Internet, the global network comprising a loose confederation of interconnected networks, is a clipping or shortening of its etymon internetwork.
The word internetted was in use from at least 1849, meaning 'interconnected or interwoven' but didn't emerge in computing until around 1968 in terms of being 'connected by or as part of a computer network'. The Oxford English Dictionary gives its etymology as the following:
Perhaps influenced by similar words in -net, as Catenet (1972), Satnet (1973), Telenet (1973), etc., ultimately after ARPANET (the name of a wide area network established in 1969 by the Advanced Research Projects Agency of the U.S. Department of Defense; the name ARPANET is attested from 1971). In subsequent use denoting the global network, probably greatly reinforced by use in the compound Internet Protocol n.
Sources: Oxford English Dictionary