How do I find out whether a network connection is full or half duplex?
You can use mii-tool :
$ sudo mii-tool eth0: negotiated 100baseTx-FD flow-control, link ok
'FD' is full duplex. 'HD' would represent half. For those who haven't seen this, it's because it generally represents a network problem -- you should always see and expect full.
If you don't have mii-tool installed, it is in the net-tools package:
$ dpkg -S mii-tool net-tools: /usr/share/man/man8/mii-tool.8.gz net-tools: /sbin/mii-tool
I believe it is included with a base install, however.
In some cases, dmesg will be sufficient.
Identify your local interface and check dmesg:
$ dmesg | grep -i duplex [ 31.920900] e1000e: eth0 NIC Link is Up 100 Mbps Full Duplex, Flow Control: Rx/Tx