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? I'm a little confused. Does anyone have any suggestions?