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The walk distances in graphs

机译:图中的步行距离

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The walk distances in graphs are defined as the result of appropriate transformations of the ∑k=0~∞(~(tA)k) proximity measures, where A is the weighted adjacency matrix of a graph and t is a sufficiently small positive parameter. The walk distances are graph-geodetic; moreover, they converge to the shortest path distance and to the so-called long walk distance as the parameter t approaches its limiting values. We also show that the logarithmic forest distances which are known to generalize the resistance distance and the shortest path distance are a specific subclass of walk distances. On the other hand, the long walk distance is equal to the resistance distance in a transformed graph.
机译:图中的步行距离定义为∑k = 0〜∞(〜(tA)k)邻近度测量值适当转换的结果,其中A是图的加权邻接矩阵,t是足够小的正参数。步行距离是大地图。此外,当参数t接近其极限值时,它们收敛到最短路径距离和所谓的长步行距离。我们还表明,已知可以概括抵抗距离和最短路径距离的对数森林距离是步行距离的特定子类。另一方面,长步行距离等于变换后的图中的电阻距离。

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