def complete_binary_tree(n: int = None,
h: int = None,
directed=False) -> Graph:
"""
Construct a perfect binary tree with n nodes/height of h.
:param n: number of nodes
:param h: height
:param directed: directed edges
:return:
"""
if n is None and h is None:
raise ValueError('One of n and h must be not-null.')
if n is None and h is not None:
n = 2**(h + 1) - 1
if n == 0:
return Graph([], [])
# check n+1 is a power of two - 1
if not (n & (n + 1)) == 0:
raise ValueError(
'Number of nodes not enough for a complete binary tree.')
vertices: List[Vertex] = [Vertex(label=f'{i}', index=i) for i in range(n)]
edges = [Edge(vertices[i], vertices[2 * i + 1]) for i in range(n // 2)]
edges += [
Edge(vertices[i], vertices[2 * i + 2]) for i in range(n // 2 - 1)
]
if directed:
return Graph(vertices, edges, directed=True)
edges += [Edge(vertices[2 * i + 1], vertices[i]) for i in range(n // 2)]
edges += [
Edge(vertices[2 * i + 2], vertices[i]) for i in range(n // 2 - 1)
]
return Graph(vertices, edges)
def test_vertex_adding(self):
n = 100
g = Graph([], [])
vertices = [Vertex(label=f'{i}', index=i) for i in range(n)]
g.add_vertices(vertices)
self.assertEqual(True, True)
def path_graph(n: int, directed=False) -> Graph:
vertices: List[Vertex] = [Vertex(label=f'{i}', index=i) for i in range(n)]
edges = [Edge(vertices[i], vertices[i + 1]) for i in range(n - 1)]
if not directed:
edges += [Edge(vertices[i], vertices[i - 1]) for i in range(1, n)]
return Graph(vertices, edges, directed=directed)
def complete_graph(n: int, directed=False) -> Graph:
vertices: List[Vertex] = [Vertex(label=f'{i}', index=i) for i in range(n)]
if directed:
edges = [Edge(v, i) for v, i in itertools.combinations(vertices, 2)]
else:
edges = [Edge(v, i) for v, i in itertools.permutations(vertices, 2)]
return Graph(vertices, edges, directed=directed)
def graph_cartesian(g1: Graph, g2: Graph):
# node labels are (v1,v2)
vertices = [
Vertex(label=f'{v}', index=i)
for i, v in enumerate(zip(g1.vertices, g2.vertices))
]
edges = []
return Graph(vertices=vertices, edges=edges)
def empty_graph(n: int = 0) -> Graph:
"""
Empty graph with or without vertices.
:param n: (optional) number of vertices
:return:
"""
vertices: List[Vertex] = [Vertex(label=f'{i}', index=i) for i in range(n)]
return Graph(vertices, [])
def euler_graph(n: int, cycle=True) -> Graph:
# TODO
"""
Create a random graph with an Euler path.
:param n: number of vertices
:param cycle: if True, there is also an Euler cycle in the graph.
:return:
"""
vertices: List[Vertex] = [Vertex(label=f'{i}', index=i) for i in range(n)]
v2 = random.choices(vertices, k=n)
edges = [Edge(v, i) for v, i in zip(vertices, v2)]