图论 - 3D 中的连接点 space 与其他三个最近的点（基于距离）
graph theory - connect point in 3D space with other three nearest points (distance based)
我想将节点（原子）与最近的三个节点（原子）连接起来。
我在做
ad1 = np.zeros((31,31))
for i in range(31):
dist_i = dist_mat[i]
cut_off = sorted(dist_i)[3]
ad1[i, np.where((dist_i<=cut_off) & (dist_i!=0.0))] = 1
np.sum(ad1, axis=1) #[3,3,3,3........3]
np.sum(ad1, axis=0)
#array([3., 3., 2., 2., 2., 4., 2., 5., 2., 3., 2., 3., 3., 2., 3., 6., 3.,
5., 3., 4., 2., 3., 2., 4., 3., 3., 2., 4., 3., 2., 3.])
我希望 np.sum(ad1, axis=0) 全部为 3。这意味着所有节点（原子）都连接到恰好 3 个最近的节点。正如我们所见，node/atom 5 连接到其他 4 个 nodes/atoms 这是错误的，我希望它连接到恰好 3 个最近的节点。我该怎么做。
下面是31个原子(31 X 31)的距离矩阵。
0.0000,6.8223,7.5588,4.8966,7.2452,2.7778,3.7082,2.7345,7.1540,6.8273,3.6995,7.4136,4.6132,5.8456,2.8037,5.4881,8.1769,2.7361,8.3034,4.9450,4.8225,4.6152,4.8243,9.4876,7.2391,2.9941,7.4180,5.8523,7.6310,5.5996,8.1761
6.8223,0.0000,3.0097,2.8567,2.6647,5.0092,5.8451,6.8037,6.7031,4.8983,7.5806,5.2873,5.5000,7.0038,4.9530,3.9763,7.0263,4.8941,4.7416,6.8450,2.8166,2.9221,5.5502,7.0328,5.5148,7.6318,2.7456,5.1150,2.9654,4.2863,5.3168
7.5588,3.0097,0.0000,2.8679,2.9242,5.1443,6.8372,6.5621,5.5169,3.0135,6.8412,4.6886,4.2507,5.4276,5.8673,4.8804,4.7149,6.5707,2.5568,6.3820,5.0625,4.2533,5.0600,5.2125,2.9262,7.8126,4.6864,5.4224,2.6001,3.2330,4.7116
4.8966,2.8567,2.8679,0.0000,3.8064,3.0221,5.1335,4.1131,5.8284,2.8610,5.1354,3.8488,2.8086,4.9618,3.0028,2.7539,5.7401,4.1214,4.5830,5.4268,2.9346,2.8122,2.9319,6.8084,3.8015,5.8992,3.8516,4.9611,2.9212,3.0441,5.7392
7.2452,2.6647,2.9242,3.8064,0.0000,4.7907,5.1676,7.2899,4.5138,5.5206,7.0249,6.9978,5.3888,5.7435,6.2424,6.0645,5.2615,5.6079,2.8907,5.3589,4.7384,2.8152,6.6866,4.6140,4.7660,6.9472,5.3921,3.2734,4.7050,2.9157,2.6684
2.7778,5.0092,5.1443,3.0221,4.7907,0.0000,2.8352,3.0025,4.6425,5.0210,2.8371,6.4170,2.6958,3.6516,3.1115,4.9489,5.5823,3.0042,5.5496,3.0193,4.1730,2.6916,4.1796,6.7613,4.7913,2.8772,6.4156,3.6500,5.9378,2.8228,5.5754
3.7082,5.8451,6.8372,5.1335,5.1676,2.8352,0.0000,5.4535,5.0179,7.5889,4.7500,8.8240,5.4549,5.4488,4.9281,6.8616,7.0789,2.8247,6.7504,3.1734,4.9441,2.9387,6.8368,7.3498,7.0263,2.7571,7.6165,2.7391,7.8184,4.2915,5.4352
