow values that in reality can differ by even 10 orders of magnitude. FCI can be decomposed …