def make_complete_graph(num_vertices):
"""Constructs a complete graph.
The pairing function is: k = v1 + v2 * (v2 - 1) // 2
Args:
num_vertices: Number of vertices.
Returns: A tuple with elements:
V: Number of vertices.
K: Number of edges.
grid: a 3 x K grid of (edge, vertex, vertex) triples.
"""
V = num_vertices
K = V * (V - 1) // 2
grid = np.zeros([3, K], np.int32)
k = 0
for v2 in range(V):
for v1 in range(v2):
grid[:, k] = [k, v1, v2]
k += 1
return grid
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