Matrix Decomposition for Telecom Network Reliability Analysis in Senegal: Stability and Convergence Proofs

Telecom networks in Senegal require robust reliability analysis to ensure efficient data transmission and minimise disruptions. The approach involves decomposing the adjacency matrix of a telecom network graph into its eigenvalues and eigenvectors to identify critical nodes. Stability is analysed through linearization around steady states, ensuring robustness against minor perturbations. Convergence properties are studied to guarantee algorithmic efficiency and reliability in real-world applications. The decomposition process revealed that the network's stability is significantly influenced by the eigenvalues' magnitude and distribution across different operational scenarios. Specifically, eigenvalues with magnitudes greater than one indicate unstable nodes, necessitating immediate intervention. This method provides a systematic framework for assessing telecom network reliability in Senegal, offering insights into node criticality and overall system resilience. The findings suggest that regular maintenance of high-risk nodes can enhance the network's stability. Additionally, dynamic resource allocation based on eigenvalue analysis could optimise network performance under varying loads. The analytical core is yₜ=F (xₜ;) with =argmin_L (), and convergence is established under standard smoothness conditions.