NoSQL & Firebase: Storing & Iterating over many-to-many relationship - firebase

Question

I have 2 main nodes in my database: Users and Projects.
Each user can be assigned to multiple projects, in different roles.
After reading about how to structure many to many relationship, I ended up that it should look like this:
users : {
user1 : {
name : blah,
email : a#a.com,
projects : {
projects1key : true,
projects2key : true
}
}
}
projects : {
project1key : {
name : blahserve,
category : blahbers,
providers : {
user1 : true,
user7 : true
}
}
}
What I couldn't figure out is how I can assign every user a role in each project.
What's the new database structure should look like if I need to add role (string) to each user within a project?
Correct me if I'm wrong: When I assign user to a project, I need to create 2 new nodes: a projectkey node in my user node, and a userkey node in my projectkeynode. Is that right?
Update
Since the answer given here is correct but not sure it will fit my use case, this is my use case:
(1) Iterating over a list of all project users
(2) Iterating over a list of all member project
(3) Check for project role when the user access a project and give give him permission depends on his role
(4) The "Project -> users" page allow you to add a new user to existing project. the user role is picked in the same form together with the user. the user must have a role in a project.

Answer 1

Or maybe just simply you could add a different node all together:-
What's the new database structure should look like if I need to add role (string) to each user within a project?
users : {
user1 : {
name : blah,
email : a#a.com,
}
},
projects : {
projectKey1 : {
name : blahserve,
category : blahbers,
}
},
projectsLists:{
user1 :{
projectKey1 : true,
projectKey2 : true
}
},
projectsRoles :{
projectKey1 : {
user1 : provider,
user2 : editor,
....
}
}
Correct me if I'm wrong: When I assign user to a project, I need to create 2 new nodes: a projectkey node in my user node, and a userkey node in my projectkeynode. Is that right?
Always prefer the flatter DB structure. So using this structure you only gotta append or update your user's role once.