  The paper investigates the problem of finding communities in complex network
systems, the detection of which allows a better understanding of the laws of
their functioning. To solve this problem, two approaches are proposed based on
the use of flows characteristics of complex network. The first of these
approaches consists in calculating the parameters of influence of separate
subsystems of the network system, distinguished by the principles of ordering
or subordination, and the second, in using the concept of its flow core. Based
on the proposed approaches, reliable criteria for finding communities have been
formulated and efficient algorithms for their detection in complex network
systems have been developed. It is shown that the proposed approaches make it
possible to single out communities in cases in which the existing numerical and
visual methods turn out to be disabled.
