Ufdjrw

We can obtain the incidence matrix of a digraph using the method incidence_matrix(oriented=None, sparse=True, vertices=None) in SageMath.

Each row is a vertex, and each column is an edge. The vertices are ordered as obtained by the method vertices(), except when parameter vertices is given, and the edges as obtained by the method edge_iterator().

My question is how to specify the vertice order and the edge order?

For example, g is a weighted digraph with 10 edges:

edges = [('s', 'x', 3), ('s', 'y', 5),
 ('x', 'y', 2), ('x', 'z', 6),
 ('y', 'x', 1), ('y', 'z', 4), ('y', 't', 6),
 ('z', 't', 2),
 ('t', 's', 3), ('t', 'z', 7)]

g = DiGraph(edges)

I want to arrange the incidence matrix such that the vertices (from top to down) are ordered as s, x, y, z, t and the edges are ordered (from left to right) as those in edges (i.e., listing the edges in the alphabetic order s, x, y, z, t).

A quick look at the code (which you can obtain by doing g.edge_iterator??) for edge_iterator() suggests

The iterator returned is over the edges incident with any vertex

given in the parameter "vertices".

if oriented:
 for e, (i, j) in enumerate(self.edge_iterator(labels=False)):
 if i != j:
 m[verts[i],e] = -1
 m[verts[j],e] = +1
else:
 for e, (i, j) in enumerate(self.edge_iterator(labels=False)):
 m[verts[i],e] += 1
 m[verts[j],e] += 1

tells me that probably one would have to hack the code for this a bit to change the order.

This seems like a reasonable request to have this customizable, so I've opened Sage Trac ticket 27513 for this.