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Spectral reconstruction of complex networks

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  • Comellas, Francesc
  • Diaz-Lopez, Jordi

Abstract

In this paper we study the reconstruction of a network topology from the eigenvalues of its Laplacian matrix. We introduce a simple cost function and consider the tabu search combinatorial optimization method, while comparing its performance when reconstructing different categories of networks–random, regular, small-world, scale-free and clustered–from their eigenvalues. We show that this combinatorial optimization method, together with the information contained in the Laplacian spectrum, allows an exact reconstruction of small networks and leads to good approximations in the case of networks with larger orders. We also show that the method can be used to generate a quasi-optimal topology for a network associated to a dynamic process (like in the case of metabolic or protein–protein interaction networks of organisms).

Suggested Citation

  • Comellas, Francesc & Diaz-Lopez, Jordi, 2008. "Spectral reconstruction of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6436-6442.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:25:p:6436-6442
    DOI: 10.1016/j.physa.2008.07.032
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Viktor Homolya & Tamás Vinkó, 2024. "Closeness centrality reconstruction of tree graphs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(4), pages 1061-1088, December.
    2. Maiorino, Enrico & Rizzi, Antonello & Sadeghian, Alireza & Giuliani, Alessandro, 2017. "Spectral reconstruction of protein contact networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 804-817.
    3. Pandey, Pradumn Kumar & Badarla, Venkataramana, 2018. "Reconstruction of network topology using status-time-series data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 573-583.
    4. Lovato, Ilenia & Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2020. "Model-free two-sample test for network-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).

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