Detect Connection Speed Remotely

Is there a way I can detect connection speeds on remote computers across a large network?

Our network has several hundred computers, all with speeds varying from 10Mb to 1Gb. I’d like to create a report or other list that would state each computer, then its connection speed (either 10Mb, 100Mb, or 1Gb) so I could find where older hubs and switches were causing network slowdowns. We have newer workstations but a lot of old network equipment and nothing is mapped! Is there a shortcut besides scouring the building to physically look for hubs?

We have an Active Directory setup with Desktop Authority, if either of these give an advantage.