If you completely trust everyone in the network and you can connect a port of the destination machine directly, you can use netcat:
Let's say the IP address of the destination machine is 192.168.1.123
On the destination run:
nc -l -p 7777 0.0.0.0 | tar zxvf - -C dest_dir
You can choose a different port, and also bind to another IP of your interfaces, 0.0.0.0 just catches on all interfaces.
On the source run:
tar zcvf - filename | nc 192.168.1.123 7777
IMHO, this is the fastest possible way to send a file from one computer to another using digital networks.
The arguments and command line options might slightly change between different versions of
tar, but it will definitely work with recent Linux distributions.