Invariance is a primary characteristic of a control system. It is strongly interrelated with the system structure where the latter provides a necessary condition for the invariance. The relationship is established by using various formal languages among which the graph-theoretic model seems most adequate when it comes to analysing the causal relations between components of the system. The present work aims to reflect the close interdependence between a number of invariance types and graph structures. Some typical algorithms for solving the problems of structure selection are demonstrated.