The phrase "a close network of" is correct and usable in written English.
It can be used to describe a tightly connected group of individuals or entities, often in a social, professional, or organizational context.
Example: "The organization thrives due to a close network of dedicated volunteers who support each other."
Alternatives: "a tight-knit group of" or "an intimate circle of".
What I don't have, though, is a close network of friends prepared to be active on my behalf.
A lively woman who loves bike riding and horses, she has built a close network of friends.
In London, he was part of a close network of old friends and relatives from the American South.
One of the more noteworthy features of the countryside of Northern Ireland is a close network of well-maintained roads that connects all parts of the region.
From a professional point of view it's fantastic to work with Eddie and, personally, it's a great challenge for me not to be surrounded by a close network of good friends.
As his political career developed, he became increasingly powerful at both a local and national level, first as a deputy in the council of Valladolid, before becoming a senator, taking charge of numerous national commissions and building a close network of contacts in Madrid.
A major factor is likely to be the less fragmented nature of NHS Scotland, with its single authority structure of Health Boards, probably supported by a closer network of research support.
These criticisms became widely known among the close network of humanists who initially had found both Luther and Erasmus appealing.
Perhaps the fundamental fallacy of Davos is that its a geographically constrained closed network of a select few when we live in a world where presidents of nations, and CEOs of companies like AirBnB, are interacting with a much larger open network of humanity through social media.
We look for small close networks of people and look for how they can be just as influential as rockstars".
