Using the Euclidean Metric When Studying Multicolor Flows in Undirected Graphs

The interaction of intelligent agents, i.e. the important part of cognitive systems, implies the existence of an environment to support such interaction. The usual representations of this environment are graphs with certain properties. Metric tasks often arise when simplifying complex and important problems on graphs. Throughput is one of the most important characteristics of such graphs. A traditional metric, such as the usual shortest paths, forms the basis of the traditional throughput index. The Euclidean metric is used to obtain advanced results. Such as representing the distribution of the flow of any color as the best approximation to the ideal distribution, or explaining the behavior of the throughput index with non-stationary traffic. Its analytical capabilities are used here to further study the behavior of multicolor flows. The theoretical results are illustrated with numerical examples.