Construct a line graph / conjugate graph
Ruby, 51 bytes



-&gt;a{a.combination(2){|x,y|p [x*'',y*'']if(x&amp;y)[0]}}


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For each combination of two edges, if they have a vertex in common (i.e. if the first element of their intersection is non-nil), print an array containing the two edges to STDOUT.