Solution 1:

The self-answer is indeed one way of modeling this. It's probably the most direct equivalent of how you'd model this in a relational database:

  • contractors
  • companies
  • companyAndContractorsAssignment (the many-to-many connector table)

An alternative would be to use 4 top-level nodes:

  • contractors
  • companies
  • companyContractors
  • contractorCompanies

The last two nodes would look like:

companyContractors
    companyKey1
        contractorKey1: true
        contractorKey3: true
    companyKey2
        contractorKey2: true
contractorCompanies
    contractorKey1
        companyKey1: true
    contractorKey2
        companyKey2: true
    contractorKey3
        companyKey1: true

This bidirectional structure allows you to both look up "contractors for a company" and "companies for a contractor", without either of these needing to be a query. This is bound to be faster, especially as you add contractors and companies.

Whether this is necessary for your app, depends on the use-cases you need, the data sizes you expect and much more.

Recommended reading NoSQL data modeling and viewing Firebase for SQL developers. This question was also featured in an episode of the #AskFirebase youtube series.

Update (2017016)

Somebody posted a follow-up question that links here about retrieving the actual items from the "contractors" and "companies" nodes. You will need to retrieve those one at a time, since Firebase doesn't have an equivalent to SELECT * FROM table WHERE id IN (1,2,3). But this operation is not as slow as you may think, because the requests are pipelined over a single connection. Read more about that here: Speed up fetching posts for my social network app by using query instead of observing a single event repeatedly.

Solution 2:

After further research, I'm going to try and answer my own question. I have reviewed a number of other posts and one solution to the many-to-many problem is to store a list of ContractorKeys within a Company object and store a list of CompanyKeys within each contractor object. This is illustrated with an example below.

companies : {
  companyKey1 : {
    name : company1
    ...
    contractors : {
      contractorKey1 : true,   
      contractorKey3 : true
    }
  }
  companyKey2 : {
    name : company2
    ...
    contractors : {
      contractorKey2 : true,  
    } 
  }
}
contrators : {
  contractorKey1 : {
     name : bill
     ...
     companies : {
        companyKey1 : true
     }
   }
  contractorKey2 : {
     name : steve
     ...
     companies : {
        companyKey1 : true
     }

   }
  contractorKey3 : {
     name : jim
     ...
     companies : {
        companyKey2 : true
     }
   }
}

This organization "works" in the sense that the aforementioned questions can be answered. But a downside of this solution is that there are two lists to maintain when the Contractor/Company assignments change. It would be better if there was a way to represent this information in a single list.

I think I have come up with a better solution. The solution is to create a third list, in addition to companies and contractors called companyAndContractorAssignment. The elements of this list will represent a relationship between a single contractor and company. Its contents will be a pair of fields, the contractorKey and the companyKey. We can then eliminate the contractors list within company and the companies list within contractor. This alternative structure is represented below. Notice there is no contractor list within a company object and no companies list with a contractor object.

companies : {
  companyKey1 : {
    name : company1
    ...
  }
  companyKey2 : {
    name : company2
    ...
  }
}
contrators : {
  contractorKey1 : {
     name : bill
     ...
  }
  contractorKey2 : {
     name : steve
     ...
  }
  contractorKey3 : {
     name : jim
     ...
  }
}
companyAndContractorsAssignment : {
  key1 : {
    contractorKey1 : true,
    companyKey1: true,
  }
  key2 : {
    contractorKey3 : true,
    companyKey1: true,
  }
  key3 : {
    contractorKey2 : true,
    companyKey2: true,
  }

This alternative structure allows one to answer the questions using an orderByChild/equalTo query on companyAndContractorsAssignment to find either all companies for a contractor or all contractors for a company. And there is now only a single list to maintain. I think this is the best solution for my requirements.