1. First off, you'll have to forgive me lack of vocabulary when speaking about the problem I will describe. I'll do my best, if I am not clear in any way let me know and I'll do what I can do clarify.

I'll pose the problem to you as follows:

Suppose you have a list of n nodes. Each node is connected to every other node with a network score (normalized) representing the strength of the connection between the two. In addition, each node has significant contributors to its network defined as those nodes whose network score with node n is >= to the mean network score of all connections for node n plus 1 standard deviation. As a result it is possible that node 2 may be a significant contributor to node 1 but node 1 need not be a significant contributor to node 2.

I want to build the network tree of each node which contains no loops. Where loops exists the weakest connection should be removed. Loops should be removed in an unbiased way. Removing loops as they occur is biased to the method used to search for loops. This is a significant part of the problem I have encountered so far, how to remove loops in an unbiased way.

In short, any ideas about how to go about finding this network, removing loops and doing this all with as little bias as possible.

Given my lack of vocabulary surrounding this topic any replies that minimize jargon or explain technical terms would be greatly appreciated. Lets see what we come up with!

—PE

2.

3. Let me say I have no idea as to what you're asking about but if you don't find any helpful answers soon you could ask in the Computer Science section.

4. While I am using a computer to do the analysis, the computer science aspect of it is not my problem The graph theory of loops and loop removal from networks is my problem. Hopefully someone has some advice or can help me clarify what it is that I am asking.

5. This is where I feel difficult to understand.

Originally Posted by PhiloEpisteme
In addition, each node has significant contributors to its network defined as those nodes whose network score with node n is >= to the mean network score of all connections for node n plus 1 standard deviation. As a result it is possible that node 2 may be a significant contributor to node 1 but node 1 need not be a significant contributor to node 2.
—PE
Anyway, the problem is like a minimum spanning tree (MST) problem. If not, maybe it is possible to convert the problem to be an MST problem.

6. Originally Posted by PhiloEpisteme
While I am using a computer to do the analysis, the computer science aspect of it is not my problem The graph theory of loops and loop removal from networks is my problem. Hopefully someone has some advice or can help me clarify what it is that I am asking.
As Julian already said, this is a minimum spanning tree (MST) problem. You want to avoid the loops? Just make a recursive function and a class that saves all previous nodes when expanding them. Coming from Computing I must say this is a very much Computing problem.