Osipov, V. P.; Rykov, Yu. G. On mathematical aspects of analyzing the structure of complex systems using weighted digraphs. (English) Zbl 1455.93073 Lobachevskii J. Math. 41, No. 11, 2231-2238 (2020). Summary: 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. MSC: 93B70 Networked control 93A15 Large-scale systems 05C20 Directed graphs (digraphs), tournaments Keywords:complex system; digraph; additive convolution; cycles in graph; paths in graph PDFBibTeX XMLCite \textit{V. P. Osipov} and \textit{Yu. G. Rykov}, Lobachevskii J. Math. 41, No. 11, 2231--2238 (2020; Zbl 1455.93073) Full Text: DOI References: [1] Roberts, F. S., Discrete Mathematical Models with Application to Social, Biological, and Environmental Problems (1976), Englewood Cliffs: Prentice-Hall, Englewood Cliffs · Zbl 0363.90002 [2] Papageorgiou, E. I., Fuzzy Cognitive Maps for Applied Sciences and Engineering. From Fundamentals to Extensions and Learning Algorithms (2014), Berlin, Heidelberg: Springer, Berlin, Heidelberg [3] Nechiporenko, V. I., Structural Analysis of Systems: Reliability and Efficiency (1977), Moscow: Sovetskoe Radio, Moscow · Zbl 0414.93001 [4] Silov, V. B., Making Strategic Decisions in a Fuzzy Environment (1995), Moscow: INPRO-RES, Moscow This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.