A class of graph-geodetic distances generalizing the shortest-path and the resistance distances Original Research Article

A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family parameters. The main property of the class is that all distances it comprises are graph-geodetic: image if and only if every path from image to image passes through image. The construction of the class is based on the matrix forest theorem and the transition inequality.