adjacency matrix of line graph

Question

For a directed graph G defined by G(E, V), how can i find the adjacency matrix of line graph of G.

I am using networkx to learn graph:

I did calculate by this:

//out-edge incidence matrix
B = np.array([[1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0,  1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 1, 0]]);

//in-edge Incidence matrix
E = np.array([[0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1]]);

ET = E.transpose();

// i created line graph from this
H = nx.line_graph(G)

//adjacency matrix of Line Graph
M = nx.to_numpy_matrix(H)

I read somewhere in internet that, this hold true for directed graph M = (Transpose of E) * B

// so i tried to check it and i got this

result = np.matmul(ET, B);
print(result)

and this is my M matrix

but this is not equal

adjacency matrix of line graph

0 Answers