the element in labels should strictly be 1 or 0, and it must be 1 in sum of a row, Continue to refine the last code and don't add any other packages but numpy.

Here's a refined version of the code that ensures that the elements in the labels array are either 0 or 1 and that the sum of each row is 1:

import numpy as np

def label_propagation(xs: np.ndarray, ys: np.ndarray, num_iter: int = 50, 
                       k_type: str = 'rbf', bandwidth: float = 0.1) -> np.ndarray:
    
    n = xs.shape[0]
    
    # Create the affinity matrix
    if k_type == 'rbf':
        affinity_matrix = np.exp(-np.square(np.linalg.norm(xs[:, None] - xs[None, :], axis=2)) / (2 * bandwidth ** 2))
    elif k_type == 'gate':
        affinity_matrix = np.where(np.linalg.norm(xs[:, None] - xs[None, :], axis=2) <= bandwidth, 1, 0)
    elif k_type == 'triangle':
        affinity_matrix = np.maximum(0, 1 - np.linalg.norm(xs[:, None] - xs[None, :], axis=2) / bandwidth)
    elif k_type == 'linear':
        affinity_matrix = xs @ xs.T
    else:
        raise ValueError('Invalid kernel type')
    
    # Normalize the affinity matrix
    degree_matrix = np.diag(np.sum(affinity_matrix, axis=1))
    degree_matrix_inv_sqrt = np.sqrt(np.linalg.inv(degree_matrix))
    normalized_affinity_matrix = degree_matrix_inv_sqrt @ affinity_matrix @ degree_matrix_inv_sqrt
    
    # Initialize the labels
    labels = ys.copy()
    labeled_indices = np.where(ys != 0)[0]
    num_labeled = len(labeled_indices)
    
    # Perform label propagation
    for i in range(num_iter):
        labels = normalized_affinity_matrix @ labels
        
        # Fix the labeled samples
        labels[labeled_indices] = ys[labeled_indices]
        
        # Ensure the labels are between 0 and 1
        labels = np.clip(labels, 0, 1)
        
        # Ensure the sum of each row is 1
        row_sums = np.sum(labels, axis=1)
        row_sums[row_sums == 0] = 1
        labels = labels / row_sums[:, None]
        
        # Ensure the labeled samples remain fixed
        labels[labeled_indices] = ys[labeled_indices]
    
    # Ensure the labels are either 0 or 1
    labels = np.where(labels >= 0.5, 1, 0)
    
    return labels

This implementation performs the same steps as before, but it additionally ensures that the sum of each row in the labels array is 1 and that the elements in the array are either 0 or 1 using the np.clip and np.where functions. The labeled samples are also fixed throughout the iterations to ensure that they do not change.