If your house has enterprise class switches/users with a management interface, the answer is yes - Log in and perform a few queries. I cannot give examples as it is very different depending on manufacturer / model.
If you do not have access to a management interface, it is impossible to know exactly where you are plugged into.
If you have just normal switches before a single router, there is simply no way to know.
If you have a few routers, you can go to Command Prompt / Terminal and type something such as "Tracert www.google.com" and you will see the amount of routers your connection passes through
For example, I have a few switches and only one router that I go through, typing tracert I see -
Tracing route to www.l.google.com [220.127.116.11]
over a maximum of 30 hops:
1 <1 ms <1 ms <1 ms 192.168.0.1
2 * * * Request timed out.
3 * * * Request timed out.
4 * * * Request timed out.
2, 3 and 4 are already outside of my network.
Even using this method, there is no way to know what port you are connected to, with standard unmanged switches.