Network analysis takes an important place in imposing structure on complex systems like telecommunication networks, power systems, or social media. However, many issues are still present in the areas of link prediction, edge weight assignment, node strength detection, or even fault detection, particularly in dynamic large scale networks. In this paper, we propose an original algorithm, based on graph theory, that tries to solve these problems in a logical and organized manner. This algorithm establishes trajectories from which links can be predicted and outlines the weight of the edges with respect to specifically defined metrics to facilitate enhancement of the network. It furthermore does the evaluation of essential nodes and edges, thus allowing for resource allocation and routing strategy development. Apart from this, the algorithm also utilizes an approach to address feature engineering aimed at enhancing other machine learning tasks such as node classification and the task of anomaly detection. Its ability to detect faults allows for the early prediction of the weaknesses of the system, hence reduces disturbances within the system. However scalable and applicable in various domains, this algorithm provides a good basis for enhancing the resiliency and the efficiency of the network. The article discusses construction of the algorithm, the processes of edge weight assessment and faults detection, and practical realization in the network systems that already exist.