There are tools (hardware and software required) that will scan the child and neighbor tables of all the Zigbee routers in your network and from that info generate a network map that shows the mesh topology.
The XBee device (you need to use the Zigbee version) and XCTU are the hardware and software components that are discussed here: Everything Xbee
I use a Digi Xstick2 (not sold anymore, it's a precursor to the XBee) and XCTU (which is free). The resulting map can take a long time (multiple scans a taking a few minutes each) before your devices all show up, and though you can customize the layout to some extent using it is very fiddly as the graph changes with each device discovered. Also you need to refer to the shortID's (rather than symbolic names) to make sense of it all. Still, it's probably the best way to get the information you're looking for.
One way to find out is to turn them off... wait a while and see what happens. Its always easier to do the opposite (gradually build out a network while observing how it performs--albeit with the limited diagnostic info you have available-- then add new stuff.... and repeat) but at this point experimenting might be your only option if you want to get to the bottom of this.
