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An attempt to classify networks from mathematical point of view is given, Also we present several examples of mathematical network models: 1. queueing-communication-transportation networks, 2. networks of chemical reactions, chemical thermodynamics and homeostasis, 3. Gibbs and quantum graphs and spaces, 4. trading networks. 1 V. A. Malyshev,. Networks and dynamical systems. Advances Appl. Probability, 25, 140-175, (1993). . [2]V. A. Malyshev,. "Random graphs and graph grammars," Discrete Mathematics Appl.. 8, No. 3, 247-262 (1998). [3]V. A. Malyshev. Macro-dimension is an invariant of local dynamics. Theory of probability and applications 45,, No. 7, 368-374 (2000) [4].V. A. Malyshev. Gibbs and quantum discrete spaces..Russian Math. Surveys, 56,, No. 5, 917-972 (2000)