How can I make a plot representing connection relationship with python matplotlib?

[Berlintofind]

I want to make a plot composed of of dots and connections lines with matplotlib. (It's not a bar chart or normal line chart with axis)

For example, I have a 5*5 matrix, symmetric about the diagonal：

Connection = np.array([0,0,1,1,1],
                      [0,0,1,0,1],
                      [1,1,0,1,0],
                      [1,0,1,0,0],
                      [1,1,0,0,0]) 

The element represent the connections relationships, if Connection[ i ][ j ] = 0, means no connections between dot i and dot j. If Connection[ i ][ j ] = 1, then there should be a connection line between dot i and j

Since it's a bidirectional relation and the matrix is symmetric , if dot 1 has connection with dot 3, then dot 3 should also has connection with dot 1.

How can I make this kind plots?
Thanks in advance!

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I think it's can be solved by networkx

[jefsummers]

So, in your example there are 5 dots?
If so, how do you want them arranged - my guess is not in a line...