A mathematical definition 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) users, (2) information 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 distinguished 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 decentralized networks are defined. The strictly hierarchical network is also defined, and the 2-regular network, reflected in the ARPA design, is identified. Measures of network structure, in particular the accessibility and flexibility in message transfer, are developed. These measures for the basic structures are used to characterize more general structures. While some comparisons of message transfer structures can be made, development of more comprehensive measures is a necessity. (Author)