Consider the following GraphML file (attached).
According to the GraphML file, it represents an undirected graph.
Therefore, I would expect that as I set it to directed graph:
gtGraph=gt.load_graph("yeast.graphml")
gtGraph.set_directed(1)

I would obtain two directed edges for every undirected edge. In particular,
the in degree of every node should be equal to the out degree. However, this
is not the case, for example:
v=gtGraph.vertex(1834)

v.in_degree()
Out[3]: 5

v.out_degree()
Out[4]: 2

I'm a bit puzzled.
A) Is the source file corrupted?
B) When I set the directedness flag to 1, am I guaranteed that every
undirected edge would be converted to two directed edges? If not, how can I
perform this operation (A = A + A', assuming the adjacency matrix is
triangular) or validate it?

B) When I set the directedness flag to 1, am I guaranteed that every
undirected edge would be converted to two directed edges?

Not at all. The set_directed() function does nothing more than to set a flag
indicating the directness, it does not modify the graph in any other way. It
is supposed to be an efficient O(1) operation. In particular, the number of
edges is exactly the same after the function is called.

If not, how can I
perform this operation (A = A + A', assuming the adjacency matrix is
triangular) or validate it?

If you want to make the graph bidirectional, you have to iterate through all
the edges and add an opposing one for each:

edges = list(g.edges())
for e in edges:
g.add_edge(e.target(), e.source())

Should not set_directed() redefine the definition of out_neighbours() and
in_neighbours()?

When I created a simple Erdős–Rényi graph, then change it to a directed
graph, out_neighbours() and in_neighbours() do not return the expected
edges:

import graph_tool.all as gt, numpy as np, numpy.random as rand
N = 12
p = 1.5 * np.log(N)/N
g = gt.random_graph(N, deg_sampler=lambda: rand.poisson((N-1)*p),
directed=False, model='erdos')
vroot = g.vertex(0)

g.set_directed(False)
print([g.edge(vroot,v) for v in vroot.out_neighbours()])
print([g.edge(v,vroot) for v in vroot.in_neighbours()])
g.set_directed(True)
print([g.edge(vroot,v) for v in vroot.out_neighbours()])
print([g.edge(v,vroot) for v in vroot.in_neighbours()])

Result:

[<Edge object with source '0' and target '3' at 0x1245b9050>, <Edge object
with source '0' and target '10' at 0x1245bbf28>, <Edge object with source
'0' and target '6' at 0x1245b90e8>]
[]
[None, None, <Edge object with source '0' and target '6' at 0x1245bf050>]
[]

You can see that out_neighbours() returns *all* edges, even ones that are
inward-pointing, and in_neighbours() fails to return any edges.

Should not set_directed() redefine the definition of out_neighbours() and
in_neighbours()?

It does.

When I created a simple Erdős–Rényi graph, then change it to a directed
graph, out_neighbours() and in_neighbours() do not return the expected
edges:

import graph_tool.all as gt, numpy as np, numpy.random as rand
N = 12
p = 1.5 * np.log(N)/N
g = gt.random_graph(N, deg_sampler=lambda: rand.poisson((N-1)*p),
directed=False, model='erdos')
vroot = g.vertex(0)

g.set_directed(False)
print([g.edge(vroot,v) for v in vroot.out_neighbours()])
print([g.edge(v,vroot) for v in vroot.in_neighbours()])
g.set_directed(True)
print([g.edge(vroot,v) for v in vroot.out_neighbours()])
print([g.edge(v,vroot) for v in vroot.in_neighbours()])

Result:

[<Edge object with source '0' and target '3' at 0x1245b9050>, <Edge object
with source '0' and target '10' at 0x1245bbf28>, <Edge object with source
'0' and target '6' at 0x1245b90e8>]
[]
[None, None, <Edge object with source '0' and target '6' at 0x1245bf050>]
[]

You can see that out_neighbours() returns *all* edges, even ones that are
inward-pointing, and in_neighbours() fails to return any edges.

What is happening here is that the vertex descriptor is still referring to
the original graph. When you do g.set_directed(True), the vroot vertex
descriptor still refers to the old graph. To get the result you were
expecting you have to do:

vroot = g.vertex(0)

after you do g.set_directed().

This is done for efficiency reasons, but is somewhat counter-intuitive. I'll
add a clear note in the documentation.