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"established a network" is correct and usable in written English.
You can use it when you want to say that someone or something created a network of people, systems, or organizations. For example, "The company established a network of distributors across the country."
Exact(59)
Like other collectors, Smith established a network to obtain indigenous remains.
The ICSF has established a network for companies, enterprises and academics interested in this subject.
He also established a network of partnerships in Europe, the Middle East and the United States.
Dudley had established a network of spies led by a former policeman, Matthew Maguire.
As part of that endeavour, Bacardi has established a network of sustainability employee champions across its business.
Before he was caught, Mr. Faruq had already established a network, which remains in place, the Western intelligence official said.
The W.H.O. has established a network of doctors who have cared for at least one patient with the illness.
I joined I.D.G. as vice president for Latin America, and we established a network of magazines in the region.
One luxury-car maker, Tesla, has established a network of high-speed chargers just for its customers.
The origins of al-Muhajiroun Formed in 1996, al-Muhajiroun established a network that stretched around the world using public meetings and lectures in radical mosques.
It is believed to have established a network in Karachi with the aid of the Taliban's consulate there in the 1990's.
More suggestions(16)
provide a network
maintained a network
states a network
establish a network
incorporated a network
discovered a network
implement a network
drew a network
partnership a network
provided a network
established a movie
established a bond
established a dialogue
established a pasta
established a theme
established a ministry
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com