Summary
In analyzing graphs with conservative flow where the node flows are of interest (e.g. algorithm flowcharts) the practice has been to measure or to analytically determine the flows in the independent edges, and to calculate all other edge flows using Kirchhoff's law of flow conservation. The node flows are then obtained as the sum of edge flows entering each node.
This paper presents a transformation on such graphs whereby the transformed graph, if analyzed for its edge flows, will directly yield the node flows of the original graph.
A proof is also given that the number of node flow measurements determined by the transformed graph never exceeds the number of edge flow measurements that would be required if the transformation were not applied.
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Nahapetian, A. Node flows in graphs with conservative flow. Acta Informatica 3, 37–41 (1973). https://doi.org/10.1007/BF00288650
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DOI: https://doi.org/10.1007/BF00288650