Deleting neighbor points

[LanoYado]

I am wondering if there is a way to find (and delete) any point from the system that make the whole network without being there two points neighbor to each? For instant, for three points connected to each other either in a series way or as a triangle shape, we can delete two of them to make no neighbor in the system. What about if we have a network similar to the one in the image?

Any idea? especially from Dan, Chris, or Xander?

Thanks

[LanoYado]

I guess this problem is similar to location allocation problem in network analysis buy without considering the line-length as a cost of optimization. I will start with it first.

[DanPatterson_Retired]

You are starting to get into the area of 'trees' for example kd tree.  it is like you want to prune the connections between points that don't have an intermediate connection.  Now don't start kd'ing your data set but think about your data structure... it doesn't appear to have any spatial sorting involved in the point arrangement and it certainly isn't a minimum spanning tree, (as mentioned earlier).  How were the points put together?

[LanoYado]

To be honest, I am not familiar with kd tree you mentioned Dan. But, the following image is the exact problem, where I only have the bold-black circle points and the lines between them only; the rest are out of the problem I can clean them later on. I tried to solved by location allocation but I have a problem as you can see from the second image.

 

[DanPatterson_Retired]

That is the whole area? Get the feature class into edit mode, select the lines you don't want and delete them

[LanoYado]

Unfortunately, that's not the whole system, but that's what I am going to do with it although my method should be generalized for any system. Thanks an.