A Graph-theoretic and Computational Framework for Robust, Energy-efficient Distributed Localization in Wireless Sensor Networks

Ashwini Pravin Bhong; Dr. Vishwajeet S. Goswam

A Graph-theoretic and Computational Framework for Robust, Energy-efficient Distributed Localization in Wireless Sensor Networks

Author(s)	Ms. Ashwini Pravin Bhong, Dr. Vishwajeet S. Goswam
Country	India
Abstract	Wireless sensor network (WSN) localization is a graph-structured estimation problem in which sensors must infer physical coordinates from inter-node measurements and a limited set of reference anchors. The attached reference manuscript establishes a vertex-centric framework in which a WSN is modeled as a weighted, time-varying graph and localization is performed through local numerical updates, graph-Laplacian consensus, rigidity information, and energy-aware communication. Building on that foundation, this paper develops a focused research framework around three objectives: (1) applying graph-theoretic properties such as connectivity, adjacency, and centrality for efficient network modeling and localization; (2) designing and validating algorithms that remain robust and adaptable under changing network conditions and topologies; and (3) evaluating the proposed approach through simulation and performance analysis against established localization strategies. The paper formulates a weighted graph model, derives a distributed nonlinear least-squares objective, introduces energy- and reliability-aware edge weights, and combines local gradient updates with consensus regularization. Connectivity is characterized using the graph Laplacian and algebraic connectivity, while rigidity and redundancy are used to assess whether geometric constraints are sufficient for unique localization. A robust Huber loss is incorporated to limit the influence of outliers. The resulting Energy-Aware Vertex-Centric Localization (EAVCL) framework uses one-hop state exchange, adaptive communication, event-triggered reactivation, and local topology updates. A synthetic evaluation protocol is specified for networks of increasing size, anchor density, communication range, noise, and packet loss. The numerical examples included in this paper are analytical illustrations rather than empirical benchmark claims; they define a reproducible methodology for future MATLAB/Python, NS-3, Cooja, or OMNeT++ validation.
Keywords	wireless sensor networks, graph theory, distributed localization, vertex-centric computing, connectivity, centrality, rigidity, graph Laplacian, consensus, energy efficiency, robustness, dynamic topology
Field	Mathematics
Published In	Volume 8, Issue 5, September-October 2026
Published On	2026-09-29

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A Graph-theoretic and Computational Framework for Robust, Energy-efficient Distributed Localization in Wireless Sensor Networks

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