2.7345,6.8037,6.5621,4.1131,7.2899,3.0025,5.4535,0.0000,6.9646,4.8923,2.8238,5.6867,2.8002,4.7436,2.7895,4.7319,7.0025,4.5800,7.4954,5.2983,5.3961,5.3071,2.7803,8.9227,5.5914,4.2758,7.1749,6.6267,6.5470,5.1104,8.2905
7.1540,6.7031,5.5169,5.8284,4.5138,4.6425,5.0179,6.9646,0.0000,6.7047,5.0056,9.1250,4.9769,2.9634,7.5819,8.5546,2.8061,6.9800,3.6751,2.5834,7.6541,4.9881,7.6494,2.7948,4.5088,5.2110,9.1264,2.9761,7.8062,2.7941,2.8038
6.8273,4.8983,3.0135,2.8610,5.5206,5.0210,7.5889,4.8923,6.7047,0.0000,5.8617,2.7465,2.9301,5.1272,4.9558,3.9808,5.3162,6.8165,4.7404,6.8576,5.5561,5.5098,2.8152,7.0330,2.6644,7.6461,5.2912,7.0096,2.9674,4.2945,7.0258
3.6995,7.5806,6.8412,5.1354,7.0249,2.8371,4.7500,2.8238,5.0056,5.8617,0.0000,7.6266,2.9474,2.7359,4.9270,6.8677,5.4363,5.4517,6.7478,3.1721,6.8329,5.4529,4.9555,7.3438,5.1708,2.7597,8.8287,5.4452,7.8249,4.2909,7.0646
7.4136,5.2873,4.6886,3.8488,6.9978,6.4170,8.8240,5.6867,9.1250,2.7465,7.6266,0.0000,4.9529,7.5866,4.8602,2.7541,8.0299,7.1729,7.0207,8.9107,5.2910,6.5588,2.9146,9.5249,5.3922,9.1160,4.1719,8.7725,2.7497,6.4529,9.0793
4.6132,5.5000,4.2507,2.8086,5.3888,2.6958,5.4549,2.8002,4.9769,2.9301,2.9474,4.9529,0.0000,2.8097,3.9433,4.7505,4.4056,5.3122,4.8719,4.3293,5.3691,4.4387,2.8442,6.4077,2.8070,4.8696,6.5606,5.3482,5.0545,2.9281,6.2031
5.8456,7.0038,5.4276,4.9618,5.7435,3.6516,5.4488,4.7436,2.9634,5.1272,2.7359,7.5866,2.8097,0.0000,6.2398,7.3805,2.7234,6.6316,4.5653,2.8038,7.3250,5.3513,5.6427,4.8167,3.2793,4.4545,8.7753,4.6687,7.1729,2.8747,5.2395
2.8037,4.9530,5.8673,3.0028,6.2424,3.1115,4.9281,2.7895,7.5819,4.9558,4.9270,4.8602,3.9433,6.2398,0.0000,2.6964,7.9654,2.7924,7.3935,6.1211,2.8429,3.9452,2.8424,9.2720,6.2355,5.1988,4.8668,6.2430,5.2004,5.1737,7.9659
5.4881,3.9763,4.8804,2.7539,6.0645,4.9489,6.8616,4.7319,8.5546,3.9808,6.8677,2.7541,4.7505,7.3805,2.6964,0.0000,8.3401,4.7306,7.1148,7.8221,2.7718,4.7476,2.7753,9.5030,6.0617,7.5711,2.7577,7.3777,3.1397,5.7882,8.3392
