SageMath - Diversity Measures of Weighted Bipartite Graphs (Tokenism & Entropy)

gistfile1.txt

#Code generated with the help of Dr. Brett Stevens @ Carleton University
#input matrices are easily generated by, G.reduced_adjacency_matrix()

#Mutual information is minimized when p(x,y)=p(x)*p(y). Otherwise, the joint probability is equal to the product of the marginals 

def mutual_entropy(input_matrix):
    
    matrix_sum = (matrix([1]*input_matrix.nrows())*input_matrix*(matrix([1]*input_matrix.ncols())).transpose())[0][0]
    
    row_probabilities = (input_matrix*(matrix([1]*input_matrix.ncols())).transpose()).transpose()[0]
    column_probabilities = ((matrix([1]*input_matrix.nrows()))*input_matrix)[0]
    
     
    entropy = 0
    for (i,j) in itertools.product(range(input_matrix.nrows()),range(input_matrix.ncols())):
        if input_matrix[i][j] > 0:
            entropy += input_matrix[i][j] *log_b(1.*(matrix_sum*input_matrix[i][j])/(row_probabilities[i]*column_probabilities[j]),2) /   (matrix_sum)
        
    return entropy
    
def joint_entropy(input_matrix):

    matrix_sum = (matrix([1]*input_matrix.nrows())*input_matrix*(matrix([1]*input_matrix.ncols())).transpose())[0][0]
    
    row_probabilities = (input_matrix*(matrix([1]*input_matrix.ncols())).transpose()).transpose()[0]
    column_probabilities = ((matrix([1]*input_matrix.nrows()))*input_matrix)[0]

#Joint entropy is maximized by a matrix who is evenly distributed. Think a complete bipartite graph with all edges of equal weight
     
    jointentropy = 0
    
    for (i,j) in itertools.product(range(input_matrix.nrows()),range(input_matrix.ncols())):
        if input_matrix[i][j] > 0:            
            jointentropy += -1.*(input_matrix[i][j]/matrix_sum *log_b((input_matrix[i][j]/matrix_sum),2))
            
    return jointentropy

#Naive tokenism is maximized by the identity matrix

def naive_tokenism(input_matrix):
    
    naive_tokenism_measure = 0
    
    for i in range(input_matrix.nrows()):
        if len(input_matrix.nonzero_positions_in_row(i)) >0:
            naive_tokenism_measure += 1
            
    for i in range(input_matrix.ncols()):
        if len(input_matrix.nonzero_positions_in_column(i)) >0:
            naive_tokenism_measure += 1
    return Fraction(naive_tokenism_measure, (input_matrix.ncols()+input_matrix.nrows()))        
    #return (naive_tokenism_measure)/(input_matrix.ncols()+input_matrix.nrows())
    
#Subtle tokenism is maximized by the matrix of all-ones    
    
def subtle_tokenism(input_matrix):
    
    subtle_tokenism_measure =  len(input_matrix.nonzero_positions())
    stm_denominator = (input_matrix.ncols()*input_matrix.nrows())
#    subtle_tokenism_meafsure =  len(input_matrix.nonzero_positions())/(input_matrix.ncols()*input_matrix.nrows())
#    print subtle_tokenism_measure, stm_denominator
    
    
    return Fraction(subtle_tokenism_measure, stm_denominator)
    #return (1*subtle_tokenism_measure)/(stm_denominator)