Unveiling the Magic Behind Google’s PageRank Algorithm

Larry Page and Sergey Brin’s background and involvement

In the late 1990s, Stanford students Larry Page and Sergey Brin faced the chaotic expansion of the internet. They introduced PageRank, an algorithm that assigned importance to web pages based on incoming links. This innovation revolutionized search engines, considering the web’s interconnectedness rather than just keywords. PageRank became the backbone of Google’s ranking system, ushering in more relevant and trustworthy search results. The algorithm’s concept of evaluating relationships between pages transformed the internet’s organization and led to the powerful search engine we rely on today.

Chaotic expansion of the internet in the late 1990s

Yahoo Directory was an early web indexing and ranking system used by Yahoo before algorithmic search engines became dominant. It relied on human editors who manually reviewed and categorized websites into specific topics and subtopics. This curated directory helped users navigate the web by providing an organized structure of websites based on human judgment rather than automated algorithms.

Need for a more effective way to rank web pages

While the original PageRank algorithm involves iterative calculations, modern search engines use advanced optimization techniques, parallel processing, and distributed systems to handle massive amounts of data efficiently. The number of iterations or the stopping criteria for the iterations could be dynamically adjusted based on the scale of the web graph and other factors.

// Function to calculate the PageRank scores
function calculatePageRank(graph, dampingFactor, iterations) {
    // The function takes three parameters:
    // 1. 'graph': A 2D array representing the web graph as an adjacency matrix.
    //    graph[i][j] = 1 means there is a link from node j to node i.
    // 2. 'dampingFactor': A value between 0 and 1 representing the probability
    //    that a user will follow a link (85% chance is commonly used, i.e., 0.85).
    // 3. 'iterations': The number of iterations to run the PageRank algorithm.
  
    const numNodes = graph.length;
    // 'numNodes' represents the number of nodes in the web graph.
  
    let pageRank = new Array(numNodes).fill(1 / numNodes);
    // 'pageRank' is an array that stores the PageRank scores for each node.
    // Initially, all nodes are assigned equal probabilities (1 / numNodes).
  
    for (let iter = 0; iter < iterations; iter++) {
      // The algorithm runs 'iterations' number of times to update the PageRank scores.
  
      let newPageRank = new Array(numNodes).fill(0);
      // 'newPageRank' is used to store the updated PageRank scores for this iteration.
  
      for (let i = 0; i < numNodes; i++) {
        for (let j = 0; j < numNodes; j++) {
          if (graph[j][i] === 1) {
            // If there is a link from node 'j' to node 'i' (graph[j][i] === 1),
            // we calculate the number of outgoing links from node 'j'.
            const outgoingLinks = graph[j].filter((value) => value === 1).length;
  
            // We update the PageRank score for node 'i' based on the PageRank score of node 'j'
            // and the number of outgoing links from node 'j'.
            newPageRank[i] += pageRank[j] / outgoingLinks;
          }
        }
      }
  
      for (let i = 0; i < numNodes; i++) {
        // After calculating the contributions from incoming nodes,
        // we apply the damping factor to the new PageRank score for node 'i'.
        newPageRank[i] = dampingFactor * newPageRank[i] + (1 - dampingFactor) / numNodes;
      }
  
      // Update the 'pageRank' array with the new PageRank scores for the next iteration.
      pageRank = newPageRank;
    }
  
    return pageRank;
    // The function returns the final PageRank scores for all nodes in the web graph.
  }
  // C , D , B , A

function mainFunction(){
    const graph = [
        [0, 1, 1, 0],
        [0, 0, 0, 1],
        [1, 1, 0, 1],
        [0, 0, 1, 0],
      ];
      const dampingFactor = 0.85; // Typical value for damping factor
      const iterations = 100; // Number of iterations to run the algorithm
      
      const pageRankScores = calculatePageRank(graph, dampingFactor, iterations);
      console.log("PageRank scores:", pageRankScores);
}
mainFunction();

The “damping factor” in the PageRank algorithm is a parameter used to model the behavior of web surfers. It represents the probability that a user will continue browsing the web by following links instead of jumping to a new random page. The most common damping factor used in the PageRank algorithm is 0.85, which means that there is an 85% chance that a user will click on a link and a 15% chance of jumping to a random page.

Iterative Formula to find Page Rank

The damping factor prevents the PageRank algorithm from getting stuck in a loop or infinite traversal, as it ensures that there is a probability of moving from one node to another in the web graph.

Result after iterations

Regarding the number of iterations, there is no fixed rule for deciding how many iterations to perform. The number of iterations required for the PageRank algorithm to converge on the stable scores can vary depending on the size and complexity of the web graph. In practice, it’s common to set a fixed number of iterations as a stopping criterion or use a threshold to check the convergence of the scores.

About the Author:

Nishant Choudhary is a Software Developer with around 2 years of experience in Software Development where he worked in multiple organizations and contributed to solving different kinds of complex problems with his creativity and enthusiasm for learning and different kinds of skills such as problem-solving, web designing and development, analysis of architecture and development of Progressive Web Applications.

About CodeStax.Ai

At CodeStax.Ai, we stand at the nexus of innovation and enterprise solutions, offering technology partnerships that empower businesses to drive efficiency, innovation, and growth, harnessing the transformative power of no-code platforms and advanced AI integrations.

But the real magic? It’s our tech tribe behind the scenes. If you’ve got a knack for innovation and a passion for redefining the norm, we’ve got the perfect tech playground for you. CodeStax.Ai offers more than a job — it’s a journey into the very heart of what’s next. Join us, and be part of the revolution that’s redefining the enterprise tech landscape.