The research develops a new graph-theoretical methodology for maximizing bandwidth use efficiency across contemporary computer networks including systems that rely on IoT and cloud-based and multi-cloud infrastructure. The technique makes use of weighted graphs in NetworkX which allows it to utilize degree centrality and edge betweenness centrality and closeness centrality together with spectral radius to recognize network bottlenecks and enhance data transmission paths. The approach provides real-time congestion detection as well as adaptive bandwidth allocation features because it differs from traditional statistical and heuristic methods. Researchers applied a methodology which consisted of conducting literature review and real-world network data acquisition before conducting graph model development followed by ns-3-based simulation testing and upcoming real-world validation preparations. Results from the simulation model reveal excellent improvements in congestion detection together with better bandwidth utilization efficiency when compared to standard methods. The framework provides strong performance in scalability, resilience and dynamic network condition adaptation but it faces issues from high computational complexity together with data quality dependency. The next line of inquiry will be predictive machine learning models, which will assist scale the framework and optimize real-time processes. This research introduces theoretical and practical progress to network optimization theory and graph theory applications through a solid system that increases network bandwidth effectiveness and develops stable adaptable infrastructure in modern digital environments.