Laplacian Harmonic Spectral Analysis for IoT Network Topology Characterization

Abstract

The rapid expansion of the Internet of Things (IoT) has led to the deployment of large-scale, heteroge neous, and dynamically evolving network topologies. Understanding the structural properties of such net works is critical for ensuring robustness, efficient communication, and fault tolerance. Spectral graph theory provides powerful tools for analyzing network structures through eigenvalues of matrix representa tions. In this paper, we introduce the Laplacian Har monic matrix as an alternative spectral framework for modeling IoT network topologies. We investigate its fundamental properties and analyze the associ ated eigenvalues for various graph families. Further more, we interpret these spectral characteristics in the context of IoT networks, including star, mesh, and bipartite topologies. The results demonstrate that Laplacian Harmonic eigenvalues provide deeper insights into connectivity, robustness, and structural balance compared to traditional Laplacian matrices. The proposed framework offers a novel approach for IoT network design, monitoring, and optimization.