给定总节点数和每个节点的度数，是否可以构造一个图？

Question

以立方体为例，有8个节点和12个边，每个节点与3个节点相连

使用networkx，我必须手动输入所有边。例如，下面的代码将构造一个包含二十面体所有边的图（12个节点，30条边，每个节点5个相邻节点）

import networkx as nx
G = nx.Graph()
nodes = list(range(12))
edges = [
    [0, 1], [0, 2], [0, 3], [0, 4], [0, 5],
    [1, 2], [1, 6], [1, 10], [1, 5],
    [2, 3], [2, 6], [2, 7],
    [3, 4], [3, 7], [3, 8],
    [4, 5], [4, 8], [4, 11], 
    [5, 11], [5, 10],
    [6, 7], [6, 9], [6, 10],
    [7, 8], [7, 9],
    [8, 9], [8, 11],
    [9, 10], [9, 11],
    [10, 11],
]
G.add_nodes_from(nodes)
G.add_edges_from(edges)

我的问题是如何在不手动写入的情况下获取所有可能的边。每个节点的名称都可以随机初始化

据我所知igraph中的Erdős–Rényi模型无法约束相邻节点

from igraph import *

g = Graph.Erdos_Renyi(12, m=30, directed=False)
g.get_edgelist()
"""
[(0, 1),
 (0, 2),
 (1, 3),
 (2, 3),
 (0, 4),
 (1, 4),
 (3, 5),
 (4, 6),
 (5, 6),
 (0, 7),
 (2, 7),
 (3, 7),
 (6, 7),
 (0, 8),
 (1, 8),
 (3, 8),
 (0, 9),
 (3, 9),
 (4, 9),
 (6, 9),
 (0, 10),    node10 has more than 5 edges.
 (2, 10),
 (3, 10),
 (5, 10),
 (7, 10),
 (8, 10),
 (1, 11),
 (2, 11),
 (4, 11),
 (9, 11)]
"""