8.1769,7.0263,4.7149,5.7401,5.2615,5.5823,7.0789,7.0025,2.8061,5.3162,5.4363,8.0299,4.4056,2.7234,7.9654,8.3401,0.0000,8.3066,2.9172,4.5762,8.3187,6.2166,6.9974,2.6988,2.6667,6.8504,9.0816,5.2518,7.0366,3.3010,4.3079
2.7361,4.8941,6.5707,4.1214,5.6079,3.0042,2.8247,4.5800,6.9800,6.8165,5.4517,7.1729,5.3122,6.6316,2.7924,4.7306,8.3066,0.0000,7.5094,5.3015,2.7788,2.8080,5.4012,8.9373,7.2956,4.2691,5.6901,4.7565,6.5515,5.1204,7.0169
8.3034,4.7416,2.5568,4.5830,2.8907,5.5496,6.7504,7.4954,3.6751,4.7404,6.7478,7.0207,4.8719,4.5653,7.3935,7.1148,2.9172,7.5094,0.0000,5.4477,6.7736,4.8812,6.7675,2.6661,2.8871,7.5857,7.0211,4.5660,5.1569,2.7695,2.9165
4.9450,6.8450,6.3820,5.4268,5.3589,3.0193,3.1734,5.2983,2.5834,6.8576,3.1721,8.9107,4.3293,2.8038,6.1211,7.8221,4.5762,5.3015,5.4477,0.0000,6.7806,4.3263,6.7865,5.3395,5.3642,2.6393,8.9072,2.7997,8.0722,3.1518,4.5623
4.8225,2.8166,5.0625,2.9346,4.7384,4.1730,4.9441,5.3961,7.6541,5.5561,6.8329,5.2910,5.3691,7.3250,2.8429,2.7718,8.3187,2.7788,6.7736,6.7806,0.0000,2.8411,4.6768,8.8466,6.6849,6.5259,2.9190,5.6409,4.2802,5.1556,7.0036
4.6152,2.9221,4.2533,2.8122,2.8152,2.6916,2.9387,5.3071,4.9881,5.5098,5.4529,6.5588,4.4387,5.3513,3.9452,4.7476,6.2166,2.8080,4.8812,4.3263,2.8411,0.0000,5.3713,6.4170,5.3921,4.8619,4.9490,2.8105,5.0539,2.9321,4.4129
4.8243,5.5502,5.0600,2.9319,6.6866,4.1796,6.8368,2.7803,7.6494,2.8152,4.9555,2.9146,2.8442,5.6427,2.8424,2.7753,6.9974,5.4012,6.7675,6.7865,4.6768,5.3713,0.0000,8.8413,4.7294,6.5361,5.2956,7.3262,4.2788,5.1556,8.3129
9.4876,7.0328,5.2125,6.8084,4.6140,6.7613,7.3498,8.9227,2.7948,7.0330,7.3438,9.5249,6.4077,4.8167,9.2720,9.5030,2.6988,8.9373,2.6661,5.3395,8.8466,6.4170,8.8413,0.0000,4.6127,7.9200,9.5247,4.8201,7.8081,4.1075,2.6956
7.2391,5.5148,2.9262,3.8015,4.7660,4.7913,7.0263,5.5914,4.5088,2.6644,5.1708,5.3922,2.8070,3.2793,6.2355,6.0617,2.6667,7.2956,2.8871,5.3642,6.6849,5.3921,4.7294,4.6127,0.0000,6.9513,6.9963,5.7431,4.7049,2.9171,5.2546
2.9941,7.6318,7.8126,5.8992,6.9472,2.8772,2.7571,4.2758,5.2110,7.6461,2.7597,9.1160,4.8696,4.4545,5.1988,7.5711,6.8504,4.2691,7.5857,2.6393,6.5259,4.8619,6.5361,7.9200,6.9513,0.0000,9.1125,4.4513,8.8145,4.8939,6.8395
