exmple.js

var gFriends = [
    {
        name: 'Sam',
        friends: ['Mat', 'Sharon'],
        gender: 'male',
        best: true
    },
    {
        name: 'Sally',
        friends: ['Brad', 'Emily'],
        gender: 'female',
        best: true
    },
    {
        name: 'Mat',
        friends: ['Sam', 'Sharon'],
        gender: 'male'
    },
    {
        name: 'Sharon',
        friends: ['Sam', 'Itan', 'Mat'],
        gender: 'female'
    },
    {
        name: 'Brad',
        friends: ['Sally', 'Emily', 'Julia'],
        gender: 'male'
    },
    {
        name: 'Emily',
        friends: ['Sally', 'Brad'],
        gender: 'female'
    },
    {
        name: 'Itan',
        friends: ['Sharon', 'Julia'],
        gender: 'male'
    },
    {
        name: 'Julia',
        friends: ['Brad', 'Itan'],
        gender: 'female'
    }
];

const findFriendByName = (name, friends) => friends.find(friend => friend.name === name);

const bfsm = (allFriends, friends, levels, visited = new Set(), level = 0) => {
    if (!friends.length) {
        return;
    }

    levels[level] = friends;
    friends.forEach(({ name }) => visited.add(name));

    const nextLevelFriends = friends.reduce((acc, friend) => {
        acc.push(...friend.friends
            .filter(friendName => !visited.has(friendName))
            .map(friendName => findFriendByName(friendName, allFriends))
        );

        return acc;
    }, []);

    bfsm(allFriends, nextLevelFriends, levels, visited, level + 1);
};

const levels = [];

bfsm(gFriends, gFriends.filter(({ best }) => best), levels);

levels.forEach((level, index) => {
    console.log(index + ' - ' + level.map(({ name }) => name));
});