#PageRank Algorithm using Random Walk
!pip install matplotlib

import random
import matplotlib.pyplot as plt

# ----------- Define the link structure (Graph) ------------
pages = {
    'Page1': ['Page2', 'Page3'],
    'Page2': ['Page3'],
    'Page3': ['Page1'],
    'Page4': ['Page1', 'Page2', 'Page3']
}

# ----------- Initialize counts and parameters ------------
visit_count = {page: 0 for page in pages}
num_steps = 100000
damping_factor = 0.85
all_pages = list(pages.keys())

# ----------- Start from a random page ------------
current_page = random.choice(all_pages)

for _ in range(num_steps):
    if random.random() < damping_factor:
        if pages[current_page]:
            current_page = random.choice(pages[current_page])
        else:
            current_page = random.choice(all_pages)
    else:
        current_page = random.choice(all_pages)

    visit_count[current_page] += 1

# ----------- Normalize and print PageRanks ------------
print("\n Estimated PageRank (based on visit frequency):")
for page in sorted(visit_count):
    rank = visit_count[page] / num_steps
    print(f"{page}: {rank:.4f}")

# ----------- Optional: Visualize with bar chart ------------
plt.bar(visit_count.keys(), [v / num_steps for v in visit_count.values()], color='skyblue')
plt.title('PageRank Estimation via Random Walk')
plt.xlabel('Web Pages')
plt.ylabel('Estimated PageRank')
plt.grid(axis='y')
plt.show()