A complex network to take one's breath away (5)
I believe the answer is:
amaze
'take one's breath away' is the definition.
(to take someone's breath away is to amaze them)
'a complex network' is the wordplay.
'complex network' becomes 'maze' (I've seen this before).
'a'+'maze'='AMAZE'
'to' acts as a link.
(Other definitions for amaze that I've seen before include "Greatly surprise, astound" , "wow!" , "shock" , "Greatly surprise, fill with wonder" , "Flummox" .)