REST API - non-static (changing) resource for single url - how to design? - rest

Question

Imagine I have an API for a school. One of the resources is Department, which has various resources on it, such as a collection of Professors, and a "Head Professor".
Department looks like this:
{
"_links": {
"self": "http://myapi.com/department/math"
}
"name": "Math Department",
"headProfessor": {
"_links": {
"self": "http://myapi.com/professor/id/2",
"headProfessor": "http://myapi.com/headprofessor/department/math"
},
"name": "George Patton",
"id": "2"
}
"professors": {
"_links": {
"self": "http://myapi.com/professors/department/math"
},
"_collectionData": [
{
"_links": {
"self": "http://myapi.com/professor/id/1"
},
"name": "John Doe",
"id": "1"
},
{
"_links": {
"self": "http://myapi.com/professor/id/2"
},
"name": "George Patton",
"id": "2"
},
{
"_links": {
"self": "http://myapi.com/professor/id/3"
},
"name": "Paul Simon",
"id": "3"
}
]
}
}
My question is regarding "headProfessor" and the links. What is the canonical link for the "head professor"? Is it http://myapi.com/professor/id/1 or is it http://myapi.com/headprofessor/department/math? Should I have both in there? Or is only one necessary? Is there a better way to represent the "head" or the "top" of something, basically a url whose resource could change because it represents a relationship and not a static resource?
NOTE
Yes, I do prefer the resource designator first in the url as it gives the resource designator the same location in every url. But my question is not about that. That's just a matter of taste and style.

Answer 1

First of all Department has professors and not vice-versa so your APIs should be designed like this
http://myapi.com/departments -> GET all departments
http://myapi.com/departments/{departmentId}/professors ---> POST to add a professor to a department , body of POST has the rank of professor has HOD, or staff
http://myapi.com/departments/{departmentId}/professors ---> GET should get all professors of that department
http://myapi.com/departments/{departmentId}/professors?rank=hod ---> Should give you the HOD
http://myapi.com/departments/{departmentId}/professors/{professorId} ---> PUT to change rank of Professor
http://myapi.com/departments/{departmentId}/professors/{professorId} ---> DELETE to remove professor from Department if he retires or moves to another college,etc.