"influential reputation" is correct and usable in written English.
You can use it to describe someone with a good reputation that is influential in their field or to a particular group of people. For example, "She has an influential reputation in business circles."
Other important factors rated as influential were "reputation of the specialty" (59%), "anticipated income" (58%) and "focus on urgent care" (55%).
During this period Böhme wrote at least six tracts that were circulated guardedly among his friends, creating an influential and respected reputation for him.
Raza Academy, one such influential group, has a reputation for violence and aggravation, but is protected and was allowed to convene the rally because of its political connections and clout.
Mr. Wood, a penetrating critic with a graceful prose style, soon emerged as one of Britain's most influential film writers, a reputation enhanced by the groundbreaking "Hitchcock's Films" (1965).
Chaudhry Nisar Ali Khan, an influential politician with a reputation for tough talk, was appointed interior minister, and the new minister for water and power, Khawaja Muhammad Asif, was charged with addressing an urgent energy crisis that has caused widespread misery and economic distress in Pakistan.
Other influential factors were the "reputation of the specialty", "anticipated income", and "focus on urgent care".
Wood is a British book reviewer who works at the New Yorker, a highly influential name-maker and reputation-wrestler, of Salman Rushdie, Jonathan Franzen and Zadie Smith, among others.
Sotatsu, who has a reputation as an influential landscape painter, is an elusive figure.
It stands in a development built by a property tycoon with a reputation for gaining influential friends.
CAROL GILLIGAN, the feminist psychologist, has made her academic reputation with her influential and controversial theories on gender difference.