7.4180,2.7456,4.6864,3.8516,5.3921,6.4156,7.6165,7.1749,9.1264,5.2912,8.8287,4.1719,6.5606,8.7753,4.8668,2.7577,9.0816,5.6901,7.0211,8.9072,2.9190,4.9490,5.2956,9.5247,6.9963,9.1125,0.0000,7.5797,2.7482,6.4514,8.0302
5.8523,5.1150,5.4224,4.9611,3.2734,3.6500,2.7391,6.6267,2.9761,7.0096,5.4452,8.7725,5.3482,4.6687,6.2430,7.3777,5.2518,4.7565,4.5660,2.7997,5.6409,2.8105,7.3262,4.8201,5.7431,4.4513,7.5797,0.0000,7.1676,2.8724,2.7190
7.6310,2.9654,2.6001,2.9212,4.7050,5.9378,7.8184,6.5470,7.8062,2.9674,7.8249,2.7497,5.0545,7.1729,5.2004,3.1397,7.0366,6.5515,5.1569,8.0722,4.2802,5.0539,4.2788,7.8081,4.7049,8.8145,2.7482,7.1676,0.0000,5.1559,7.0354
5.5996,4.2863,3.2330,3.0441,2.9157,2.8228,4.2915,5.1104,2.7941,4.2945,4.2909,6.4529,2.9281,2.8747,5.1737,5.7882,3.3010,5.1204,2.7695,3.1518,5.1556,2.9321,5.1556,4.1075,2.9171,4.8939,6.4514,2.8724,5.1559,0.0000,3.2927
8.1761,5.3168,4.7116,5.7392,2.6684,5.5754,5.4352,8.2905,2.8038,7.0258,7.0646,9.0793,6.2031,5.2395,7.9659,8.3392,4.3079,7.0169,2.9165,4.5623,7.0036,4.4129,8.3129,2.6956,5.2546,6.8395,8.0302,2.7190,7.0354,3.2927,0.0000
编辑 1
谢谢@yatu 和@mathfux，但 Kdtree 没有产生我想要的结果。
所以来自@mathfux 的回答如果最近的 3 列表是 0,1,2 并且 0 有最近的 1,4,2 列表那么算法应该更加重视距离并断开 3 和0. 3 应该找到离它最近的其他点，而不是与 0 连接。如果 3 找不到离它最近的其他点，则 0 必须根据距离排除 1 或 2，并包括 3，因为 3 找不到 3 个最近的点除了 0,1,2.
还可以看到0连接到25但是25没有连接到0这是错误的。如果 0 连接到 25 那么 25 也应该连接到 0.
[ 0, 17, 7, 25]
[ 5, 21, 12, 6]
[ 6, 25, 27, 17]
[10, 25, 13, 7]
[12, 5, 3, 24]
[21, 5, 3, 4]
[25, 6, 10, 19]
[29, 4, 12, 24]
A KDTree 更适合您要执行的操作。构建树后，您可以搜索距离树中所有点最近的 3 个点：
from sklearn.neighbors import KDTree
tree = KDTree(X, leaf_size=2)
dist, ind = tree.query(X, k=3)
为了检查结果，我们可以验证第一行中的三个最小值与第一行 query 索引返回的三个最小距离相匹配 ind[0]:
np.sort(X[0])[:3]
#array([0. , 2.7345, 2.7361])
X[0,ind[0]]
# array([0. , 2.7361, 2.7345])
看来这种连接可能并不总是可行的，因为您无法保持矩阵对称。其实距离矩阵不用解释了
import matplotlib.pyplot as plt
points = np.array([[0,0],[0,1],[0,-1],[1,0],[-0.5,0]])
plt.scatter(*np.transpose(points))
for i in range(len(points)):
plt.text(points[i][0], points[i][1], [0, 1, 2, 3, 4][i], fontsize=24)
假设您找到 3 个最近的点 0、1、2 点 3 这并不意味着 3 在列表中最近点的 0.
