'network-veined' is a compound formed from 'network' and 'veined'. 'network' is built from English elements 'net' + 'work' (modern English 'network', attested from the 17th century), where 'net' meant 'mesh' and 'work' meant 'something made or done'; 'vein' originates from Old French 'veine', from Latin 'vena' meaning 'a blood vessel or vein'.

'network-veined' arose in modern English by compounding the noun 'network' with the past-participial adjective 'veined' (from 'vein'). 'Vein' passed into English via Old French 'veine' from Latin 'vena', while 'network' developed from the combination of 'net' + 'work' into a single lexical item in Early Modern English.

Originally 'vein' primarily meant a blood vessel ('vena' in Latin) and later was extended to mean any threadlike or stripe-like channel (including leaf veins); 'network' originally referred to an object made like a net but extended to any netlike arrangement or pattern; together they now mean 'having a net-like arrangement of veins'.