We propose a new method for assessing agents' influence in financial network structures, which takes into consideration the intensity of interactions. A distinctive feature of this approach is that it considers not only direct interactions of agents of the first level and indirect interactions of the second level, but also long-range indirect interactions. At the same time we take into account the attributes of agents as well as the possibility of impact to a single agent from a group of other agents. This approach helps us to identify systemically important elements which cannot be detected by classical centrality measures or other indices. The proposed method was used to analyze the banking foreign claims for the end of 1Q 2015. Under the approach, two types of key borrowers were detected: a) major players with high ratings and positive credit history; b) intermediary players, which have a great scale of financial activities through the organization of favorable investment conditions and positive business climate.