A Family of Graph Distances Generalizing both the Shortest-Path and the Resistance Distances
نویسنده
چکیده
A new family of distances for graph vertices is proposed. These distances reduce to the shortest path distance and to the resistance distance at the extreme values of the family parameter. The most important property of them is that they are graphgeodetic: d(i, j)+d(j, k) = d(i, k) if and only if every path from i to k passes through j. The construction of the distances is based on the matrix forest theorem and the graph bottleneck inequality.
منابع مشابه
A Class of Graph-Geodetic Distances Generalizing the Shortest-Path and the Resistance Distances
A new family of distances for graph vertices is proposed. These distances reduce to the shortest path distance and to the resistance distance at the extreme values of the family parameter. The most important property of them is that they are graphgeodetic: d(i, j)+d(j, k) = d(i, k) if and only if every path from i to k passes through j. The construction of the distances is based on the matrix f...
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