# --------------
# Code starts here

import numpy as np

# Code starts here

# Adjacency matrix
adj_mat = np.array([[0,0,0,0,0,0,1/3,0],
                   [1/2,0,1/2,1/3,0,0,0,0],
                   [1/2,0,0,0,0,0,0,0],
                   [0,1,0,0,0,0,0,0],
                  [0,0,1/2,1/3,0,0,1/3,0],
                   [0,0,0,1/3,1/3,0,0,1/2],
                   [0,0,0,0,1/3,0,0,1/2],
                   [0,0,0,0,1/3,1,1/3,0]])

# Compute eigenvalues and eigencevectrs
eigenvalues, eigenvectors = np.linalg.eig(adj_mat)
print('Eigen values are', eigenvalues)
print('*'*25)
#print(eigenvectors)
print('Eigen Vector are', abs(eigenvectors[:,0]))
print('*'*25)
eigen_1 = abs(eigenvectors[:,0]) / np.linalg.norm(eigenvectors[:,0],1)
print('Normalize eigen vector are', eigen_1)
print('*'*50)
page =  np.where(np.max(eigen_1) == eigen_1)[0][0] + 1 
print('The most important page is', page)


# Eigen vector corresponding to 1


# most important page


# Code ends here


# --------------
# Code starts here

# Initialize stationary vector I
# Code starts here

# Initialize stationary vector I
init_I = np.array([1,0,0,0,0,0,0,0])

# Perform iterations for power method
for i in range(10):
    init_I = np.dot(adj_mat, init_I)
    init_I /= np.linalg.norm(init_I, 1)


print(init_I)
power_page = np.where(np.max(init_I) == init_I)[0][0] + 1
print(power_page)

# Code ends here

print('*'*100)
print('*'*100)
print('*'*100)
print('*'*100)
print('*'*100)



# Code ends here


# --------------
# Code starts here

# New Adjancency matrix
# New Adjancency matrix
new_adj_mat = np.array([[0,0,0,0,0,0,0,0],
                   [1/2,0,1/2,1/3,0,0,0,0],
                  [1/2,0,0,0,0,0,0,0],
                   [0,1,0,0,0,0,0,0],
                   [0,0,1/2,1/3,0,0,1/2,0],
                   [0,0,0,1/3,1/3,0,0,1/2],
                   [0,0,0,0,1/3,0,0,1/2],
                   [0,0,0,0,1/3,1,1/2,0]])

# Initialize stationary vector I
new_init_I = np.array([1,0,0,0,0,0,0,0])
#print(new_init_I)

# Perform iterations for power method
for  i in range (10):
     new_init_I = np.dot(new_adj_mat, new_init_I)
     new_init_I /= np.linalg.norm(new_init_I, 1)
print(new_init_I)





# Code ends here


# --------------
# Alpha value
alpha = 0.85

# Code starts here

# Modified adjancency matrix
G = (alpha*new_adj_mat) + (1-alpha)*(1/len(new_adj_mat))*np.ones(new_adj_mat.shape)
print(G)                                                                    

# Initialize stationary vector I
final_init_I = np.array([1,0,0,0,0,0,0,0])

# Perform iterations for power method
for i in range (1000):
    final_init_I = np.dot(new_adj_mat, final_init_I)
    final_init_I /= np.linalg.norm(final_init_I, 1)
print(final_init_I)
# Code ends here


