Create a directed graph and compute in degrees in Python

I have implemented a couple of functions in python as part of an online course. Although the functions seem to work fine I feel that the code is inefficient with a lot of nested loops. Are there any improvements I can make? I am new to the language so any advice is welcome.

Here is the code and some simple tests:

```
def make_complete_graph(num_nodes):
"""
Takes the number of nodes num_nodes
and returns a dictionary corresponding to a complete directed graph
with the specified number of nodes
"""

result = dict()
for i in range(num_nodes):
set_per_node = set()
for num in range(num_nodes):
if num != i:
set_per_node.add(num)
result[i] = set_per_node

return result

def compute_in_degrees(digraph):
"""
Takes a directed graph digraph (represented as a dictionary) and computes
the in-degrees for the nodes in the graph.
Returns a dictionary with the same set of keys (nodes) as digraph
whose corresponding values are the number of edges
whose head matches a particular node.
"""
result = dict()
count = 0
for key in digraph:
count = 0
for key2, value in digraph.iteritems():
if key != key2:
for val in value:
if val == key:
count += 1
result[key] = count
count = 0

return result

class TestStringMethods(unittest.TestCase):

def test_make_complete_graph(self):
expected_dict_one = {0: set([1, 2]), 1: set([0, 2]), 2: set([0, 1])}
expected_dict_two = {}

actual_dict_one = at_project1.make_complete_graph(3)
actual_dict_two = at_project1.make_complete_graph(0)

self.assertEquals(actual_dict_one, expected_dict_one)
self.assertEquals(actual_dict_two, expected_dict_two)

def test_compute_in_degrees(self):
given_dict_one = {0: set([1, 2]), 1: set([0, 2]), 2: set([0, 1])}
given_dict_two =

In make_complete_graph, the inner loop could be written with a list comprehension:

result[i] = set([num for num in range(num_nodes) if num != i])

In compute_in_degrees, instead of iterating over all nodes for all nodes x to find links going to x, you could build a dictionary of counts easier:

counts = dict([(x, 0) for x in digraph])
for targets in digraph.values():
    for target in targets:
        counts[target] += 1

StackExchange Code Review Q#92258, answer score: 2