representing a city org structure

I am continuing my exploration about representing New York City using
Schema.org.

I am now looking at the city org structure.
Here is the official org chart:
https://www.nyc.gov/assets/home/downloads/pdf/office-of-the-mayor/misc/NYC-Organizational-Chart.pdf
.
People, roles and orgs are all mixed up together, which makes things really
messy. But assuming we can fix that, I have a few questions.

*Org hierarchy*
For "agencies", we can use GovernmentOrganization and property
parentOrganization and subOrganization to represent the relationships.
However, it is not totally clear when to use subOrganization vs department.

*Org <-> People relationships*
How would you represent the person running the agency (the head of the
agency)?
We can use property employee, but it does not convey the management part.
founder and member are not ideal either.
Should we create a new property for this?

*Org <-> Org relationships*
How would you represent the fact that a given org oversees/regulates/etc.
another one?

regards,

-- 
Arnaud

PS: There is a saying in the NYC Civic Tech community: "New York City is
where new technologies come to audition".
Schema.org needs no audition. If we can find an intuitive way of
representing NYC org chart, we should be able to represent any city org
chart :-)