def test_get_adjacency_matrix(self):
json_graph = {"graph": {"A": ["B"], "B": []}}
graph = Graph(input_graph=json.dumps(json_graph))
matrix = graph.get_adjacency_matrix()
answer = np.array([[0, 1], [0, 0]])
np.testing.assert_equal(matrix, answer)
self.assertEqual(answer.size, matrix.size)
def is_sparse(graph: Graph) -> bool:
"""
Checks if |E| <= |V^2| / 2
:param graph:
:return:
"""
return graph.size() <= (graph.order()**2 / 2)
def test_is_complete(self):
graph = Graph(input_graph=json.dumps(self.complete_graph))
self.assertTrue(is_complete(graph))
graph = Graph(input_graph=json.dumps(self.isolated_graph))
self.assertFalse(is_complete(graph))
json_graph = {"name": "", "graph": {"A": ["B"], "B": []}}
graph = Graph(input_graph=json.dumps(json_graph))
self.assertFalse(is_complete(graph))
def test_read_graph_from_file(self):
json_graph = {"label": "my graph", "graph": {"A": ["B"], "B": []}}
with open(path.join(self.test_dir, 'test.txt'), 'w') as out_file:
out_file.write(json.dumps(json_graph))
graph = Graph(input_file=str(path.join(self.test_dir, 'test.txt')))
self.assertEqual(json_graph["label"], graph.get_label())
self.assertEqual(False, graph.is_directed())
self.assertEqual(json_graph["graph"], graph.get_graph())
def test_density(self):
graph = Graph(input_graph=json.dumps(self.connected_graph))
self.assertAlmostEqual(0.4666666666666667, density(graph))
graph = Graph(input_graph=json.dumps(self.complete_graph))
self.assertEqual(1.0, density(graph))
graph = Graph(input_graph=json.dumps(self.isolated_graph))
self.assertEqual(0.0, density(graph))
def get_complement(graph: Graph) -> Graph:
"""
If graph is represented as a matrix, invert that matrix
:param graph:
:return: inversion of graph
"""
adj = graph.get_adjacency_matrix()
complement = invert(adj)
return Graph(label=f"{graph.get_label()} complement",
input_array=complement)
def test_save_to_json(self):
answer = "{\"label\": \"my graph\", \"directed\": false," \
" \"graph\": {\"A\": [\"B\"], \"B\": []}}"
json_graph = {"label": "my graph", "graph": {"A": ["B"], "B": []}}
graph = Graph(input_graph=json.dumps(json_graph))
save_to_json(graph, self.test_dir)
outfile = path.join(self.test_dir, graph.get_label() + ".json")
with open(outfile) as dot_file:
dot_lines = "".join(dot_file.readlines())
self.assertEqual(dot_lines, answer)
def density(graph: Graph) -> float:
"""
The graph density is defined as the ratio of the number of edges of a given
graph, and the total number of edges, the graph could have.
A dense graph is a graph G = (V, E) in which |E| = Θ(|V|^2)
:param graph:
:return:
"""
V = len(graph.vertices())
E = len(graph.edges())
return 2.0 * (E / (V**2 - V))
def test_complete_digraph(self):
graph = Graph(input_graph=json.dumps(self.complete_digraph))
self.assertTrue(is_complete(graph))
json_graph = {
"name": "",
"directed": True,
"graph": {
"A": ["B"],
"B": []
}
}
graph = Graph(input_graph=json.dumps(json_graph))
self.assertFalse(is_complete(graph))
def save_to_dot(graph: Graph, out_dir: str):
"""
:param graph: the graph to render in dot
:param out_dir: the absolute path of the gv file to write
:return:
"""
if not graph.is_directed():
dot = GraphViz(comment=graph.get_label())
for node in graph:
dot.node(node, node)
for edge in graph[node]:
dot.edge(node, edge)
dot.render(path.join(out_dir, f"{graph.get_label()}.gv"), view=False)
def test_str(self):
answer = """my graph
A -> B
B -> 0"""
json_graph = {"label": "my graph", "graph": {"A": ["B"], "B": []}}
graph = Graph(input_graph=json.dumps(json_graph))
self.assertEqual(answer, str(graph))
def arrival_departure_dfs(graph: Graph,
v: str,
discovered: Dict[str, bool],
arrival: Dict[str, int],
departure: Dict[str, int],
time: int) -> int:
"""
Method for DFS with arrival and departure times for each vertex
O(V+E) -- E could be as big as V^2
:param graph:
:param v:
:param discovered:
:param arrival:
:param departure:
:param time: should be initialized to -1
:return:
"""
