# Connection strength in a weighted social digraph, based on weights of individual links

Given a network where edges represent entities and directed vertices represent relationships between entities, and each vertex has a strength between 0 (no relationship) and 1 (strongest).

I'm looking for a method to calculate the path strength between two entities.

For simple cases, I'm considering the following formulas:

• Path: The strength of the connection is the multiplication of all weights of the links along the path.

• Parallel direct links: The strength of the connection is 1-(1-w1)(1-w2)...(1-wn)

My questions:

• Were these formulas suggested before?
• How can this method be extended to more complex cases, such as the graphs given below:

• I don't know where your intuition for those formulas came from, but I recommend the formulas for resistance or capacitance. Nov 18 '12 at 13:56
• @TysonWilliams: These formulas are similar to resistance formulas, but '+' is replaced with '*', and '/' is replaced with '-'. More important - network resistance formulas are suitable only for non-directed graphs. Nov 18 '12 at 14:08
• Aren't these just Markov state diagrams? Nov 18 '12 at 22:09
• @JohnMoeller: The Diagrams are similar, however the sum of weights of all outgoing edges for any given vertex is not bounded. Furthermore, there are no 'moves', and time does not play a role either. Nov 19 '12 at 7:04
• @LiorKogan : Ah, ok, the sum property is the important difference. In your case, you're saying a node could have a very small relationship with its neighbors (sum < 1) or it could have a very important relationship with its neighbors (sum > 1). Nov 19 '12 at 7:12