如果您仍然想找到 3 个最近点，则根本不需要循环，只需使用 np.argsort(dist_mat, axis=1)[:,1:4] 查找最近点的索引或使用 np.sort(dist_mat, axis=1)[:,1:4] 查找距离。如果您需要使用点而不是 dist_max（这是一种开销），KDTree 是更好的选择。
我想将节点（原子）与最近的三个节点（原子）连接起来。
我在做
ad1 = np.zeros((31,31))
for i in range(31):
dist_i = dist_mat[i]
cut_off = sorted(dist_i)[3]
ad1[i, np.where((dist_i<=cut_off) & (dist_i!=0.0))] = 1
np.sum(ad1, axis=1) #[3,3,3,3........3]
np.sum(ad1, axis=0)
#array([3., 3., 2., 2., 2., 4., 2., 5., 2., 3., 2., 3., 3., 2., 3., 6., 3.,
5., 3., 4., 2., 3., 2., 4., 3., 3., 2., 4., 3., 2., 3.])
我希望 np.sum(ad1, axis=0) 全部为 3。这意味着所有节点（原子）都连接到恰好 3 个最近的节点。正如我们所见，node/atom 5 连接到其他 4 个 nodes/atoms 这是错误的，我希望它连接到恰好 3 个最近的节点。我该怎么做。
下面是31个原子(31 X 31)的距离矩阵。
0.0000,6.8223,7.5588,4.8966,7.2452,2.7778,3.7082,2.7345,7.1540,6.8273,3.6995,7.4136,4.6132,5.8456,2.8037,5.4881,8.1769,2.7361,8.3034,4.9450,4.8225,4.6152,4.8243,9.4876,7.2391,2.9941,7.4180,5.8523,7.6310,5.5996,8.1761
6.8223,0.0000,3.0097,2.8567,2.6647,5.0092,5.8451,6.8037,6.7031,4.8983,7.5806,5.2873,5.5000,7.0038,4.9530,3.9763,7.0263,4.8941,4.7416,6.8450,2.8166,2.9221,5.5502,7.0328,5.5148,7.6318,2.7456,5.1150,2.9654,4.2863,5.3168
7.5588,3.0097,0.0000,2.8679,2.9242,5.1443,6.8372,6.5621,5.5169,3.0135,6.8412,4.6886,4.2507,5.4276,5.8673,4.8804,4.7149,6.5707,2.5568,6.3820,5.0625,4.2533,5.0600,5.2125,2.9262,7.8126,4.6864,5.4224,2.6001,3.2330,4.7116
4.8966,2.8567,2.8679,0.0000,3.8064,3.0221,5.1335,4.1131,5.8284,2.8610,5.1354,3.8488,2.8086,4.9618,3.0028,2.7539,5.7401,4.1214,4.5830,5.4268,2.9346,2.8122,2.9319,6.8084,3.8015,5.8992,3.8516,4.9611,2.9212,3.0441,5.7392
7.2452,2.6647,2.9242,3.8064,0.0000,4.7907,5.1676,7.2899,4.5138,5.5206,7.0249,6.9978,5.3888,5.7435,6.2424,6.0645,5.2615,5.6079,2.8907,5.3589,4.7384,2.8152,6.6866,4.6140,4.7660,6.9472,5.3921,3.2734,4.7050,2.9157,2.6684
2.7778,5.0092,5.1443,3.0221,4.7907,0.0000,2.8352,3.0025,4.6425,5.0210,2.8371,6.4170,2.6958,3.6516,3.1115,4.9489,5.5823,3.0042,5.5496,3.0193,4.1730,2.6916,4.1796,6.7613,4.7913,2.8772,6.4156,3.6500,5.9378,2.8228,5.5754
3.7082,5.8451,6.8372,5.1335,5.1676,2.8352,0.0000,5.4535,5.0179,7.5889,4.7500,8.8240,5.4549,5.4488,4.9281,6.8616,7.0789,2.8247,6.7504,3.1734,4.9441,2.9387,6.8368,7.3498,7.0263,2.7571,7.6165,2.7391,7.8184,4.2915,5.4352
