The thing about these coaching searches is that the sphere of influence radiates out from the candidates, reaching not only their inner circle but also those who are on the outside, looking in with pride and anticipation.

So it is with the three coordinators the Giants are eyeing this weekend – Matt Patricia and Josh McDaniels on Saturday night in the Patriots-Titans AFC divisional playoff game and Pat Shurmur on Sunday afternoon in the Vikings-Saints NFC matchup.

“I think it is very high for anyone that’s been associated with Matthew through the college, though his high school, through any of his coaching ranks,’’ Ray Moran, Patricia’s offensive line coach at Rensselaer Polytechnic Institute told The Post. “People are excited for that, as well they should be.

“I said to someone the other day it’s exciting even if you are associated through a distant third person relationship with Matthew, it’s exciting to know this is a small town kid in upstate New York, went to a small technical school in Troy, New York, who is potentially on the short list for a head coaching position, for only 32 of those in the world. That’s pretty darn exciting.’’

Patricia is on the shortest of lists with the Giants. Shurmur and McDaniels are also on the Giants’ list. All three are also high on other lists, as there are four remaining head coaching vacancies: Giants, Lions, Colts and Cardinals. According to various reports, Patricia was and remains the presumed favorite in Detroit because of the presence of general manager Bob Quinn, a former executive with the Patriots. McDaniels and Texans defensive coordinator Mike Vrabel are the top choices for the Colts’ job. Shurmur has long been linked to the Cardinals.

If the Giants are unable to land one of their top three choices, they could double back to Steve Wilks, who was the Panthers defensive backs coach when Giants general manager Dave Gettleman held that title in Carolina. Wilks was one of six interviews the Giants conducted. Another name to keep an eye on with the Giants is Mike Munchak, the Steelers’ offensive line coach. Munchack, a Hall of Fame lineman, went 22-26 in a three-year stint as the Titans head coach and is well-regarded by the Giants.

Shurmur, the former head coach of the Browns, is also a legitimate Giants’ candidate and not much credence should be attached to the theory Shurmur and his Vikings quarterback, soon-to-be free agent Case Keenum, are a package deal. The Giants are not going to sign Keenum and Shurmur “is not going to turn down a job for a guy who is a career backup who is going to cash in someplace,’’ according to a Giants source.

McDaniels and Shurmur have previously been head coaches – co-owner John Mara has stated that is preferable for the 18th head coach in Giants history – and Patricia has the extensive (six years) NFL coordinator experience Mara also set as a prerequisite.

Patricia, 43, did not come to coaching immediately after leaving RPI with a degree in aeronautical engineering.

“We just assumed he was going to use his engineering degree,’’ Joe King, Patricia’s former head coach at RPI, told The Post recently. “The majority of the kids on the team were in engineering. There was a demand for RPI engineers. It wasn’t a question could get a job, it was only a question of where you wanted to go and how much you were gonna sign for. I can’t say we thought he was gonna do anything other than use his degree.’’

Patricia scratched his coaching itch as a graduate assistant for one year at RPI.

After two years in the workforce designing and selling centrifuges at Hoffman Air & Filtration in Syracuse, hear his hometown of Sherill, Patricia put his college schooling to the side and became the defensive line coach at Amherst College, a Division III school, making $8,000 per year. Nineteen years later, he is a hot NFL head coach candidate.

“That’s the excitement, the nervousness, the chaos of the moment, it’s all really good stuff,’’ said Moran, who keeps in frequent contact with Patricia. “I just know no matter what, that man is focused on first-and-ten, second-and-short, third-and-long, inside the red zone. That’s a testament to him, to be able to stay singularly focused on the job at hand. He’ll deal with the other stuff as it comes.’’