The branches from the Bill Parcells coaching tree — Bill Belichick (4), Tom Coughlin (2) and Sean Payton (1) — have totaled seven Super Bowl championships. No one should be surprised if Vikings head coach Mike Zimmer one day hoists a Lombardi Trophy of his own.

So much depends on the development of quarterback Teddy Bridgewater, as well as the relationship with the front office and the organization’s commitment to winning, but Zimmer looks like a Purple People Eating dream.

“First of all, his father was a coach, and I always think that’s a good thing, because these guys have lived this all their lives,” Bill Parcells told The Post. “They’re around it from the time they’re young boys at the dinner table. It’s being talked about, and it kind of gives them a little jump. They’ve got information at an earlier age than the people that don’t live it everyday.

“He’s got good leadership ability. He’s very, very honest. He’s very candid with the players. … I mean, there’s no possible way they could mistake what he’s thinking, or what he’s saying. It’s not ambiguous.”

Zimmer was the defensive coordinator in Dallas under Parcells from 2003-06. Zimmer was a student of the 4-3, but Parcells was a 3-4 guy. They made it work together. It was not unlike Parcells’ telepathic relationship with Belichick.

“The players responded in a positive way to his coaching,” Parcells said. “He’s not the easiest guy. He’s on their butt pretty good most of the time. He’s insistent on certain things, and he’s not afraid to be critical of them. He doesn’t try to sugarcoat anything. He’s just a straightforward guy, and after a while the players get to understand that and they respect him. He’s not harassing the players, but he’s not coddling them either.”

Parcells saw a lot of himself in Zimmer.

“We would have conversations — sometimes I’d go to him, and just volunteer stuff, and other times he would come to me and … we still talk a little now,” Parcells said. “He’s up to his rear end in alligators right now, you know?”

Parcells had invaluable advice for Zimmer when he was hired.

“I’d say we had a couple of lengthy conversations about things,” Parcells said. “I told him some people that he thought were one way would disappoint him once he got the head coaching job. And there’d be people that wouldn’t tell him the truth.”

Zimmer called out the Rams and safety Lamarcus Joyner for a dirty hit last week, when Joyner launched a flying elbow that left Bridgewater concussed. Zimmer’s reaction hardly came as a surprise to Parcells.

“He’s not a political guy, you know what I mean?” Parcells said. “He’s not a schmoozer. He’s not a guy that’s going to ingratiate himself to anybody. He just wants to coach football, and get his guys out there and get them to practice well and get them to play well. He doesn’t have a lot of other things on his mind. He’s a very dedicated football guy, he really is. He’s not a celebrity, he’s not looking for attention. He’s just kind of a coach’s son.”

Asked what makes Zimmer tick, longtime Vikings linebacker Chad Greenway said over the phone, “Football. He’s a guy that wants people to come in, do their jobs, and be a tough, hard-nosed group that continues to grind away, and that’s the type of team that he’s built. We’re built sort of from his mentality, and we sort of try to win that way. Never give up something easy. I think it just comes from the way he grew up in Illinois, and his tutelage under his dad, with him being his coach. It’s been fun playing for him, but he’s also a guy you want to make right. He knows what he’s doing, and it’s fun to play for him.”

Greenway, the three-time team defensive MVP over his exemplary 10-year Vikings career, was asked for an example of Zimmer’s motivational style.

“His ability to just kind of be straight with you, and tell you that’s where you’re at, good, bad or indifferent,” Greenway said. “It’s totally blue-collar mentality and that lunch pail idea. We’re not going to be sexy or frilly. We’re just going to do our jobs, and it’s going to be a full day when you play us, or at least we hope it’s going to be. In every speech, it’s about doing your job, getting your job done, and win the battle across from you.”

Parcells said he likes that Bridgewater is not a celebrity quarterback.

“That problem isn’t totally solved, but getting a guy that’s committed like Bridgewater is, I think is a big step for a coach, particularly in his first job as a head coach, because that’s a vital spot. You don’t see anything about him other than football,” Parcells said.

Bridgewater engineers the 30th-ranked passing attack. Offensive coordinator Norv Turner would like him to be less cautious at times.

“You’ve seen him grow, you’ve seen him make big throws in big spots, and that’s something we’re becoming accustomed to now with Teddy,” Greenway said. “His leadership ability has really grown, and it’s something we’ll look to continue to lean on as we move forward.”

The Vikings, who play at Oakland on Sunday, are 6-2, with 30-year-old running back Adrian Peterson back from his suspension last season to take some heat off Bridgewater.

“He’s still able to do a lot of great things — put his foot in the ground and make people miss, still get down the field vertically and run fast,” Greenway said. “He’s in a place where he’s happy and he wants to be here, he wants to help his team and he’s done a good job.”

Defensive tackle Linval Joseph, an ex-Giant, has been a force.

“He’s a great weight room guy, great teammate,” Greenway said. “He definitely wants to be great, and he’s proven that. From a standpoint of strength and unique abilities, he definitely has that. I played with a guy like Pat Williams, Kevin Williams, the ‘Williams Wall’ earlier in my career, and just to see what Linval’s able to do, kind of bouncing off and compared to what the Williams Wall was doing, it’s pretty impressive.”

Zimmer has young talent all across his second-ranked defense. Rookie receiver Stefon Diggs has been a revelation. But Bridgewater is not Aaron Rodgers as the Vikings challenge the Packers for the NFC North crown.

“This team he has … they make me nervous,” Parcells said of Zimmer’s Vikings. “Because they’re a team that really has to play to their potential pretty much every week if they’re going to have a chance. They’re not a team that’s going to go in and blow people out, or dominate them. They have to be on all cylinders.

“Their kicking game is very good. They got to avoid penalties, which is what they’re doing. They are winning by being smart and tough and mentally resilient. I wouldn’t say they are the most talented team that I’ve seen, I don’t think they are. … They haven’t been behind too far where they got to try to really catch up, and put a lot of pressure on Bridgewater to do that. They got to play a certain way to win.”

Greenway, whose role has shifted from young playmaker to elder statesman, deserves to go out a winner, if in fact this is his last hurrah.

“I’m just proud to have spent my time in one place,” he said. “My goal coming into the NFL was to start and finish with one organization, and I’ve been blessed enough to do that.”

Greenway said he is not ready to consider this team “a year away.”

“Some of us don’t have another year,” he said with a laugh. “We’re a young football team, obviously a growing quarterback and a growing young defense. But I just think we’re trying to just stay in our lane and do our jobs.”

Take it from Bill Parcells: They’ve got the right driver.