The article presents an analysis of the network stability of modern banking systems from the point of view of graph theory. The use of graph models makes it possible to effectively describe complex network structures, identify bottlenecks, and predict system behavior during failures or attacks. Algorithms based on graph theory, such as Dijkstra's Algorithm, have been proposed to ensure minimal transaction processing time and improve system reliability. A comparative analysis of various optimization methods through modeling on abstract graphs and real banking network data was carried out. As a result of the study, solutions were proposed to protect the banking system, as well as improve its connectivity and fault tolerance.

Keywords: banking system, graph theory, Dijkstra's algorithm, blockchain, transactions, cyber attack, network stability analysis, banking infrastructure, cyber security, DDoS attack