Correctness of networkx line digraph construction - networkx

Question

The following Python code:
import networkx as nx
g = nx.DiGraph()
g.add_nodes_from([0, 1])
g.add_edges_from([(0,0), (0,1), (1,0), (1,1)])
nx.write_dot(g, 'g.dot')
gl = nx.line_graph(g)
nx.write_dot(gl, 'gl.dot')
creates the following dot format graphs:
--- g.dot ---
digraph {
0 -> 0;
0 -> 1;
1 -> 0;
1 -> 1;
}
--- gl.dot ---
strict digraph {
"(0, 1)" -> "(1, 1)";
"(1, 0)" -> "(0, 0)";
"(0, 0)" -> "(0, 1)";
"(1, 1)" -> "(1, 0)";
}
Should the edges:
"(1, 0)" -> "(0, 1)";
"(0, 1)" -> "(1, 0)";
"(0, 0)" -> "(1, 1)";
"(1, 1)" -> "(0, 0)";
be in the line graph construction?
http://en.wikipedia.org/wiki/Line_graph#Line_digraph

Answer 1

nx.line_graph creates a strict DiGraph. Strict means there are no loops and no repeated edges. "(0, 1)" -> "(1, 0)" is a loop, so it is not included. In other words, "Two vertices representing directed edges from u to v and from w to x in G are connected by an edge from uv to wx in the strict line digraph when v = w and u != x". (Quote from Wikipedia - my insertions are bold).

Answer 2

The NetworkX line digraph code doesn't add isolates for self-loops nor does it allow creation of a self-loop in the line graph (loop of length 2 in original graph).
This may be a bug or a feature. If someone could point me to the definition of the line graph for these cases maybe we can at least clarify the documentation or update the code.
Note that the dot file keyword "strict" in this case is basically true but just a happy coincidence that the code that writes dot files checks for self loops and multi-edges and uses "strict" if it doesn't find any.
Meantime here is a way to generate a directed line graph allowing both kinds of loops:
import networkx as nx
def directed_line_graph(G):
L = nx.DiGraph()
for u, adj in G.adjacency_iter():
for v in adj:
L.add_node((u,v)) # add self loops and single edges as nodes
for w in G[v]: # neighbors of v
if not (u == v and v == w):
L.add_edge((u,v),(v,w))
return L
g = nx.DiGraph()
g.add_edges_from([(0,0), (0,1), (1,0), (1,1)])
gl = directed_line_graph(g)
for e in gl.edges():
print e
# ((0, 1), (1, 0))
# ((0, 1), (1, 1))
# ((1, 0), (0, 1))
# ((1, 0), (0, 0))
# ((0, 0), (0, 1))
# ((1, 1), (1, 0))