  The flow models of complex network system are developed and main flow
characteristics of its elements are defined. Those characteristics are applied
for determining actual structure of the system, analyzing its development on
all lifecycle stages and finding alternative flow directions that bypass
isolated areas of network. Influence and betweenness parameters of components
of network systems are defined. Using those parameters, the conditions were
studied under which system is resistant to negative internal and external
influence. The notion of flow core of complex network systems is defined, that
allows to distinguish the most important components of system structure in
terms of operation to solve the problem of finding communities within the
network. The notions of p-core and kernel of mono flow partially overlapped
multilayered network are defined that allow to determine components of system
structure that play the most important role in implementation of interactions
between systems. The methodology is developed for complex evaluation of quality
of complex hierarchical network systems. This methodology combines the
interconnected methods of local, forecasting, interactive and aggregated
analysis of system components behavior on all hierarchy levels. It is
demonstrated that application of proposed complex evaluation methodology is
efficient for solving problem of defining practically possible criteria of
network system element quality, novelty detection, determining critical and
optimal system operation modes and selecting optimal system of given class of
systems.
