A data network is a communication network used to carry data. There have been several kinds:

analog circuit-switching networks: the original analog voice communication system can be used to carry data by use of a modem
digital virtual circuit-switching networks: the first generation of pure data networks, such as the ARPANET and X.25 networks; although they used packets internally, the service model presented to the user is virtual circuits only
packet switching networks: in these, the datagram service is exposed to the software on the user's host, which has to build reliable byte streams on top of them; the first was CYCLADES, and the later PUP and TCP/IP protocol suites followed this example

The latter are now the basic information carrying substrate for all communication networks.

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Data network