def test_self_loops_2(self):
graph = Graph()
node_1 = Node(graph)
branch_a = Branch(node_1, node_1, "a")
cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertCountEqual([[branch_a.id]], cycles)
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_1, "c")
Branch(node_3, node_4, "d")
branch_e = Branch(node_1, node_1, "e")
branch_f = Branch(node_2, node_2, "f")
branch_g = Branch(node_3, node_3, "g")
branch_h = Branch(node_4, node_4, "h")
cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertTrue(self.__check_loop_order(
[[branch_e.id],
[branch_a.id, branch_b.id, branch_c.id],
[branch_f.id], [branch_g.id], [branch_h.id]], cycles))
def test_graph_copy(self):
# Create graph
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
Branch(node_1, node_2)
Branch(node_2, node_2)
Branch(node_2, node_3)
Branch(node_3, node_1)
Branch(node_1, node_4)
# Make copy
graph_copy = graph.copy()
# Assert
nodes_original = list(graph.nodes)
nodes_original.sort(key=lambda n: n.id)
nodes_copy = list(graph_copy.nodes)
nodes_copy.sort(key=lambda n: n.id)
branches_original = list(graph.branches)
branches_original.sort(key=lambda n: n.id)
branches_copy = list(graph_copy.branches)
branches_copy.sort(key=lambda n: n.id)
for node_original, node_copy in zip(nodes_original, nodes_copy):
self.assertTrue(self.__node_equals(node_original, node_copy))
for branch_original, branch_copy in zip(branches_original,
branches_copy):
self.assertTrue(self.__branch_equals(branch_original, branch_copy))
def test_add_remove_branches(self):
graph = Graph()
branch1 = MagicMock(Branch)
branch2 = MagicMock(Branch)
branch3 = MagicMock(Branch)
branch1.start = MagicMock(Node)
branch1.end = MagicMock(Node)
branch1.graph = graph
branch2.start = MagicMock(Node)
branch2.end = MagicMock(Node)
branch2.graph = graph
branch3.start = MagicMock(Node)
branch3.end = MagicMock(Node)
branch3.graph = graph
graph.add_branch(branch1)
self.assertSetEqual({branch1}, graph.branches)
graph.add_branch(branch2)
graph.add_branch(branch3)
self.assertSetEqual({branch1, branch2, branch3}, graph.branches)
def add_branch_again():
graph.add_branch(branch1)
self.assertRaises(ValueError, add_branch_again)
branch4 = MagicMock(Branch)
branch4.start = MagicMock(Node)
branch4.end = MagicMock(Node)
branch4.graph = None
def add_branch4():
graph.add_branch(branch4)
branch4.end = None
self.assertRaises(ValueError, add_branch4)
self.assertSetEqual({branch1, branch2, branch3}, graph.branches)
branch1.start = None
branch1.end = None
branch2.start = None
branch2.end = None
branch3.start = None
branch3.end = None
graph.remove_branch(branch1)
self.assertSetEqual({branch2, branch3}, graph.branches)
graph.remove_branch(branch2)
graph.remove_branch(branch3)
self.assertSetEqual(set(), graph.branches)
def test_not_touching_loops(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
branch_a = Branch(node_1, node_1, "a")
branch_b = Branch(node_2, node_2, "b")
branch_c = Branch(node_3, node_3, "c")
res = find_loop_groups([
[branch_a],
[branch_b],
[branch_c]
])
loops = [(loopGroup.loops, loopGroup.loop_count) for loopGroup
in res]
expected = [
([[branch_a]], 1),
([[branch_b]], 1),
([[branch_c]], 1),
([[branch_b], [branch_a]], 2),
([[branch_c], [branch_b]], 2),
([[branch_c], [branch_a]], 2),
([[branch_c], [branch_b], [branch_a]], 3),
]
self.assertCountEqual(expected, loops)
def test_johnson_4(self):
graph = Graph()
node_a = Node(graph)
node_b = Node(graph)
node_c = Node(graph)
node_d = Node(graph)
