Does this mathematical result help to explain why groups polarize?

For any group of sufficient size, there is a tendency to polarize into two opposing camps. There is a simply stated mathematical result that might help to explain why.

Suppose we model a group of people as follows.
1. Every pair of people is mutually friendly or are mutual enemies.

2. If two people have a mutual friend then they will be friends with each other. – The friend of my friend is my friend.

3. If two people have a mutual enemy they will be friends. – The enemy of my enemy is my friend.

If these conditions hold then either everyone will be friends with one another or, more interestingly, there will be two groups such that within each group everyone is mutually friendly and everyone in one group is an enemy of everyone in the other. That is, a single enmity will splinter the group.

Granted that the model is simplistic, but it seems to roughly model normal human tendencies.