"Friendship"...a name for an amazing bonding...
We humans have so complex social structure and complex structure of emotional attachments that if any mathematician (may be John Nash, who was trying to develop mathematical function for the random movement of the pigeons on the field infront of his home!! What a man! ) tries to develop an equation for describing this structure, the equation will be of the order of 'n' where n may tend to infinity!! :)
Thinking of writing a small piece of my thinkings on this sometime in the future.
To chew something until then here is a link which throws some light on this aspect.