branch_ac = Branch(node_a, node_c, "ac")
branch_ca = Branch(node_c, node_a, "ca")
branch_ab = Branch(node_a, node_b, "ab")
branch_ba = Branch(node_b, node_a, "ba")
branch_bc = Branch(node_b, node_c, "bc")
branch_cd = Branch(node_c, node_d, "cd")
branch_db = Branch(node_d, node_b, "db")
actual = strongly_connected_components(graph)
expected = [[node_a, node_b, node_c, node_d]]
self.assertTrue(self.__check_strongly_connected_components(
expected, actual))
cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertTrue(
self.__check_loop_order([[branch_ac.id, branch_ca.id],
[branch_ab.id, branch_ba.id],
[branch_ab.id, branch_bc.id,
branch_ca.id],
[branch_ac.id, branch_cd.id,
branch_db.id, branch_ba.id],
[branch_bc.id, branch_cd.id,
branch_db.id]],
cycles))
def test_johnson_3(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_6 = Node(graph)
node_7 = Node(graph)
Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_4, "c")
Branch(node_4, node_5, "d")
branch_e = Branch(node_5, node_6, "e")
Branch(node_6, node_7, "f")
branch_g = Branch(node_6, node_5, "g")
branch_h = Branch(node_4, node_3, "h")
branch_i = Branch(node_4, node_2, "i")
Branch(node_2, node_6, "j")
cycles = cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertTrue(self.__check_loop_order(
[[branch_b.id, branch_c.id, branch_i.id],
[branch_h.id, branch_c.id],
[branch_e.id, branch_g.id]],
cycles))
def test_johnson_2(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_1, "b")
branch_c = Branch(node_2, node_4, "c")
branch_d = Branch(node_4, node_3, "d")
branch_e = Branch(node_3, node_1, "e")
branch_f = Branch(node_1, node_3, "f")
components = strongly_connected_components(graph)
self.assertEqual(1, len(components))
self.assertCountEqual([node_3, node_4, node_2, node_1], components[0])
cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertTrue(self.__check_loop_order(
[[branch_f.id, branch_e.id],
[branch_a.id, branch_c.id, branch_d.id, branch_e.id],
[branch_a.id, branch_b.id],
], cycles))
def test_add_remove_nodes(self):
graph = Graph()
node1 = MagicMock(Node)
node2 = MagicMock(Node)
node3 = MagicMock(Node)
node1.graph = graph
node2.graph = graph
node3.graph = graph
graph.add_node(node1)
self.assertSetEqual({node1}, graph.nodes)
graph.add_node(node2)
graph.add_node(node3)
def add_node_again():
graph.add_node(node1)
self.assertRaises(ValueError, add_node_again)
self.assertSetEqual({node1, node2, node3}, graph.nodes)
node4 = MagicMock(Node)
node4.graph = MagicMock(Graph)
def add_node4():
graph.add_node(node4)
self.assertRaises(ValueError, add_node4)
self.assertSetEqual({node1, node2, node3}, graph.nodes)
node4.graph = graph
node4.ingoing = [1, 2, 3]
self.assertRaises(ValueError, add_node4)
self.assertSetEqual({node1, node2, node3}, graph.nodes)
graph.remove_node(node1)
self.assertSetEqual({node2, node3}, graph.nodes)
graph.remove_node(node2)
graph.remove_node(node3)
self.assertSetEqual(set(), graph.nodes)
def test_find_paths_line(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
self.assertCountEqual([[branch_a, branch_b]],
find_paths(node_1, node_3))
def test_loop_to_expression_1(self):
graph = Graph()
node_1 = Node(graph)
branch_a = Branch(node_1, node_1, "a")
branches = [branch_a]
expectedExpression = Symbol(branch_a.weight)
expression = loop_to_expression(branches)
self.assertEqual(srepr(expression), srepr(expectedExpression))
def test_johnson_1(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_1, "c")
cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertTrue(self.__check_loop_order(
