Brown is in the Scotland squad to face Denmark on Tuesday.
The 30-year-old is set to bring up his half-century when Gordon Strachan's men take on Denmark this coming week. And Mulgrew has explained how his ability to lead a team has made him such a key player for both club and country.
"I wouldn't say he does a lot of shouting, on the pitch he leads by example. When he does shout the people who are getting it usually need it - and it brings out the best in them," he told The Scottish Sun.
"But there's more to him than that, the way he plays, the way he tackles, the way he starts games, the way he's up for the fight - and with all those things he drags people with him.
"That's why he's has been Celtic skipper for a long time and is captain of his country now."
Like Mulgrew, Brown has spent a significant part of the campaign on the sidelines due to injury. He went through a period of the season where he made just one appearance in three months. However, luckily for Ronny Deila, the former Hibernian midfielder has been a constant in the Hoops' side for the last two months and appears to have come through that period unscathed.
And that could be crucial heading into the final part of the season. While the Bhoys have an excellent opportunity to slam the door on Aberdeen's title challenge - as they currently boast a four point lead at the top of the Scottish Premiership with a game in hand also - they will know that things can quickly change if they allow their standards to slip.
However, with Brown's consistency and ability to be a calming influence on those around him, the Hoops have got an excellent chance of building on the momentum they have gained in recent weeks, and Scotland have arguably got the perfect leader to guide them through their transitional period.