LINX: A topology based methodology to rank the importance of flow measurements in compartmental systems

Abstract In ecological and other transactional energy–matter flow networks, accurate quantification of flows between compartments can be difficult and costly. For models at steady state or undergoing linear change, energy–matter conservation together with the steady-state condition can be exploited to estimate unknown flows from known ones. In compartmental network models, some flows are more important than others in terms of their connections to other flows, participation in cycles, geodesic distance to the environment (in the graph theoretical sense), and other topological features. In respect to estimating unknown flows, such importance differences also come into play. Pursuing this, we formulate a Link Importance iNdeX (LINX) that quantifies each flow’s importance in a model. This index identifies and quantifies the redundancy imposed by network topology and mathematical conservation rules. We anticipate that it will find use in minimizing the cost and effort of data collection while also increasing model accuracy.