Subject of research is complex networks and network systems. The network system is defined as a complex network in which flows are moved. Classification of flows in the network is carried out on the basis of ordering and continuity. It is shown that complex networks with different types of flows generate various network systems. Flow analogues of the basic concepts of the theory of complex networks are introduced and the main problems of this theory in terms of flow characteristics are formulated. Local and global flow characteristics of networks bring closer the theory of complex networks to the systems theory and systems analysis. Concept of flow core of network system is introduced and defined how it simplifies the process of its investigation. Concepts of kernel and flow core of multiplex are determined. Features of operation of multiplex type systems are analyzed.