[[branch_a.id, branch_b.id, branch_c.id]], cycles))
def test_find_paths_self_loop4(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
Branch(node_1, node_3, "b")
Branch(node_3, node_4, "c")
Branch(node_4, node_1, "d")
paths = find_paths(node_1, node_2)
self.assertCountEqual([[branch_a]], paths)
def test_strongly_connected_components(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
Branch(node_1, node_2, "a")
Branch(node_2, node_3, "b")
Branch(node_2, node_3, "c")
Branch(node_3, node_1, "d")
components = strongly_connected_components(graph)
self.assertEqual(1, len(components))
component = components[0]
self.assertCountEqual([node_3, node_2, node_1], component)
def test_loop_to_expression_3(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_6 = Node(graph)
node_7 = Node(graph)
node_8 = Node(graph)
node_9 = Node(graph)
node_10 = Node(graph)
node_11 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_4, "c")
branch_d = Branch(node_4, node_5, "d")
branch_e = Branch(node_5, node_6, "e")
branch_f = Branch(node_6, node_7, "f")
branch_g = Branch(node_7, node_8, "g")
branch_h = Branch(node_8, node_9, "h")
branch_j = Branch(node_9, node_10, "j")
branch_k = Branch(node_10, node_11, "k")
branch_l = Branch(node_11, node_1, "l")
branches = [
branch_a, branch_b, branch_c, branch_d, branch_e, branch_f,
branch_g, branch_h, branch_j, branch_k, branch_l
]
expectedExpression = Mul(Symbol(branch_a.weight),
Symbol(branch_b.weight),
Symbol(branch_c.weight),
Symbol(branch_d.weight),
Symbol(branch_e.weight),
Symbol(branch_f.weight),
Symbol(branch_g.weight),
Symbol(branch_h.weight),
Symbol(branch_j.weight),
Symbol(branch_k.weight),
Symbol(branch_l.weight))
expression = loop_to_expression(branches)
self.assertEqual(srepr(expression), srepr(expectedExpression))
def test_loop_to_expression_2(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_1, "b")
branches = [branch_a, branch_b]
expectedExpression = Mul(Symbol(branch_a.weight),
Symbol(branch_b.weight))
expression = loop_to_expression(branches)
self.assertEqual(srepr(expression), srepr(expectedExpression))
def test_find_paths_self_loop3(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_4, "c")
branch_d = Branch(node_4, node_5, "d")
Branch(node_4, node_2, "e")
paths = find_paths(node_1, node_5)
self.assertCountEqual([[branch_a, branch_b, branch_c, branch_d]],
paths)
def test_mason_1(self):
# Create graph
graph = Graph()
# Add nodes
node_x = Node(graph) # input node
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_z = Node(graph) # output node
# Add branches
Branch(node_x, node_1, "a")
Branch(node_1, node_2, "b")
Branch(node_2, node_3, "c")
Branch(node_3, node_4, "d")
Branch(node_4, node_5, "e")
Branch(node_5, node_z, "f")
Branch(node_5, node_4, "g")
Branch(node_3, node_2, "h")
Branch(node_3, node_1, "j")
Branch(node_1, node_5, "k")
# Execute
result = mason(graph, node_x, node_z)
# Assert
expected = [
"(a*b*c*d*e*f + a*f*k*(-c*h + 1))",
"/(b*c*e*g*j - b*c*j + c*e*g*h - c*h - e*g + 1)"
]
T = result.transfer_function[0][0]
actual = T.subs(result.transfer_function) \
.subs(result.numerator) \
.subs(result.denominator) \
.subs(result.determinant) \
.subs(result.paths) \
.subs(result.loops)
self.assertEqual(expected[0] + expected[1], str(actual))
def test_johson_multiple_scc(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_6 = Node(graph)
node_7 = Node(graph)
node_8 = Node(graph)
node_9 = Node(graph)
Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_4, "c")
branch_d = Branch(node_4, node_2, "d")
branch_e = Branch(node_1, node_5, "e")
branch_f = Branch(node_5, node_6, "f")
branch_g = Branch(node_6, node_1, "g")
branch_h = Branch(node_9, node_7, "h")
branch_i = Branch(node_7, node_8, "i")
branch_j = Branch(node_8, node_9, "j")
Branch(node_6, node_9, "k")
actual = strongly_connected_components(graph)
expected = [[node_9, node_8, node_7],
[node_3, node_2, node_4],
[node_6, node_5, node_1]]
self.assertTrue(self.__check_strongly_connected_components(
expected, actual))
cycles = [[branch.id for branch in cycle]
for cycle in simple_cycles(graph)]
self.assertTrue(
self.__check_loop_order([[branch_b.id, branch_c.id, branch_d.id],
[branch_e.id, branch_f.id, branch_g.id],
[branch_h.id, branch_i.id, branch_j.id]],
cycles))
def test_find_paths_self_loops(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
branch_a = Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_2, node_3, "c")
Branch(node_2, node_2, "d")
branch_e = Branch(node_2, node_1, "e")
branch_f = Branch(node_3, node_1, "f")
self.assertCountEqual([[branch_a, branch_b], [branch_a, branch_c]],
find_paths(node_1, node_3))
paths = find_paths(node_2, node_1)
self.assertCountEqual(
[[branch_c, branch_f], [branch_e], [branch_b, branch_f]], paths)
def test_mason_3(self):
# Create graph
graph = Graph()
# Add nodes
node_x = Node(graph) # input node
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_z = Node(graph) # output node
# Add branches
Branch(node_x, node_z, "g7")
Branch(node_z, node_x, "h7")
Branch(node_z, node_1, "g8")
Branch(node_1, node_2, "C")
Branch(node_2, node_3, "g3")
Branch(node_3, node_4, "g4")
Branch(node_4, node_5, "g5")
Branch(node_5, node_x, "g6")
Branch(node_2, node_1, "h2")
Branch(node_4, node_3, "N")
# Execute
result = mason(graph, node_x, node_z)
# Assert
expected_num = "g7*(C*N*g4*h2 - C*h2 - N*g4 + 1)"
actual_num = result.numerator[0][1] \
.subs(result.numerator) \
.subs(result.denominator) \
.subs(result.determinant) \
.subs(result.paths) \
.subs(result.loops)
self.assertEqual(expected_num, str(actual_num))
def test_find_paths_loop_over_loop(self):
# <--j ------------|
# | <--h----| <--g----
# | | | | |
# X --a--> 1 --b--> 2 --c--> 3 --d--> 4 --e--> 5 --f--> Z
# | |
# -------------------------------k-->
# Create graph
graph = Graph()
# Create nodes
node_x = Node(graph) # input node
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_z = Node(graph) # output node
# Create branches and connect nodes
branch_a = Branch(node_x, node_1, "a")
branch_b = Branch(node_1, node_2, "b")
branch_c = Branch(node_2, node_3, "c")
branch_d = Branch(node_3, node_4, "d")
branch_e = Branch(node_4, node_5, "e")
branch_f = Branch(node_5, node_z, "f")
Branch(node_5, node_4, "g")
Branch(node_3, node_2, "h")
Branch(node_3, node_1, "j")
branch_k = Branch(node_1, node_5, "k")
# Assert
paths = find_paths(node_x, node_z)
self.assertCountEqual(
[[branch_a, branch_b, branch_c, branch_d, branch_e, branch_f],
[branch_a, branch_k, branch_f]], paths)
def test_touching_loops(self):
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
node_4 = Node(graph)
node_5 = Node(graph)
node_6 = Node(graph)
node_7 = Node(graph)
Branch(node_1, node_2, "a")
branch_b = Branch(node_2, node_3, "b")
branch_c = Branch(node_3, node_4, "c")
Branch(node_4, node_5, "d")
branch_e = Branch(node_5, node_6, "e")
Branch(node_6, node_7, "f")
branch_g = Branch(node_6, node_5, "g")
branch_h = Branch(node_4, node_3, "h")
