A system that connects multiple computers and allows the exchange of data through EDI and/or other protocols.

Merriam-Webster Online Dictionary
network (noun)
1.
a fabric or structure of cords or wires that cross at regular intervals and are knotted or secured at the crossings
2.
a system of lines or channels resembling a network
3.
a) an interconnected or interrelated chain, group, or system - a network of hotels
b) a system of computers, peripherals, terminals, and databases connected by communications lines
4.
a) a group of radio or television stations linked by wire or radio relay
b) a radio or television company that produces programs for broadcast over such a network
5.
a usually informally interconnected group or association of persons (as friends or professional colleagues)
network (verb)
transitive verb
1.
to cover with or as if with a network - a continent … so networked with navigable rivers and canals Lamp
2.
chiefly British to distribute for broadcast on a television network , also - broadcast
3.
intransitive verb
to join (as computers) in a network to engage in - networking