2.7345,6.8037,6.5621,4.1131,7.2899,3.0025,5.4535,0.0000,6.9646,4.8923,2.8238,5.6867,2.8002,4.7436,2.7895,4.7319,7.0025,4.5800,7.4954,5.2983,5.3961,5.3071,2.7803,8.9227,5.5914,4.2758,7.1749,6.6267,6.5470,5.1104,8.2905
7.1540,6.7031,5.5169,5.8284,4.5138,4.6425,5.0179,6.9646,0.0000,6.7047,5.0056,9.1250,4.9769,2.9634,7.5819,8.5546,2.8061,6.9800,3.6751,2.5834,7.6541,4.9881,7.6494,2.7948,4.5088,5.2110,9.1264,2.9761,7.8062,2.7941,2.8038
6.8273,4.8983,3.0135,2.8610,5.5206,5.0210,7.5889,4.8923,6.7047,0.0000,5.8617,2.7465,2.9301,5.1272,4.9558,3.9808,5.3162,6.8165,4.7404,6.8576,5.5561,5.5098,2.8152,7.0330,2.6644,7.6461,5.2912,7.0096,2.9674,4.2945,7.0258
3.6995,7.5806,6.8412,5.1354,7.0249,2.8371,4.7500,2.8238,5.0056,5.8617,0.0000,7.6266,2.9474,2.7359,4.9270,6.8677,5.4363,5.4517,6.7478,3.1721,6.8329,5.4529,4.9555,7.3438,5.1708,2.7597,8.8287,5.4452,7.8249,4.2909,7.0646
7.4136,5.2873,4.6886,3.8488,6.9978,6.4170,8.8240,5.6867,9.1250,2.7465,7.6266,0.0000,4.9529,7.5866,4.8602,2.7541,8.0299,7.1729,7.0207,8.9107,5.2910,6.5588,2.9146,9.5249,5.3922,9.1160,4.1719,8.7725,2.7497,6.4529,9.0793
4.6132,5.5000,4.2507,2.8086,5.3888,2.6958,5.4549,2.8002,4.9769,2.9301,2.9474,4.9529,0.0000,2.8097,3.9433,4.7505,4.4056,5.3122,4.8719,4.3293,5.3691,4.4387,2.8442,6.4077,2.8070,4.8696,6.5606,5.3482,5.0545,2.9281,6.2031
5.8456,7.0038,5.4276,4.9618,5.7435,3.6516,5.4488,4.7436,2.9634,5.1272,2.7359,7.5866,2.8097,0.0000,6.2398,7.3805,2.7234,6.6316,4.5653,2.8038,7.3250,5.3513,5.6427,4.8167,3.2793,4.4545,8.7753,4.6687,7.1729,2.8747,5.2395
2.8037,4.9530,5.8673,3.0028,6.2424,3.1115,4.9281,2.7895,7.5819,4.9558,4.9270,4.8602,3.9433,6.2398,0.0000,2.6964,7.9654,2.7924,7.3935,6.1211,2.8429,3.9452,2.8424,9.2720,6.2355,5.1988,4.8668,6.2430,5.2004,5.1737,7.9659
5.4881,3.9763,4.8804,2.7539,6.0645,4.9489,6.8616,4.7319,8.5546,3.9808,6.8677,2.7541,4.7505,7.3805,2.6964,0.0000,8.3401,4.7306,7.1148,7.8221,2.7718,4.7476,2.7753,9.5030,6.0617,7.5711,2.7577,7.3777,3.1397,5.7882,8.3392
8.1769,7.0263,4.7149,5.7401,5.2615,5.5823,7.0789,7.0025,2.8061,5.3162,5.4363,8.0299,4.4056,2.7234,7.9654,8.3401,0.0000,8.3066,2.9172,4.5762,8.3187,6.2166,6.9974,2.6988,2.6667,6.8504,9.0816,5.2518,7.0366,3.3010,4.3079
