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Find a set of points with the same distance in a euclidean matrix Python

I have a list with coordinates and this Euclidean matrix which represents the distance between each point:

 [0, 0], [0, 1], [0, 2], [0, 3], [0, 4]

 [0. 1. 2. 3. 4.]
 [1. 0. 1. 2. 3.]
 [2. 1. 0. 1. 2.]
 [3. 2. 1. 0. 1.]
 [4. 3. 2. 1. 0.]

And what I want to do is check how many sets of two distinct but equal-length line segments which have one shared endpoint exists, for example: As we can see in the following image from the coordinate (0,0) to the coordinate (0,1) there is a distance equal to 1 and from the coordinate (0,2) to the coordinate (0,1) there is a distance equal to 1 (we already have two line segments with the same distance) and both share a point at the coordinate ( 0, 1).

As shown in the following image:

Segments and sharepoint enter image description here

S1 represents the segment from the point (0, 0) to the point (0, 1) and S2 the segment from the point (0, 2) to the point (0, 1).

And what I want as my output is the number of cases that match the requirements that I mentioned above, in the images below we can see that there are 4 cases that match the requirements.

enter image description here enter image description here enter image description here

How would it be implemented in python? And is there a library that facilitates this analysis?

I was thinking of divide the euclidean matrix in two halves and then compare if they have the same distance and a zero in the middle, if it's the case then it's a match, but I don't know how to manipulate the matrix in order to do that.



source https://stackoverflow.com/questions/73186540/find-a-set-of-points-with-the-same-distance-in-a-euclidean-matrix-python
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