The phrase "a complicated network" is correct and usable in written English.
You can use it to describe a system or structure that is intricate and interconnected, often in contexts like technology, biology, or social systems.
Example: "The internet is often described as a complicated network of servers, routers, and data pathways that connect users around the globe."
Alternatives: "a complex web" or "an intricate system".
The explanation for Nixon's bizarre apportionment of blame lies in a complicated network of regional loyalties.
Even a simplified food web can show a complicated network of trophic relationships.
The clans diffuse responsibility and blame through a complicated network of part-time workers, many of them teenagers.
There is a complicated network of smugglers and a huge trade in the trafficking of fraudulent work documents.
Which was why we all lived together in the first place, our sleeping areas cordoned off with a complicated network of towels hung as curtains from clotheslines.
The railroads ended isolation, and packed the metropolis with people whose work was defined by a complicated network of social obligations.
Known as "the Conqueror," he is said to have consolidated the area he subjugated by a complicated network of marriage and diplomatic obligations.
It is not a simple ribbon of moving water but rather a complicated network of currents that tend to shift course over time, to disappear and then reappear, and to develop eddies along the margins.
When one looks for something that all games have in common, one finds only "a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail".
Inspired by a 1996 New York murder -- the killing and dismemberment of a 25-year-old club denizen, Angel Melendez -- the play constructs a complicated network of characters who become involved in the mysterious disappearance of a young Trinidadian immigrant named Dominic.
In just a few years, a vibrant, competitive and largely self-contained economy had materialized around the bus stop, or bah-see zhan, an economy that employed at least 200 people, all of them bound to one another in a complicated network of alliances, dependencies and feuds.
