# 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.
• This may be too broad a question, as I suspect that large parts of social network research is about this exact question. Community votes, please! – Raphael Jan 20 '16 at 16:10
• But, what about the bounty, if this question is closed, then will it go wasted ? @Raphael – azam Jan 27 '16 at 11:02
• @azam Yes, but that should not influence voting decisions. The author can always improve their question and have it reopened before the period runs out. (Assuming the bounty will stay in place, which I am not completely sure about.) – Raphael Jan 27 '16 at 12:02
• Also, possible duplicate? – Raphael Jan 27 '16 at 12:10