I have an undirected weighted graph:

I manually calculated the centrality for each node.

1 - 0
2 - 1.5
3 - 0
4 - 3
5 - 2

Then I calculated the centrality using this algorithm

import networkx as nx

G = nx.Graph()

adj_matrix = [
    [0, 4, 0, 0, 1],
    [4, 0, 3, 1, 0],
    [0, 3, 0, 4, 0],
    [0, 1, 4, 0, 2],
    [1, 0, 0, 2, 0],
]

for i in range(len(adj_matrix)):
    for j in range(len(adj_matrix[i])):
        if adj_matrix[i][j] != 0:
            G.add_edge(i, j, weight=adj_matrix[i][j])

betweenness = nx.centrality.betweenness_centrality(G, k=None, normalized=False, weight="weight", endpoints=False, seed=None)
print(betweenness)

And got slightly different values.

1 - 0
2 - 1.667
3 - 0
4 - 3.167
5 - 2.167

Why are they different? I tried to use direct calculation of deltas instead of a recursive formula in the program.