Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Geometry of Cuts and Metrics
Metric and ultrametric spaces of resistances
Discrete Applied Mathematics
A class of graph-geodetic distances generalizing the shortest-path and the resistance distances
Discrete Applied Mathematics
The tau constant and the discrete Laplacian matrix of a metrized graph
European Journal of Combinatorics
Graph metrics and dimension reduction
Graph metrics and dimension reduction
The Structure of Complex Networks: Theory and Applications
The Structure of Complex Networks: Theory and Applications
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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.