centrality_scores.py

import pandas as pd
import numpy as np
from typing import Union


def eig_vec_cent(cov: pd.DataFrame, 
                 n_components: int = 3, 
                 largest: bool = True) -> Union[pd.Series, None]:

    ''' Return "Eigenvector Centrality" from the covariance matrix (=cov)
            
    Args:
        
        cov (required): pandas.core.frame.DataFrame
            Estimated covariance matrix on specific date.
        
        n_components (optional): int 
            Number of components used to estimate the centrality score
            
        largest (optional): bool
           If True, LARGEST n_components number of (eigen values, eigen vectors) will be used to compute centrality score.
           Else, LOWEST n_componets number of (eigen values, eigen vectors) will be used to compute centrality score.
    
    Returns:
        
        Centrality score for every asset.
        
        Centrality scores = ( EigenValue_i * ( abs(EigenVector_i) / sum(abs(EigenVector_i)) ) ) / (Σ EigenValue_i)
        
            i: ith of eigen value/vector
            Sum of Centrality scores of every asset will sum up to 1
    
    Example:

        cov_dfs = cov_dfs.groupby('Dates').apply(eig_vec_cent)

    * np.linalg.eigh returns the same result as np.linalg.eig when 'cov' is symmetric.

    '''
    if cov.isnull().values.any(): 
        return None 

    eig_vals, eig_vecs = np.linalg.eigh(cov.values)
    sort_permutation = eig_vals.argsort()
    eig_vals.sort()
    eig_vecs = eig_vecs[:, sort_permutation]
    
    if largest:
        eig_vals = eig_vals[-n_components:]
        eig_vecs = abs(eig_vecs[:, -n_components:])
    else:
        eig_vals = eig_vals[:n_components]
        eig_vecs = abs(eig_vecs[:, :n_components])
    
    return pd.Series(np.sum(eig_vals * eig_vecs / np.sum(eig_vecs, axis=0), axis=1) / np.sum(eig_vals), index=cov.columns)