The paper deals with the basic concepts of graph theory. The main theoretical concepts an undirected graph and metric characteristics of graph are considered: vertices, edges, distances, eccentricities, adjacency and distance matrices. The concept of connectivity is one of the basic concepts of graph theory. In modern networks – transportation, communication, logistics – the problem of fragmentation often arises: some parts of the system are not directly connected to each other. Accordingly, the task of combining the components of graph connectivity into one connected graph arises. The paper proposes a method for constructing such a union by adding connections between the central vertices of the connectivity components. The formulas for calculating the diameter and radius of the resulting graph are also derived. The proposed method of unification is illustrated by an example related to the problem of logistics communication.