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. •The simplified calculation method similar to electrical engineering one is proposed.•The method is devoid of the main contradictions inherent in the impulse method.•New weight characteristics of the concept nodes are proposed: pressure and influence.•The results obtained by using the K-method are in accordance with the impulse method.