Cycling and reciprocity in weighted food webs and economic networks

Networks of mass flows describe the basic structure ecosystems as food webs, and economy input–output tables. Matter leaving a node in these networks can return to it immediately part reciprocal flow, or completing longer, multi-node cycle. Previous research comparing cycling matter was limited by relying on unweighted few networks. Overcoming this limitation, we study large datasets weighted real-world networks: 169 mostly aquatic webs 155 economic We quantify portion all that is due cycles, known Finn Cycling Index (FCI). find no correlation between FCI largest eigenvalues adjacency matrices used proxy past. Unweighted ignore actual flow values reality differ even 10 orders magnitude. be decomposed into sum contributions individual nodes. This enables us how organisms recycling dead organic dominate webs. has geometric mean 5%. observe lower average The global production network had an 3.7% 2011. (input–output tables trade relationships) strongly correlates with reciprocity. Encouraging reciprocity could enhance acting locally, without need perfectly know its structure.