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[Requirements](#requirements)\n2. [Implementation Notes](#implementation-notes)\n3. [Mathematical Background](#mathematical-background)\n\n---\n\n## Requirements📋\n\n1. Each student will draw (on a sheet of paper) a **directed graph** with n = 10 nodes and random arcs.\n2. The graph will be represented using Python data structures (any representation can be used).\n3. Based on the graph, construct the transition matrix M.\n4. The vector v₀ will be initialized as:\n   ```\n   v₀ = [1/n]\n        [1/n]\n        [...]\n        [1/n]\n   ```\n   and will be updated through repeated multiplications with the transition matrix M.\n5. The algorithm stops when the ranks vector changes sufficiently little between two generations (`|v' - v| \u003c ε`).\n6. Graphically represent using a bar chart the color rankings of n nodes at each step.\n\n---\n\n## Implementation Notes📝\n\n- The program should use Python's built-in data structures.\n- The transition matrix M represents the probability of transitioning from one node to another.\n- The initial vector v₀ assigns equal probability to all nodes.\n- The convergence criterion ε determines when the algorithm stops.\n- The visualization should show how node rankings evolve over iterations.\n\n---\n\n## Mathematical Background📚\n\nThe PageRank algorithm uses an iterative approach where:\n- M is the transition matrix.\n- v is the ranking vector.\n- The process continues until convergence.\n- Final values represent the relative importance of each node in the graph.\n\n---\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frobcyberlab%2Fpage-rank-algorithm","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Frobcyberlab%2Fpage-rank-algorithm","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frobcyberlab%2Fpage-rank-algorithm/lists"}