branch_i = Branch(node_4, node_2, "i")
Branch(node_2, node_6, "j")
res = find_loop_groups([[branch_h, branch_c], [branch_g, branch_e],
[branch_i, branch_b, branch_c]])
loops = [(loopGroup.loops, loopGroup.loop_count) for loopGroup
in res]
expected = [
([[branch_h, branch_c]], 1),
([[branch_g, branch_e]], 1),
([[branch_i, branch_b, branch_c]], 1),
([[branch_g, branch_e], [branch_h, branch_c]], 2),
([[branch_i, branch_b, branch_c], [branch_g, branch_e]], 2)
]
self.assertCountEqual(expected, loops)
def test_subgraph(self):
graph = Graph()
node = Node(graph)
subgraph = graph.subgraph({node})
self.assertEqual(1, len(subgraph.nodes))
self.assertEqual(0, len(graph.nodes))
self.assertEqual(node, list(subgraph.nodes)[0])
self.assertEqual(node.graph, subgraph)
graph = Graph()
node_1 = Node(graph)
node_2 = Node(graph)
node_3 = Node(graph)
branch_1 = Branch(node_1, node_2, "1")
branch_2 = Branch(node_2, node_1, "2")
Branch(node_2, node_3, "3")
Branch(node_3, node_1, "4")
branch_5 = Branch(node_3, node_3, "5")
branch_6 = Branch(node_2, node_2, "6")
subgraph = graph.subgraph([node_1, node_2])
self.assertCountEqual([node_1, node_2], subgraph.nodes)
self.assertCountEqual([node_3], graph.nodes)
self.assertCountEqual([branch_1, branch_2, branch_6],
subgraph.branches)
self.assertCountEqual([branch_5], graph.branches)
self.assertEqual(node_1.graph, subgraph)
self.assertEqual(node_2.graph, subgraph)
self.assertEqual(node_3.graph, graph)
self.assertEqual(branch_1.graph, subgraph)
self.assertEqual(branch_2.graph, subgraph)
self.assertEqual(branch_5.graph, graph)
self.assertEqual(branch_6.graph, subgraph)
def simple_cycles(g: Graph) -> List[List[Branch]]:
"""Find all simple cycles in a graph"""
# Make copy because the graph gets altered during the algorithm
graph_copy = g.copy()
branch_map = {}
copy_result = list()
# Create map to allow returning original branches
for branch in g.branches:
branch_map[branch.id] = branch
# Yield every elementary cycle in python graph G exactly once
# Expects a dictionary mapping from vertices to iterables of vertices
def _unblock(thisnode, blocked, B):
stack = set([thisnode])
while stack:
node = stack.pop()
if node in blocked:
blocked.remove(node)
stack.update(B[node])
B[node].clear()
sccs = [(graph_copy, scc)
for scc in strongly_connected_components(graph_copy)]
while sccs:
current_graph, scc = sccs.pop()
startnode = scc.pop()
path = [startnode.id]
pathBranches = []
blocked = set()
closed = set()
blocked.add(startnode.id)
B = defaultdict(set)
stack = [(startnode, list(startnode.outgoing))]
while stack:
thisnode, nbrs = stack[-1]
if nbrs:
branch = nbrs.pop()
nextnode = branch.end
if nextnode.id == startnode.id:
result = pathBranches[:]
result.append(branch)
copy_result.append(result)
closed.update(path)
elif nextnode.id not in blocked:
path.append(nextnode.id)
pathBranches.append(branch)
stack.append((nextnode, list(nextnode.outgoing)))
closed.discard(nextnode.id)
blocked.add(nextnode.id)
continue
if not nbrs:
if thisnode.id in closed:
_unblock(thisnode.id, blocked, B)
else:
for nbr in map(lambda x: x.end, thisnode.outgoing):
if thisnode.id not in B[nbr.id]:
B[nbr.id].add(thisnode.id)
stack.pop()
path.pop()
if (pathBranches):
pathBranches.pop()
startnode.remove()
subgraph = current_graph.subgraph(set(scc))
new_scc = strongly_connected_components(subgraph)
sccs.extend([(subgraph, scc) for scc in new_scc])
for loop in copy_result:
yield list(map(lambda b: branch_map[b.id], loop))
