New method (the K-method) for calculation of characteristics of complex networks is proposed. The method is based on transformation of the initial network and subsequent application of the Kirchhoff rules. The field of application of the method for sparse networks (in which nodes have a cause.effect character of the so-called .cognitive maps.) is proposed. Two new characteristics of concept nodes (.pressure. and .influence.) having a semantic interpretation are proposed. The advantages of the proposed K-method include its computational simplicity (in comparison with other known algorithms) comparable with the task of enumerating subgraphs for sparse networks of relatively small size (in practice - several hundred nodes). At the same time, the results obtained with the help of the K-method for a real network are correlating well enough with the results obtained using the impulse method.
Complex networks; K-method; Mutual influence; Nodes ranking