On Mathematical Aspects of Analyzing the Structure of Complex Systems Using Weighted Digraphs

The paper deals with the structure of complex systems represented as directed graphs with the values assigned to a graph’s vertices and edges. The natural procedure of determining the values of vertices through the input ones is introduced. The formulas are proved in order to calculate the influence of input vertices to others in case of linear relations. These formulas are closely connected with the internal structure of considered graph. The example of application of the formulas is described.