# Importance of a person to another person in social network

In social network (an unweighted indirect network), is there some measure of importance of a person A on another person B, denote as I(A,B), so that (approximately):

1. The smaller the shortest distance between A, B in the the network, the higher the I(A,B) (closeness)
2. If A_1 is 1 of the 100 friends of B_1, A_2 is 1 of the 2 friends of B_2, then I(A_1,B_1) < I(A_2,B_2) (the more friends I have, the less importance of each one)
3. Some other reasonable properties that resemble the importance of a friend to another friend in real society.