time += 1
# when did we arrive at vertex 'v'?
arrival[v] = time
discovered[v] = True
for n in graph.get_neighbors(v):
if not discovered.get(n, False):
time = arrival_departure_dfs(graph, n, discovered, arrival, departure, time)
time += 1
# increment time and then set departure
departure[v] = time
return time
def test_save_to_graphviz(self):
answer = """// my graph
graph {
A [label=A]
A -- B
B [label=B]
}
"""
json_graph = {"label": "my graph", "graph": {"A": ["B"], "B": []}}
graph = Graph(input_graph=json.dumps(json_graph))
save_to_dot(graph, self.test_dir)
outfile = path.join(self.test_dir, graph.get_label() + ".gv")
with open(outfile) as dot_file:
dot_lines = "".join(dot_file.readlines())
self.assertEqual(dot_lines, answer)
def mark_visited(g: Graph, v: str, v_map: Dict[str, bool],
t_sort_results: List[str]):
v_map[v] = True
for n in g.get_neighbors(v):
if not v_map[n]:
mark_visited(g, n, v_map, t_sort_results)
t_sort_results.append(v)
def save_to_json(graph: Graph, out_dir):
"""
:param graph: the graph to write to json
:param out_dir: the absolute path to the dir to write the file
:return:
"""
g_dict = {
"label": graph.get_label(),
"directed": graph.is_directed(),
"graph": graph.get_graph()
}
with open(path.join(out_dir, f"{graph.get_label()}.json"),
'w',
encoding="utf8") as out:
out.write(json.dumps(g_dict))
def test_is_dag(self):
cycle_graph = {
"directed": True,
"graph": {
"A": ["B"],
"B": ["C", "D"],
"C": [],
"D": ["E", "A"], # cycle A -> B -> D -> A
"E": []
}
}
graph = Graph(input_graph=json.dumps(cycle_graph))
self.assertFalse(is_dag(graph))
dag = cycle_graph
# remove the cycle
dag["graph"]["D"] = ["E"]
graph2 = Graph(input_graph=json.dumps(dag))
self.assertTrue(is_dag(graph2))
def test_arrival_departure_dfs(self):
disjoint_graph = {
"graph": {
"a": ["b", "c"],
"b": [],
"c": ["d", "e"],
"d": ["b", "f"],
"e": ["f"],
"f": [],
"g": ["h"],
"h": []
},
"directed": True
}
graph = Graph(input_graph=json.dumps(disjoint_graph))
# list to store the arrival time of vertex
arrival = {v: 0 for v in graph.vertices()}
# list to store the departure time of vertex
departure = {v: 0 for v in graph.vertices()}
# mark all the vertices as not discovered
discovered = {v: False for v in graph.vertices()}
time = -1
for v in graph.vertices():
if not discovered[v]:
time = arrival_departure_dfs(graph, v, discovered, arrival,
departure, time)
# pair up the arrival and departure times and ensure correct ordering
result = list(zip(arrival.values(), departure.values()))
expected_times = [(0, 11), (1, 2), (3, 10), (4, 7), (8, 9), (5, 6),
(12, 15), (13, 14)]
self.assertListEqual(expected_times, result)
def test_edges(self):
json_graph = {"label": "my graph", "graph": {"A": ["B"], "B": []}}
graph = Graph(input_graph=json.dumps(json_graph))
self.assertEqual(json_graph['label'], graph.get_label())
self.assertEqual(False, graph.is_directed())
self.assertEqual(json_graph['graph'], graph.get_graph())
self.assertEqual([Edge('A', 'B')], graph.edges())
def test_find_circuit(self):
circuit_graph = {
"directed": True,
"graph": {
"A": ["B"],
"B": ["C"],
"C": ["A"] # circuit A -> C -> B -> A
}
}
graph = Graph(input_graph=json.dumps(circuit_graph))
circuit = find_circuit(graph)
expected_circuit = ["A", "C", "B", "A"]
self.assertListEqual(circuit, expected_circuit)
def is_complete(graph: Graph) -> bool:
"""
Checks that each vertex has V(V-1) / 2 edges and that each vertex is
connected to V - 1 others.
