Spectral Graph Theory-Based Knowledge Representation for Analyzing Wireless Mesh Networks

Abstract

Wireless Mesh Networks (WMNs) have been widely analyzed through conventional performance metrics such as throughput, delay, and connectivity. However, these classical approaches often overlook the deeper structural properties that determine the robustness and efficiency of network communication. This paper proposes a novel analytical framework based on spectral graph theory to represent and evaluate WMNs through their topological and functional characteristics. By computing and examining the eigenvalues and eigenvectors of the graph Laplacian, the proposed method reveals intrinsic patterns in network connectivity, algebraic connectivity, spectral radius, and resilience to signal degradation. A dedicated software tool was developed to model WMN topologies, compute spectral metrics, and evaluate how variations in signal strength influence network robustness. The results demonstrate that algebraic connectivity increases when signal strength is optimized between critical nodes identified by the Fiedler vector, while minimizing the spectral radius enhances resilience to failures and attacks. This spectral perspective enables systematic visualization, diagnosis, and optimization of WMN structures, providing actionable guidelines for efficient network design. The approach contributes to both theoretical understanding and practical optimization of wireless networks, offering a scalable foundation for applications in IoT, smart cities, and next-generation communication systems.

Received: 30 December 2022 | Revised: 17 January 2023 | Accepted: 22 February 2023

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

Nenad M. Jovanovic: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration, Funding acquisition.