The intense diversity of the Next-Generation Networking environments like 6G and the forthcoming deployment of immersive applications with varied user-specific requirements transform the efficient allocation of resources into a real challenge. Traditional solutions like the shortest path algorithm and mono-constraint methodologies are inadequate to handle customized user-defined performance parameters and effectively classify physical resources according to these intricate demands. This research offers a new evaluation mechanism to successfully replace the aforementioned traditional path ranking and path selection techniques. Specifically, the proposed framework is integrated with optimization-oriented metrics, each indicating a unique aspect of performance for evaluating candidate network paths. The deployed metrics are then algebraically synthesized to provide a distinctive multidimensional description of the examined substrate resources. These primary and composite metrics adhere to the fundamental monotonicity and isotonicity properties of a Path Algebra; hence, the validity and optimality of the proposed evaluation mechanism is guaranteed by design. To tackle the complexity created by the variety of human-centric customization, a novel methodology that analyzes and determines the weighted influence of the synthesized metrics depending on the characteristics of the served user-centric application is also introduced. The chosen suitable weights address performance-oriented mission-critical tailored objectives for adaptive optimizations. Its innovative algebraic design allows it to successfully describe and rank candidate paths in a versatile way, whether in legacy or modern architectures. The experimental data of the first scenario show that 62.5% and 50% of highlighted path evaluations proposed by the shortest path and unidimensional constraint strategies, respectively, suffer from moderate performance-oriented values compared to the proposed framework. Likewise, the results of the second examined scenario reveal that the proposed composite metric yields more suitable path rankings by 50% in contrast to its traditional counterparts, rendering the contested evaluation mechanisms obsolete.