I thought the Ethernet is logically a one-line communication bus (for argument's sake, I am excluding hubs). All machines attached on the bus hears the same signals and the machines themselves try to avoid collisions by randomly backing off.

http://computer.howstuffworks.com/ethernet6.htm

If so, why would splitting one Ethernet line from my home router into two and connecting two computers not work? Why do I have to add a switch to it?

*What the Internet said would not work.

[4 port home router] ------[one Ethernet cable]-----[simple splitter]======[two computers]

*What the Internet said I should do

[4 port home router] ------[one Ethernet cable]-----[switch]======[two computers]

Is this because of the signal degradation (reduced electric current)?

Thank you for all the answers! The reason why I did not just use the two ports of my home router is...

The 4-port gigabit router is in my room, and I had put a computer in another room (also my room, though). Since a wired network is far more reliable and secure, I had bought a long Ethernet cable and and connected the computer to the router. Now I was thinking about adding another computer to that room. I could buy another long Ethernet cable, but then there will be two cables between the rooms. The one line already is a minor annoyance, so I thought if I could share the one line between the two computers in that room. A switch would work, but it requires power and is a little bit pricey. That is why I wondered why it would not work to simply split the physical Ethernet cable.

Apparently I do not completely understand how Ethernet and a switch work. I just have some bit of knowledge I heard in my college class.