Closed volumes?

How do you know if a mesh of polygons forms a closed volume?

Every edge of every triangle must be connected to excactly one other triangle.

Yes, I have that data structure already. I know how to detect if it is closed or not, searching connectivity.

The problem is that you might have several closed volumes. How do you detect each one? It is easy if they are separated, but in some cases they might be connected to each other by some edges.

first problem - single closed volume:
in a closed volume, every verticle(vertex?) touches the same number of verticles (vertexes?).

second problem - several closed volumes :
in a closed volume, every verticle can be reached by jumping from triangle to triangle
in 2 seperated volumes, it’s not possible

to kill the misunderstandings :

lets say u have a simple box, then every verticle in contained in the same number of polys (3 in this case)