runtime: O(n^2)
:param graph:
:return: true or false
"""
V = len(graph.vertices())
max_edges = (V**2 - V)
if not graph.is_directed():
max_edges //= 2
E = len(graph.edges())
if E != max_edges:
return False
for vertex in graph:
if len(graph[vertex]) != V - 1:
return False
return True
def check_for_cycles(graph: Graph, v: str, visited: Dict[str, bool],
rec_stack: List[bool]) -> bool:
"""
:param graph:
:param v: vertex to start from
:param visited: list of visited vertices
:param rec_stack:
:return: whether or not the graph contains a cycle
"""
visited[v] = True
rec_stack[graph.vertices().index(v)] = True
for neighbour in graph[v]:
if not visited.get(neighbour, False):
if check_for_cycles(graph, neighbour, visited, rec_stack):
return True
elif rec_stack[graph.vertices().index(neighbour)]:
return True
rec_stack[graph.vertices().index(v)] = False
return False
def is_simple(graph: Graph) -> bool:
"""
A simple graph has no cycles
:param graph:
:return: whether or not the graph is simple
"""
visited = {k: False for k in graph}
rec_stack = [False] * graph.order()
for v in graph:
if not visited[v]:
if check_for_cycles(graph, v, visited, rec_stack):
return False
return True
def topological(graph: Graph) -> List[str]:
"""
O(V+E)
:param graph:
:return: List of vertices sorted topologically
"""
def mark_visited(g: Graph, v: str, v_map: Dict[str, bool],
t_sort_results: List[str]):
v_map[v] = True
for n in g.get_neighbors(v):
if not v_map[n]:
mark_visited(g, n, v_map, t_sort_results)
t_sort_results.append(v)
visited = {v: False for v in graph.vertices()}
result: List[str] = []
for v in graph.vertices():
if not visited[v]:
mark_visited(graph, v, visited, result)
# Contains topo sort results in reverse order
return result[::-1]
def test_topological_sort(self):
t_sort_graph = {
"directed": True,
"graph": {
"A": [],
"B": [],
"C": ["D"],
"D": ["B"],
"E": ["A", "B"],
"F": ["A", "C"]
}
}
graph = Graph(input_graph=json.dumps(t_sort_graph))
expected_results = ["F", "E", "C", "D", "B", "A"]
results = topological(graph)
self.assertListEqual(expected_results, results)
def diameter(graph: Graph) -> int:
"""
:param graph:
:return: length of longest path in graph
"""
vee = graph.vertices()
pairs = [(vee[i], vee[j]) for i in range(len(vee) - 1)
for j in range(i + 1, len(vee))]
smallest_paths = []
for (start, end) in pairs:
paths = find_all_paths(graph, start, end)
smallest = sorted(paths, key=len)[0]
smallest_paths.append(smallest)
smallest_paths.sort(key=len)
# longest path is at the end of list,
# i.e. diameter corresponds to the length of this path
dia = len(smallest_paths[-1]) - 1
return dia
def test_find_all_paths(self):
json_graph = {
"label": "test2",
"directed": False,
"graph": {
"a": ["d", "f"],
"b": ["c"],
"c": ["b", "c", "d", "e"],
"d": ["a", "c"],
"e": ["c"],
"f": ["d"]
}
}
graph = Graph(input_graph=json.dumps(json_graph))
paths = find_all_paths(graph, "a", "b")
self.assertListEqual([['a', 'd', 'c', 'b'], ['a', 'f', 'd', 'c', 'b']],
paths)
paths = find_all_paths(graph, "z", "b")
self.assertListEqual([], paths)
def test_iterator(self):
json_graph = {
"name": "my graph",
"graph": {
"A": ["B", "C", "D"],
"B": [],
"C": [],
"D": []
}
}
graph = Graph(input_graph=json.dumps(json_graph))
iterations = 0
for key in graph:
iterations += 1
if key == "A":
self.assertEqual(len(graph[key]), 3)
else:
self.assertEqual(len(graph[key]), 0)
self.assertEqual(iterations, 4)
def test_find_path(self):
json_graph = {
"label": "test",
"directed": False,
"graph": {
"a": ["d"],
"b": ["c"],
"c": ["b", "c", "d", "e"],
"d": ["a", "c"],
"e": ["c"],
"f": []
}
}
graph = Graph(input_graph=json.dumps(json_graph))
path = find_path(graph, "a", "b")
self.assertListEqual(['a', 'd', 'c', 'b'], path)
path = find_path(graph, "a", "f")
self.assertListEqual([], path)
path = find_path(graph, "c", "c")
self.assertListEqual(['c'], path)
path = find_path(graph, "z", "a")
self.assertListEqual([], path)
def breadth_first_search(graph: Graph, start: str) -> List[str]:
"""
:param graph:
:param start: the vertex to start the traversal from
:return:
"""
# Mark all the vertices as not visited
visited = {k: False for k in graph.vertices()}
# Mark the start vertices as visited and enqueue it
visited[start] = True
queue = [start]
walk = []
while queue:
cur = queue.pop(0)
walk.append(cur)
for i in graph[cur]:
if not visited[i]:
queue.append(i)
visited[i] = True
return walk
def is_connected(graph: Graph,
start_vertex: str = None,
vertices_encountered: Set[str] = None) -> bool:
"""
:param graph:
:param start_vertex:
:param vertices_encountered:
:return: whether or not the graph is connected
"""
if vertices_encountered is None:
vertices_encountered = set()
vertices = graph.vertices()
if not start_vertex:
# choose a vertex from graph as a starting point
start_vertex = vertices[0]
vertices_encountered.add(start_vertex)
if len(vertices_encountered) != len(vertices):
for vertex in graph[start_vertex]:
if vertex not in vertices_encountered:
if is_connected(graph, vertex, vertices_encountered):
return True
else:
return True
return False