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

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  • J. M. Calabuig

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, Valencia 46022, Spain)

  • H. Falciani

    (Tactical Whistleblower, Universitat Politècnica de València, Camino de Vera s/n Valencia 46022, Spain)

  • A. Ferrer Sapena

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, Valencia 46022, Spain)

  • L. M. García Raffi

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, Valencia 46022, Spain)

  • E. A. Sánchez Pérez

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, Valencia 46022, Spain)

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 Ω and a proximity function ϕ:Ω×Ω→℠+, we define a new metric for Ω by considering a path distance in Ω that is considered as a graph. We analyze the properties of such a distance, and several procedures for defining the initial proximity matrix (ϕ(a,b))(a,b)∈Ω×Ω. 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.

Suggested Citation

  • J. M. Calabuig & H. Falciani & A. Ferrer Sapena & L. M. García Raffi & E. A. Sánchez Pérez, 2023. "Graph Distances for Determining Entities Relationships: A Topological Approach to Fraud Detection," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1403-1438, July.
    • Handle: RePEc:wsi:ijitdm:v:22:y:2023:i:04:n:s0219622022500730
    DOI: 10.1142/S0219622022500730
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