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Updating Authority and Hub Scores: A Simple Example of Iterative Calculation

This document provides a detailed example of how to update authority and hub scores in a network using the HITS algorithm. It demonstrates the calculation across multiple iterations, showcasing how the authority scores are influenced by incoming edges and the cumulative effects of previous iterations. Key metrics such as the sum of squares and final convergence rates are highlighted. This example serves as a foundational demonstration of the concept and practical implementations of the algorithm within graph theory.

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Updating Authority and Hub Scores: A Simple Example of Iterative Calculation

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  1. A Simple Example Update Authority Scores first 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  2. A Simple Example Update Authority Scores first, using Hub scores One incoming edge 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  3. A Simple Example Update Authority Scores first 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  4. A Simple Example Update Authority Scores first 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  5. A Simple Example Update Authority Scores first Three incoming edges 1.000 3.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  6. A Simple Example Update Authority Scores first One incoming edge 1.000 3.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  7. A Simple Example Update Authority Scores first 1.000 3.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  8. A Simple Example Update Authority Scores first 1.000 3.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub

  9. A Simple Example Update Authority Scores first 1.000 3.000 1.000 1.000 1.000 1.000 1.000 1.000 Auth 1.000 1.000 Key: Hub No Incoming Edges

  10. A Simple Example Update Authority Scores first 1.000 3.000 1.000 1.000 1.000 1.000 0.000 1.000 Auth 1.000 1.000 Key: Hub

  11. A Simple Example Update Authority Scores first 1.000 3.000 1.000 1.000 1.000 1.000 0.000 1.000 Auth 1.000 1.000 Key: Hub Two incoming edges

  12. A Simple Example Update Authority Scores first 1.000 3.000 1.000 1.000 1.000 1.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  13. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 1.000 1.000 1.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  14. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 1.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  15. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 1.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  16. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 1.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  17. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 1.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  18. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 2.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  19. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 2.000 0.000 2.000 Auth 1.000 1.000 Key: Hub

  20. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 2.000 0.000 2.000 Auth 6.000 1.000 Key: Hub

  21. A Simple Example Update Hub Scores using new Authority Scores 1.000 3.000 1.000 3.000 1.000 2.000 0.000 2.000 Auth 6.000 1.000 Key: Hub

  22. A Simple Example 1.000 3.000 1.000 3.000 1.000 2.000 0.000 2.000 Auth 6.000 3.000 Key: Hub

  23. A Simple Example 1.000 3.000 1.000 3.000 1.000 2.000 0.000 2.000 Auth 6.000 3.000 Key: Hub Sum of Squares: 15.000

  24. A Simple Example 0.258 0.775 0.258 3.000 1.000 2.000 0.000 0.516 Auth 6.000 3.000 Key: Hub Divide By: 3.873 (sqrt(15))

  25. A Simple Example 0.258 0.775 0.258 3.000 1.000 2.000 0.000 0.516 Auth 6.000 3.000 Key: Hub Sum of Squares: 59

  26. A Simple Example 0.258 0.775 0.258 0.391 0.130 0.260 0.000 0.516 Auth 0.781 0.391 Key: Hub Divide By: 7.681 (sqrt(59))

  27. A Simple Example 0.258 0.775 0.258 0.391 0.130 0.260 0.000 0.516 Auth 0.781 0.391 Key: Hub After First Iteration

  28. A Simple Example 0.383 0.767 0.064 0.374 0.031 0.249 0.000 0.511 Auth 0.811 0.374 Key: Hub After Second Iteration

  29. A Simple Example 0.395 0.760 0.015 0.370 0.007 0.252 0.000 0.517 Auth 0.814 0.370 Key: Hub After Third Iteration

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