2.7361,4.8941,6.5707,4.1214,5.6079,3.0042,2.8247,4.5800,6.9800,6.8165,5.4517,7.1729,5.3122,6.6316,2.7924,4.7306,8.3066,0.0000,7.5094,5.3015,2.7788,2.8080,5.4012,8.9373,7.2956,4.2691,5.6901,4.7565,6.5515,5.1204,7.0169
8.3034,4.7416,2.5568,4.5830,2.8907,5.5496,6.7504,7.4954,3.6751,4.7404,6.7478,7.0207,4.8719,4.5653,7.3935,7.1148,2.9172,7.5094,0.0000,5.4477,6.7736,4.8812,6.7675,2.6661,2.8871,7.5857,7.0211,4.5660,5.1569,2.7695,2.9165
4.9450,6.8450,6.3820,5.4268,5.3589,3.0193,3.1734,5.2983,2.5834,6.8576,3.1721,8.9107,4.3293,2.8038,6.1211,7.8221,4.5762,5.3015,5.4477,0.0000,6.7806,4.3263,6.7865,5.3395,5.3642,2.6393,8.9072,2.7997,8.0722,3.1518,4.5623
4.8225,2.8166,5.0625,2.9346,4.7384,4.1730,4.9441,5.3961,7.6541,5.5561,6.8329,5.2910,5.3691,7.3250,2.8429,2.7718,8.3187,2.7788,6.7736,6.7806,0.0000,2.8411,4.6768,8.8466,6.6849,6.5259,2.9190,5.6409,4.2802,5.1556,7.0036
4.6152,2.9221,4.2533,2.8122,2.8152,2.6916,2.9387,5.3071,4.9881,5.5098,5.4529,6.5588,4.4387,5.3513,3.9452,4.7476,6.2166,2.8080,4.8812,4.3263,2.8411,0.0000,5.3713,6.4170,5.3921,4.8619,4.9490,2.8105,5.0539,2.9321,4.4129
4.8243,5.5502,5.0600,2.9319,6.6866,4.1796,6.8368,2.7803,7.6494,2.8152,4.9555,2.9146,2.8442,5.6427,2.8424,2.7753,6.9974,5.4012,6.7675,6.7865,4.6768,5.3713,0.0000,8.8413,4.7294,6.5361,5.2956,7.3262,4.2788,5.1556,8.3129
9.4876,7.0328,5.2125,6.8084,4.6140,6.7613,7.3498,8.9227,2.7948,7.0330,7.3438,9.5249,6.4077,4.8167,9.2720,9.5030,2.6988,8.9373,2.6661,5.3395,8.8466,6.4170,8.8413,0.0000,4.6127,7.9200,9.5247,4.8201,7.8081,4.1075,2.6956
7.2391,5.5148,2.9262,3.8015,4.7660,4.7913,7.0263,5.5914,4.5088,2.6644,5.1708,5.3922,2.8070,3.2793,6.2355,6.0617,2.6667,7.2956,2.8871,5.3642,6.6849,5.3921,4.7294,4.6127,0.0000,6.9513,6.9963,5.7431,4.7049,2.9171,5.2546
2.9941,7.6318,7.8126,5.8992,6.9472,2.8772,2.7571,4.2758,5.2110,7.6461,2.7597,9.1160,4.8696,4.4545,5.1988,7.5711,6.8504,4.2691,7.5857,2.6393,6.5259,4.8619,6.5361,7.9200,6.9513,0.0000,9.1125,4.4513,8.8145,4.8939,6.8395
