When you say permissions you mean visibility, I'm right? If that's the case, Network content doesn't gets filtered by Visibility, I mean a network it's just a list of Thing Names, that's the reason you see all the network nodes. Then when you will try to access the specified Thing by Thing Name if you don't have access to it, then you will be blocked.
If your logged in User cannot see the entities representing the child nodes in the Composer view they should not be able to see those same entities in a Network view.
Have you tried using a User with no Visibility permissions assigned?
By removing the "Users" Group from the "Everyone" Organization, when you create a new User they will not be able to see any entities, so that would be a good start to test if Visibility permissions are really taking effect.
Thingworx Navigate content has a new home! Click here to access the new Thingworx Navigate forum!