Is nx.eigenvector_centrality_numpy() using the Arnoldi iteration instead of the basic power method? - numpy

Question

Since nx.eigenvector_centrality_numpy() using ARPACK, is it mean that nx.eigenvector_centrality_numpy() using Arnoldi iteration instead of the basic power method?
because when I try to compute manually using the basic power method, the result of my computation is different from the result of nx.eigenvector_centrality_numpy(). Can someone explain it to me?
To make it more clear, here is my code and the result that I got from the function and the result when I compute manually.
import networkx as nx
G = nx.DiGraph()
G.add_edge('a', 'b', weight=4)
G.add_edge('b', 'a', weight=2)
G.add_edge('b', 'c', weight=2)
G.add_edge('b','d', weight=2)
G.add_edge('c','b', weight=2)
G.add_edge('d','b', weight=2)
centrality = nx.eigenvector_centrality_numpy(G, weight='weight')
centrality
The result:
{'a': 0.37796447300922725,
'b': 0.7559289460184545,
'c': 0.3779644730092272,
'd': 0.3779644730092272}
Below is code from Power Method Python Program and I did a little bit of modification:
# Power Method to Find Largest Eigen Value and Eigen Vector
# Importing NumPy Library
import numpy as np
import sys
# Reading order of matrix
n = int(input('Enter order of matrix: '))
# Making numpy array of n x n size and initializing
# to zero for storing matrix
a = np.zeros((n,n))
# Reading matrix
print('Enter Matrix Coefficients:')
for i in range(n):
for j in range(n):
a[i][j] = float(input( 'a['+str(i)+']['+ str(j)+']='))
# Making numpy array n x 1 size and initializing to zero
# for storing initial guess vector
x = np.zeros((n))
# Reading initial guess vector
print('Enter initial guess vector: ')
for i in range(n):
x[i] = float(input( 'x['+str(i)+']='))
# Reading tolerable error
tolerable_error = float(input('Enter tolerable error: '))
# Reading maximum number of steps
max_iteration = int(input('Enter maximum number of steps: '))
# Power Method Implementation
lambda_old = 1.0
condition = True
step = 1
while condition:
# Multiplying a and x
ax = np.matmul(a,x)
# Finding new Eigen value and Eigen vector
x = ax/np.linalg.norm(ax)
lambda_new = np.vdot(ax,x)
# Displaying Eigen value and Eigen Vector
print('\nSTEP %d' %(step))
print('----------')
print('Eigen Value = %0.5f' %(lambda_new))
print('Eigen Vector: ')
for i in range(n):
print('%0.5f\t' % (x[i]))
# Checking maximum iteration
step = step + 1
if step > max_iteration:
print('Not convergent in given maximum iteration!')
break
# Calculating error
error = abs(lambda_new - lambda_old)
print('errror='+ str(error))
lambda_old = lambda_new
condition = error > tolerable_error
I used the same matrix and the result:
STEP 99
----------
Eigen Value = 3.70328
Eigen Vector:
0.51640
0.77460
0.25820
0.25820
errror=0.6172133998483682
STEP 100
----------
Eigen Value = 4.32049
Eigen Vector:
0.71714
0.47809
0.35857
0.35857
Not convergent in given maximum iteration!
I've to try to compute it with my calculator too and I know it's not convergent because |lambda1|=|lambda2|=4. I've to know the theory behind nx.eigenvector_centrality_numpy() properly so I can write it right for my thesis. Help me, please