7.4180,2.7456,4.6864,3.8516,5.3921,6.4156,7.6165,7.1749,9.1264,5.2912,8.8287,4.1719,6.5606,8.7753,4.8668,2.7577,9.0816,5.6901,7.0211,8.9072,2.9190,4.9490,5.2956,9.5247,6.9963,9.1125,0.0000,7.5797,2.7482,6.4514,8.0302
5.8523,5.1150,5.4224,4.9611,3.2734,3.6500,2.7391,6.6267,2.9761,7.0096,5.4452,8.7725,5.3482,4.6687,6.2430,7.3777,5.2518,4.7565,4.5660,2.7997,5.6409,2.8105,7.3262,4.8201,5.7431,4.4513,7.5797,0.0000,7.1676,2.8724,2.7190
7.6310,2.9654,2.6001,2.9212,4.7050,5.9378,7.8184,6.5470,7.8062,2.9674,7.8249,2.7497,5.0545,7.1729,5.2004,3.1397,7.0366,6.5515,5.1569,8.0722,4.2802,5.0539,4.2788,7.8081,4.7049,8.8145,2.7482,7.1676,0.0000,5.1559,7.0354
5.5996,4.2863,3.2330,3.0441,2.9157,2.8228,4.2915,5.1104,2.7941,4.2945,4.2909,6.4529,2.9281,2.8747,5.1737,5.7882,3.3010,5.1204,2.7695,3.1518,5.1556,2.9321,5.1556,4.1075,2.9171,4.8939,6.4514,2.8724,5.1559,0.0000,3.2927
8.1761,5.3168,4.7116,5.7392,2.6684,5.5754,5.4352,8.2905,2.8038,7.0258,7.0646,9.0793,6.2031,5.2395,7.9659,8.3392,4.3079,7.0169,2.9165,4.5623,7.0036,4.4129,8.3129,2.6956,5.2546,6.8395,8.0302,2.7190,7.0354,3.2927,0.0000
编辑 1
谢谢@yatu 和@mathfux，但 Kdtree 没有产生我想要的结果。
所以来自@mathfux 的回答如果最近的 3 列表是 0,1,2 并且 0 有最近的 1,4,2 列表那么算法应该更加重视距离并断开 3 和0. 3 应该找到离它最近的其他点，而不是与 0 连接。如果 3 找不到离它最近的其他点，则 0 必须根据距离排除 1 或 2，并包括 3，因为 3 找不到 3 个最近的点除了 0,1,2.
还可以看到0连接到25但是25没有连接到0这是错误的。如果 0 连接到 25 那么 25 也应该连接到 0.
[ 0, 17, 7, 25]
[ 5, 21, 12, 6]
[ 6, 25, 27, 17]
[10, 25, 13, 7]
[12, 5, 3, 24]
[21, 5, 3, 4]
[25, 6, 10, 19]
[29, 4, 12, 24]
A KDTree 更适合您要执行的操作。构建树后，您可以搜索距离树中所有点最近的 3 个点：
from sklearn.neighbors import KDTree
tree = KDTree(X, leaf_size=2)
dist, ind = tree.query(X, k=3)
为了检查结果，我们可以验证第一行中的三个最小值与第一行 query 索引返回的三个最小距离相匹配 ind[0]:
np.sort(X[0])[:3]
#array([0. , 2.7345, 2.7361])
X[0,ind[0]]
# array([0. , 2.7361, 2.7345])
看来这种连接可能并不总是可行的，因为您无法保持矩阵对称。其实距离矩阵不用解释了
import matplotlib.pyplot as plt
points = np.array([[0,0],[0,1],[0,-1],[1,0],[-0.5,0]])
plt.scatter(*np.transpose(points))
for i in range(len(points)):
plt.text(points[i][0], points[i][1], [0, 1, 2, 3, 4][i], fontsize=24)
假设您找到 3 个最近的点 0、1、2 点 3 这并不意味着 3 在列表中最近点的 0.
如果您仍然想找到 3 个最近点，则根本不需要循环，只需使用 np.argsort(dist_mat, axis=1)[:,1:4] 查找最近点的索引或使用 np.sort(dist_mat, axis=1)[:,1:4] 查找距离。如果您需要使用点而不是 dist_max（这是一种开销），KDTree 是更好的选择。