Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. Thus, although our algorithm is based on arguments similar to those at work for the Bellman-Ford and Dijkstra methods, it is in fact essentially different. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples.

翻译：考虑一个不含环的有限有向图，其中每条边均被赋予权重。本文提出一种用于计算新型距离（称为路径长度加权距离）的算法，该距离在欺诈检测的图分析场景中已被证明具有实用价值。其核心思想在于，新距离在计算过程中显式地考虑了路径的规模。因此，尽管我们的算法基于与Bellman-Ford和Dijkstra方法相似的理论依据，但其本质存在显著差异。我们构建了适用于该算法的计算框架，阐明了其使用时的约束条件与要求，并提供了若干示例加以说明。