<p>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).</p>

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

<p>For simple cases, I'm considering the following formulas:</p>

<ul>
<li>Path: The strength of the connection is the multiplication of all weights of the links along the path.</li>
</ul>

<p><img src="https://i.sstatic.net/MxUdM.png" alt="enter image description here"></p>

<ul>
<li>Parallel direct links: The strength of the connection is <em>1-(1-w1)(1-w2)...(1-wn)</em>
<img src="https://i.sstatic.net/j0atJ.png" alt="enter image description here"></li>
</ul>

<p>My questions:</p>

<ul>
<li>Were these formulas suggested before?</li>
<li><p>How can this method be extended to more complex cases, such as the graphs given below:</p>

<p><img src="https://i.sstatic.net/eV3lI.png" alt="enter image description here"></p>

<p><img src="https://i.sstatic.net/Pjkc6.png" alt="enter image description here"></p></li>
</ul>

CC BY-SA 3.0
2012-11-18T13:56:50.853Z
I don't know where your intuition for those formulas came from, but I recommend the formulas for resistance or capacitance.
Tyson Williams
CC BY-SA 3.0
2012-11-18T14:08:05.787Z
@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.
Lior Kogan
CC BY-SA 3.0
2012-11-18T22:09:28.880Z
Aren't these just Markov state diagrams?
Josephine Moeller
CC BY-SA 3.0
2012-11-19T07:04:02.490Z
@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.
Lior Kogan
CC BY-SA 3.0
2012-11-19T07:12:31.397Z
@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).
Josephine Moeller
<ds.algorithms><graph-algorithms><social-sciences>
Connection strength in a weighted social digraph, based on weights of individual links
Lior Kogan
# Connection strength in a weighted social digraph, based on weights of individual links

(Asked by: username_0 on 2012-11-18)

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.

![enter image description here](https://i.sstatic.net/MxUdM.png)

* Parallel direct links: The strength of the connection is *1-(1-w1)(1-w2)...(1-wn)*
  ![enter image description here](https://i.sstatic.net/j0atJ.png)

My questions:

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

  ![enter image description here](https://i.sstatic.net/eV3lI.png)

  ![enter image description here](https://i.sstatic.net/Pjkc6.png)

**Tags:** ds.algorithms, graph-algorithms, social-sciences

> **Comments:**
> **username_1**: I don't know where your intuition for those formulas came from, but I recommend the formulas for resistance or capacitance.  
> **username_0**: @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.  
> **username_2**: Aren't these just Markov state diagrams?  
> **username_0**: @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.  
> **username_2**: @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).  

---

## 0 answers

