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.

在生态的和其他交易性的能量-物质流网络中，精确量化各隔室之间的流动可能是困难且昂贵的。对于处于稳态或经历线性变化的模型，可以利用能量物质守恒和稳态条件来估计来自已知流动的未知流量。在分区网络模型中，某些流在与其他流的连接，参与循环，到环境的测地距离（在图形上为理论意义）以及其他拓扑特征方面比其他流更为重要。关于估计未知流量，这种重要性差异也起作用。为此，我们制定了链接重要性iNdeX（LINX），以量化模型中每个流的重要性。该索引标识并量化由网络拓扑和数学守恒规则所施加的冗余。我们预计它将在最小化数据收集成本和工作量的同时提高模型准确性。