如何根据FIPS邻接矩阵向dataframe添加一个列，该列对相邻县的机构数进行求和

import pandas as pd

adjacency_matrix = pd.DataFrame({
    'County1': ['A', 'B', 'C', 'D'],
    'County2': ['B', 'C', 'D', 'A'],
    'Institutions': [2, 3, 1, 4]
})

county_df = pd.DataFrame(columns=['County', 'Total Institutions'])

for i in range(len(adjacency_matrix)):
    county1 = adjacency_matrix.loc[i, 'County1']
    county2 = adjacency_matrix.loc[i, 'County2']
    institutions = adjacency_matrix.loc[i, 'Institutions']
    
    if county1 in county_df['County'].values:
        county_df.loc[county_df['County'] == county1, 'Total Institutions'] += institutions
    else:
        county_df = county_df.append({'County': county1, 'Total Institutions': institutions}, ignore_index=True)
        
    if county2 in county_df['County'].values:
        county_df.loc[county_df['County'] == county2, 'Total Institutions'] += institutions
    else:
        county_df = county_df.append({'County': county2, 'Total Institutions': institutions}, ignore_index=True)

print(county_df)