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The phrase "within a network of" is grammatically correct and can be used in written English.
It typically refers to something being situated or operating as a part of a larger system or group of interconnected parts. Example: "The company operates within a network of global partners, allowing for efficient and diverse distribution of their products."
Exact(60)
That means he wants to eat locally, within a network of familiarity.
The Aztecs built Mexico City, or Tenochtitlán, on an island within a network of shallow lakes.
The Contemporary Art Society sits within a network of 70 museums and purchases for them on a regular basis.
A preferred provider organization works within a network of doctors and hospitals; people who go outside the network have to pay more.
Modern rulers, by contrast, are supposed to be emotionally detached; they work within a network of laws and systems designed to eliminate nonrational considerations like love and hatred.
Cameron and other senior politicians such as Michael Gove, Brooks and the Met co-existed within a network of power and privilege that was highly personal – mixing at family meals, horse riding, commuting on trains.
Recent research into online abuse has identified a new type of paedophile: hyper-sexualised, within a network of other offenders, owns thousands of indecent images of children, high IQ, married, professional.
They are embedded within a "Network" of unarticulated beliefs and other mental states and within a "Background" of capacities, all of which must exist if the illocutionary point of the act is to be served.
Still, it is a huge leap from a time even a few years ago when marriages were arranged within a network of connections, longstanding business relationships and the extended caste circle after matching astrological horoscopes.
We enter the world already within a network of relationships and obligations.
Recall that this shift simulates a GABAergic IPSC within a network of neurons.
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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