modeling friends and calculating mutual friends w/ mongodb

gistfile1.js

// ------------------------------------------------------------------
// Friend collection, where _id is a user.Id and Friends is a list, of user.Id.
// Note: friending and unfriending is a two step operation in this scheme:

> db.friends.find()
{ "_id" : 1, "friends" : [    2, 3, 4    ] }
{ "_id" : 2, "friends" : [ 1,    3,    5 ] }
{ "_id" : 3, "friends" : [ 1, 2,    4, 5 ] }
{ "_id" : 4, "friends" : [ 1,    3,    5 ] }
{ "_id" : 5, "friends" : [    2, 3, 4    ] }

// 1 and 2 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [1,2]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 3 } ], "ok" : 1 }

// 1 and 3 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [1,3]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 4 }, { "_id" : 2 } ], "ok" : 1 }

// 1 and 4 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [1,4]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 3 } ], "ok" : 1 }

// 1 and 5 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [1, 5]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 4 }, { "_id" : 3 }, { "_id" : 2 } ], "ok" : 1 }

// 2 and 4 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [2, 4]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 5 }, { "_id" : 3 }, { "_id" : 1 } ], "ok" : 1 }

// 1, 2 and 3 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [1,2,3]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 3}}, {$project: {_id: 1}}])
{ "result" : [ ], "ok" : 1 }  // have no friends in common.

// 1, 2 and 4 mutual friends:
> db.friends.aggregate([{$match: {_id: {$in: [1,2,4]}}}, {$unwind: "$friends"}, {$group: {_id: "$friends", count: {$sum: 1}}}, {$match: {count: 3}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 3 } ], "ok" : 1 } // have one friend in common: user 3



// ------------------------------------------------------------------
// Friendship collection, where _id is calculated by sorting and 
// and joining two friends user.Id
//
// Note: friending and unfriending is a one step operation in this
// scheme:

// encode the exact same friend relationships as above.
> db.friendships.insert([
	{ "_id" : "1|2", "u" : [1, 2] },
	{ "_id" : "1|3", "u" : [1, 3] },
	{ "_id" : "1|4", "u" : [1, 4] },

//{ "_id" : "1|2", "u" : [2, 1] }, // omit -- id exists above
	{ "_id" : "2|3", "u" : [2, 3] },
	{ "_id" : "2|5", "u" : [2, 5] },

//{ "_id" : "1|3", "u" : [3, 1] }, // omit -- id exists above
//{ "_id" : "2|3", "u" : [3, 2] }, // omit -- id exists above
	{ "_id" : "3|4", "u" : [3, 4] },
	{ "_id" : "3|5", "u" : [3, 5] },

//{ "_id" : "1|4", "u" : [4, 1] }, // omit -- id exists above
//{ "_id" : "3|4", "u" : [4, 3] }, // omit -- id exists above
	{ "_id" : "4|5", "u" : [4, 5] },

//{ "_id" : "2|5", "u" : [5, 2] }, // omit -- id exists above
//{ "_id" : "3|5", "u" : [5, 3] }, // omit -- id exists above
//{ "_id" : "4|4", "u" : [5, 4] }, // omit -- id exists above
])

> db.friendships.find()
{ "_id" : "1|2", "u" : [ 1, 2 ] }
{ "_id" : "1|3", "u" : [ 1, 3 ] }
{ "_id" : "1|4", "u" : [ 1, 4 ] }
{ "_id" : "2|3", "u" : [ 2, 3 ] }
{ "_id" : "2|5", "u" : [ 2, 5 ] }
{ "_id" : "3|4", "u" : [ 3, 4 ] }
{ "_id" : "3|5", "u" : [ 3, 5 ] }
{ "_id" : "4|5", "u" : [ 4, 5 ] }

//# 1 and 2 mutual friends:
> db.friendships.aggregate([{$match: {u: {$in: [1,2]}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: [1,2]}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 3 } ], "ok" : 1 }

//# 1 and 3 mutual friends:
> db.friendships.aggregate([{$match: {u: {$in: [1,3]}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: [1,3]}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 4 }, { "_id" : 2 } ], "ok" : 1 }

//# 1 and 4 mutual friends:
> db.friendships.aggregate([{$match: {u: {$in: [1,4]}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: [1,4]}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 3 } ], "ok" : 1 }

//# 1 and 5 mutual friends:
> db.friendships.aggregate([{$match: {u: {$in: [1,5]}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: [1,5]}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 4 }, { "_id" : 3 }, { "_id" : 2 } ], "ok" : 1 }

//# 2 and 4 mutual friends:
> db.friendships.aggregate([{$match: {u: {$in: [2,4]}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: [2,4]}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: 2}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 5 }, { "_id" : 3 }, { "_id" : 1 } ], "ok" : 1 }

//# 1, 2 and 3 mutual friends:
> users = [1,2,3]
> db.friendships.aggregate([{$match: {u: {$in: users}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: users}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: users.length}}, {$project: {_id: 1}}])
{ "result" : [ ], "ok" : 1 }

//# 1, 2 and 4 mutual friends:
> users = [1,2,4]
> db.friendships.aggregate([{$match: {u: {$in: users}}}, {$project: {_id: 0, u: 1}}, {$unwind: "$u"}, {$match: {u: {$nin: users}}}, {$group: {_id: "$u", count: {$sum: 1}}}, {$match: {count: users.length}}, {$project: {_id: 1}}])
{ "result" : [ { "_id" : 3 } ], "ok" : 1 }

It's better rename the first collection from friends to users (

friendship relation schema can be {source:String, target:String, status:String}
status can be accepted,pending,rejected,muted.. like that. instead of using _id to store both users id.