from scipy.sparse.linalg import eigsh, eigs
from scipy.sparse import bmat, diags
import numpy as np
def SpectralRadius(A):
'''This function computes the spectral radius of an Hermitian matrix A
Use: ρ = SpectralRadius(A)
Input:
* A (scipy sparse array)
Output:
* ρ (float)
'''
ρ, _ = eigsh(A.astype(float), k = 1, which = 'LM')
return ρ[0]
def SpectralRadiusNB(A):
'''This function computes the spectral radius of the non-backtracking matrix
Use: ρ = SpectralRadiusNB(A)
Input:
* A (scipy sparse array): graph adjacency matrix
Outoput:
* ρ (float)
'''
n, _ = A.shape
D = diags(A@np.ones(n))
Id = diags(np.ones(n))
Bp = bmat([[A, -Id], [D-Id, None]])
ρB, _ = eigs(Bp, k = 1, which = 'LM')
return ρB[0].real
