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A mathematical definit on of an information network is constructed with the purpose of developing a theory useful in answering practical questions concerning information transfer. An information network inCludes: (1) use,-s, (2) inf rmation resources, (3) information centers, and (4) the total information transfer structure linking (1), (2), and (3). Emphasis is placed on the message transfer structure, as distinguish d from the document transfer structure, to identify some basic network configurations. Any message transfer structure Is shown in graph theory concepts to be either isographic or nonisographic. Among the isographic structures, the cyclic and decentralited networks are defined. The strictly hierarchical network is also defined and the 2-regular netw rk, reflected in the ARPA design, is identified. Measures of network structure, in particul r the accessibility and flexibility in message transfer, are developed. These basic stuctures are used to characterize more general some comparisons of measage ttansfdr structures can he of more comprehensive measures is a necessity. 2 measures for the structures. While made, development