用python求解特征向量和拉普拉斯矩阵

import scipy as sc


#返回特征值，按照升序排列，num定义返回的个数
def eignvalues(matrix, num):
    return sc.linalg.eigh(matrix, eigvalues(0, num-1))[0]


#返回特征向量
def eighvectors(matrix):
    return sc.linalg.eigh(matrix, eigvalues(0, num-1))[1]

#创建一个对角矩阵，很容易得知它的特征值是1,2,3
matrix = sc.diag([1,2,3])


#调用特征值函数,获取最小的特征值
minValue = eighvalues(matrix, 1)


#调用特征向量函数，获取所有的特征向量
vectors = eighvectors(matrix, 3)

#laplacian矩阵
import numpy as np
def unnormalized_laplacian(adj_matrix):
    # 先求度矩阵
    R = np.sum(adj_matrix, axis=1)
    degreeMatrix = np.diag(R)
    return degreeMatrix - adj_matrix
    
def normalized_laplacian(adj_matrix):
    R = np.sum(adj_matrix, axis=1)
    R_sqrt = 1/np.sqrt(R)
    D_sqrt = np.diag(R_sqrt)
    I = np.eye(adj_matrix.shape[0])
    return I - D_sqrt * adj_matrix * D_sqrt