International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

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Volume 7 Issue 6
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SPECTRAL METHODS FOR THE ANALYSIS OF DYNAMIC AND NON-SYMMETRIC NETWORKS: A LITERATURE REVIEW

Author(s) Ms. Shareena NP, Dr. A Punitha
Country India
Abstract Modern data science increasingly relies on the analysis of complex networks, which power applications from neuroscience to social media. Traditional network models, built on static and undirected graphs, are often insufficient for capturing the dynamic, directed, and signed interactions that characterise real-world systems. This literature review examines advanced spectral methods designed to overcome these challenges. We focus on the creation of Hermitian matrix proxies, such as the Hermitian Adjacency Matrix and the Magnetic Laplacian, from non-symmetric or signed data, which enables the application of powerful and well-established spectral theory. Our synthesis demonstrates that these Hermitian surrogates effectively encode directional and signed information within their complex spectra, facilitating novel insights into community structure, node centrality, and system stability that are beyond the reach of classical methods. The review further explores how these spectral properties are leveraged to characterise network dynamics and robustness, particularly in evolving systems. We conclude by identifying persistent research gaps and suggesting future directions to improve the robustness and interpretability of spectral analysis for non-normal and time-varying networks.
Keywords Complex Networks, Spectral Analysis, Hermitian Matrices, Graph Neural Networks and Network Dynamics
Field Computer > Network / Security
Published In Volume 7, Issue 6, November-December 2025
Published On 2025-12-02
DOI https://doi.org/10.36948/ijfmr.2025.v07i06.62318
Short DOI https://doi.org/hbdsh3
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