Graphs and models with finite chains

We investigate some properties of graphs with finite simple chains. In every countably categorical infinite graph there is a subgraph, which could be obtained from the infinite complete graph by the exshanging of some chains of the fixed lenght by edges. Classes of all graphs with finite chains and all finite graphs have the same elementary theory. The elementary theory of every graph of the finite lenght desidable. At the end we also introduce the notion. Of the graph of an arbitrary structure and shows that all obtained facts remaines true for classes of structures which graphs have prescribed properties.