On Thursday, March 29, 2018 at 2:46:22 PM UTC+1, HG wrote:
>
>
> https://www.usna.edu/Users/math/wdj/_files/documents/teach/sm444/sm444_alg-graph-thry-notes.pdf
>
> This example (figure 4, page11) is the fano plane, I thaught the the 
> following example was how to make it but no....
> sage: for x in GF(7):
> ....: L = [x+1,x+2,x+4]
> ....: L.sort()
> ....: print x, L
>
> B = matrix(ZZ,[[0,0,0,1,0,1,1],[1,0,0,0,1,0,1], 
> [1,1,0,0,0,1,0],[0,1,1,0,0,0,1],
> [1,0,1,1,0,0,0],[0,1,0,1,1,0,0],[0,0,1,0,1,1,0]])
>
> A = block_matrix(2, 2, [ B*0, B, B.transpose(), B*0 ]) 
> sage: Gamma = Graph(A, format=’adjacency_matrix’)
> sage: Gamma.is_bipartite()
>

this constructs the incidence point-line graph of the Fano plane.
There is no regular way to draw configurations like the one you would like, 
other than indeed using points, lines, and circles...
  

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