What is a good measure of strength of a link and influence of a node?

Question

In the context of social networks, what is a good measure of strength of a link between two nodes? I am currently thinking that the following should give me what I want:

For two nodes A and B:
Strength(A,B) = (neighbors(A) intersection neighbors(B))/neighbors(A)

where neighbors(X) gives the total number of nodes directly connected to X and the intersection operation above gives the number of nodes that are connected to both A and B.

Of course, Strength(A,B) != Strength(B,A).

Now knowing this, is there a good way to determine the influence of a node? I was initially using the Degree Centrality of a node to determine its "influence" but I somehow think its not a good idea because just because a node has a lot of outgoing links does not mean anything. Those links should be powerful as well. In that case, maybe using an aggregate of the strengths of each node connected to this node is a good idea to estimate its influence? Am I in the right direction? Does anyone have any suggestions?

My Philosophy (and understanding of the terms):

• Strength indicates how far A is willing to do what B has already done
• Influence indicates how far A can make B do something (persuasion perhaps?)

Constraints: Access to only a subgraph. I mean, I am trying to be realistic here because social networks are huge and having a complete view is not so practical.

Answer 1

you might want to check out some more sophisticated notions of distance. A really cool one is "resistance distance", which lets you view distance as how likely a random path from one node will lead you to another

there are several days of lecture notes plus references to further reading at http://www.cs.yale.edu/homes/spielman/462/.