A Bellman-Ford algorithm for the path-length-weighted distance in graphs

TL;DR

This paper introduces a novel Bellman-Ford based algorithm to compute a path-length-weighted distance in directed acyclic graphs, enhancing graph analysis for applications like fraud detection.

Contribution

It presents a new algorithm for path-length-weighted distances that differs from traditional methods, tailored for specific graph analysis tasks.

Findings

Effective in fraud detection scenarios

Handles path-length considerations explicitly

Applicable to directed acyclic graphs

Abstract

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.