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

Question

In the context of social networks, what is a good measure of the strength of the connection between two nodes? I now think 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) give the total number of nodes directly connected to X, and the above intersection 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? Initially, I used the degree of centrality of the node to determine its "influence", but for some reason I think this is not a good idea, because just because the node has many outbound links does not mean anything. These links should also be effective. In this case, perhaps using the combination of strengths of each node associated with that node is a good idea to evaluate its impact? Am I in the right direction? Anyone have any suggestions?

My philosophy (and understanding of terms):

• Strength indicates how far A is ready to do what B has already done.
• Influence indicates how far B can get B to do something (maybe a conviction?)

Limitations: Access to only a subgraph. I mean, I'm trying to be realistic here, because social networks are huge and the full presentation is not so practical.

Answer 1

You can check out more complex concepts of distance. Really cool is the “resistance distance”, which allows you to view the distance, since a likely random path from one node will lead you to another

There are several days of lectures, plus links to further reading at http://www.cs.yale.edu/homes/spielman/462/ .

Answer 2

A few thoughts on this:

When you talk about the influence of a node on a graph of one dimension of centrality, which recalls its proximity. The proximity integrity looks at the number of shortest paths on the graph on which the node is located. In terms of influence, a node that is on the shortest paths is a node that can exchange information the easiest way, that is, it is closer to more nodes than any other.

Also mentioned is the use of the strengths of each node connected to the node. Perhaps you should take a look at the central role of the eigenvector, which is very different from node if it is associated with other nodes of a high degree. This is a non-oriented version of PageRank.

Some questions that may affect your choice are:

• Is the graph directed?
• Do you have any weight? You are talking about power ... do you mean some kind of scales?

If you have weights, maybe the next step from a simple degree of center is to try and evaluate the degree of centrality. Thus, simply having a large number of connections does not automatically make you the most influential.