Centrality in Complex Networks and Betweenness in Network Systems

The concepts of centrality and influence of complex network nodes are analyzed for the purpose of determining their impor­tance in the systems structure. The notions of measure, domain and power of betweenness of network nodes and edges are introduced to identify their importance in the operation process of network systems. These indicators quantitatively express the degree of assistance of the corresponding ele­ment for the motion of flows in the system and determine the losses that are expected in the case of blocking this node or edge or targeted attack on it. Similar notions of betweenness are introduced to determine the functio­nal importance of separate subsystems of network systems. Examples of practical use of the obtained results are given