Virtual COM port using only USB cable

I have seen that it is possible to connect two computers by USB cable and make a virtual ethernet bridge or something like that. My question is, can we do something similar but configure the connection as a SERIAL interface? To be exact: Is it possible to connect two computers with a USB cable (I do not know what the correct name is, I mean a cable that has USB-A connector on both ends) without any Serial adapter involved and then configure the usb port as a serial.