The most effective representation of the class of ordinary graphs (in the sense of in-formation capacity) is representation of the structure of the trees. The paper considers the different ways of the graphs assignments. The theorem on the possibility of networks representation by a tree structure is given. In proving this theorem the necessary and sufficient conditions compliance with their representation is formulated. The issues of representations transformation are considered. An example of network coding is given. The network can be set by any tree representation if this represen-tation sets a tree accurate within the numbering of all its vertices.
graph, multigraph, networks, tree graph, links, apexes(apices), system of natural numbers.
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