  This paper provides the analysis for structural and functional approaches of
complex network systems research. In order to study the behavior of these
systems the flow adjacency matrices were introduced, and local and global
dynamic characteristics of system elements were defined. The notion of the flow
core of network system was introduced and its advantages over the k-core of
complex network were analyzed. The methods were proposed for identifying real
structure of network system and reducing the dimensionality of its model.
