Graph Distances for Determining Entities Relationships: A Topological Approach to Fraud Detection

Abstract

A new model for the control of financial processes based on metric graphs is presented. Our motivation has its roots in the current interest in finding effective algorithms to detect and classify relations among elements of a social network. For example, the analysis of a set of companies working for a given public administration or other figures in which automatic fraud detection systems are needed. Given a set [Formula: see text] and a proximity function [Formula: see text], we define a new metric for [Formula: see text] by considering a path distance in [Formula: see text] that is considered as a graph. We analyze the properties of such a distance, and several procedures for defining the initial proximity matrix [Formula: see text]. Using this formalism, we state our main idea regarding fraud detection: financial fraud can be detected because it produces a meaningful local change of density in the metric space defined in this way.