How to get an arbitrary orientation of a graph.

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I'VE COMPLETELY REVISED MY QUESTION

I wish to take a simple undirected graph (i.e. the complete graph K_4) Arbitrarily direct said graph, and then create a line graph from the directed version of the graph.

However, in Sage it appears to create a line graph that shows a connection between two edges (that are just inverses of each other), so what I really want is a line graph that doesn't give an edge connected to its own inverse.

That's why I asked if we could remove cycles of length 2, but that doesn't seem to solve the problem.

Here's what I am trying to work out:

G = graphs.RandomGNP(4,1)  
GD = G.to_directed()     #orients G  
m = GD.size()            #number of edges of digraph GD  
LG = GD.line_graph()     #the line graph of the digraph  
IM = identity_matrix(QQ,GD.size())  
T = LG.adjacency_matrix()#returns the adjacency matrix of the line graph   
var('u')                 #defines u as a variable  
X=IM-u*T                 #defines a new matrix X  
Z=X.det()                #defines polynomial in u  aka inverse of the Ihara zeta function
Z                        #computes determinant of X  
Z.coefficients(u)        #extracts coefficients

considering my graph is a complete graph on 4 vertices - the coefficients should be as such:
[coeff,degree of u]
[1,0], [0,1], [0,2],[-8,3],[-2,4]

NOTE:
im only interested in coefficients up to the order of n=#of nodes in the graph, so here for K_4 obviously n=4.
where the coefficient of u^3 corresponds to the negative of twice the number of triangles in K_4
where the coefficient u^4 corresponds to the negative of twice the number of squares in K_4

Here is an image of a K_4 graph minus an edge and the line graph construction of K_4 that i want