Risk function of statistical procedures for network structures identification

Problems of network structures identification by sample of fixed size are considered. The concepts of random variables network and network model as complete weighted graph are introduced. Two types of network structures are introduced: network structures with fixed and arbitrary numbers of network model elements. Problems of network structures identification as multiple decision problems are considered. It is proved that risk functions of statistical procedures for network structures identification can be considered as linear combination of mean numbers of errors of incorrect inclusions and exclusions elements from network model to network structure.