Network model for statistical data sets is a complete weighted graph where the nodes are represented by a random variables and weights of edges reflect interconnection between corresponding nodes (measure of similarity). Network structure in this model is a characteristic of some sub graphs of this graph. Identification of network structures from observations is an important problem in applied network analysis. Despite the growing number of publications on the subject there is a big gap in theoretical foundations of applied techniques. In the present paper we develop a new approach for identification of network structures based on the theory of multiple decision statistical procedures.