WEEK 12.md

How does google work

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Part 1: Introduction

• Introduction to PageRank and how it works.
• Mention of creating a directed graph using NetworkX.
• Setting up Python libraries.

import networkx as nx
import matplotlib.pyplot as plt

G = nx.DiGraph()

Part 2: Directed Graph and Edge Data

• Explanation of the edge list data.
• Using nx.read_edge_list to read the data.
• Displaying the directed graph.

G = nx.read_edgelist("page_rank.txt", create_using=nx.DiGraph(), nodetype=int)
nx.draw(G, with_labels=True)
plt.show()

Part 3: Points Distribution Method

• Introduction to the concept of distributing points based on edges.
• Explaining how nodes distribute points to their neighbors.
• Describing the iterative process.

Part 4: Simulating Points Distribution in Excel

• Demonstrating the points distribution in an Excel sheet.
• Showing how to manually distribute points based on the edges.

Part 5: Programming a Complex Network

• Starting with a more complex network with many nodes and edges.
• Creating a random network for demonstration.

import random

G = nx.gnp_random_graph(25, 0.2, directed=True)

Part 6: Visualizing the Complex Network

• Visualizing the complex network using NetworkX.
• Showing how to plot the directed graph.

nx.draw(G, with_labels=True)
plt.show()

Part 7: Equal Points to All Nodes

• Initializing equal points to all nodes in the network.
• Starting the points distribution game.

Part 8: Points Distribution Based on Outgoing Edges

• Describing how nodes distribute points based on their outgoing edges.
• Simulating the distribution process.

Part 9: User-Controlled Stopping of Points Distribution

• Allowing the user to control when the points distribution process stops.

Part 10: Converting Point List to Dictionary

• Explaining the need to convert the list of points to a dictionary to preserve node information.

points_dict = {}
for i in range(len(points)):
    points_dict[i] = points[i]

Part 11: Ranking Nodes by Points

• Describing the process of ranking nodes based on their points.
• Using sorted to sort the dictionary by point values.

sorted_points = sorted(points_dict.items(), key=lambda x: x[1], reverse=True)
print(sorted_points)

Part 12: Comparing with NetworkX PageRank

• Using NetworkX's nx.pagerank to compute PageRank values for the graph.
• Comparing the results with the manually calculated PageRank.

networkx_pagerank = nx.pagerank(G)
sorted_networkx_pagerank = sorted(networkx_pagerank.items(), key=lambda x: x[1], reverse=True)
print(sorted_networkx_pagerank)

Part 13: Proving PageRank Convergence

• Mentioning the mathematical proof of PageRank convergence.
• Explaining the convergence state of PageRank.
• Emphasizing that even if different methods or seeds are used, the distribution is the same.

Part 14: Creating a Directed Graph from Edge Data

• Using NetworkX to create a directed graph from edge data.
• Reading data from a file using nx.read_edgelist.

G = nx.read_edgelist("page_rank.txt", create_using=nx.DiGraph(), nodetype=int)

Part 15: Visualizing the Directed Graph

• Visualizing the directed graph created from edge data.
• Showing how to draw the graph with labels.

nx.draw(G, with_labels=True)
plt.show()

Part 16: Task for the Audience

• Assigning a task to the audience: Running PageRank on the graph created in Part 15 to determine the leader of the group.

Collatz Conjecture

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Collatz Conjecture: Part 1

• Introduction to the Collatz Conjecture.
• Explaining the simplicity and complexity of the conjecture.
• The conjecture states that for any given positive integer n:
  • If n is even, divide it by 2.
  • If n is odd, multiply it by 3 and add 1.
• Demonstrating the application of the conjecture with examples.

def collatz(n):
    iterations = 0
    while n != 1:
        if n % 2 == 0:
            n = n // 2
        else:
            n = 3 * n + 1
        iterations += 1
    print(f'Number 1 achieved after {iterations} iterations.')

# Example usage:
collatz(12)

Collatz Conjecture: Part 2

• Revisiting the Collatz Conjecture.
• A reminder of the operations to apply to n.
• The Collatz Conjecture is tested using a Python function.

def check_collatz(number):
    iterations = 0
    while number != 1:
        if number % 2 == 0:
            number = number // 2
        else:
            number = 3 * number + 1
        iterations += 1
    print(f'Number 1 achieved after {iterations} iterations.')

# Example usage:
check_collatz(12)
check_collatz(20)

Collatz Conjecture: Part 3

• Introducing a Python function to check the Collatz Conjecture for any given number.
• Demonstrating how different numbers reach 1 in varying numbers of iterations.

def check_collatz(number):
    iterations = 0
    while number != 1:
        if number % 2 == 0:
            number = number // 2
        else:
            number = 3 * number + 1
        iterations += 1
    print(f'Number 1 achieved after {iterations} iterations.')

# Example usage:
check_collatz(12)
check_collatz(20)
check_collatz(64)

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thank you ~created by Goutham