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Modeling and predicting cascading removal phenomenon over social networks

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Abstract

Innovations, opinions, ideas, recommendations or tendencies emerge in a variety of social networks. They can either disappear quickly or propagate and create considerable impact on the network. Their disappearance may also spread from one node to another across the network creating cascading behavior. Cascading phenomenon is mainly analyzed either by identifying the most influential nodes according to their features in the network, detecting quickly the phenomenon or targeting a minimum set of nodes that could maximize the spread of influence or minimize the propagation of a rumor or an outbreak. The objective of the present work is to predict the nodes to be deleted in cascade following the disappearance of one or many nodes. The cascading removal phenomenon is imitated by three well-known influence maximization cascading models in addition to two variants of a new cascading strategy which sound more consistent with human intuition over cascading removals. The prediction is done for an individual iteration of the cascading models, with the ability to be projected over the entire course of cascades without any loss of generality. We compare the prediction accuracy over three real-life networks and five synthetically generated schemas that imitate real social networks.

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Notes

  1. A cut-point is a node whose removal from a graph disconnects it or, more generally, increases the number of components in the structure.

  2. The normalized value of a given feature is computed as follows: (V f – MIN f)/(MAX f – MIN f ), where V f is the value of one of the mentioned features.

  3. Parameter values are listed to help the reproducibility of the research.

  4. This attribute can be also justified by increasing the number of training data.

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Acknowledgments

This study has been financially supported by the natural sciences and engineering research council of Canada (NSERC) research grant. The authors would like to thank the reviewers for their comments that help improve the manuscript.

Author information

Authors and Affiliations

  1. Department of Computer Science, Université du Québec en Outaouais (UQO), Gatineau, QC, Canada

    Amir H. Razavi, Dyah Anggraini, Rokia Missaoui, Jean Vaillancourt & Mohamed Talbi

Authors
  1. Amir H. Razavi
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  2. Dyah Anggraini
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  3. Rokia Missaoui
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  4. Jean Vaillancourt
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  5. Mohamed Talbi
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Corresponding author

Correspondence to Dyah Anggraini.

Appendix A

Appendix A

List of 100 network features that have been engineered, calculated and used in this paper:

  1. 1.

    Average incoming weights before deletion.

  2. 2.

    Minimum incoming weights before deletion.

  3. 3.

    Maximum incoming weights before deletion.

  4. 4.

    Average outgoing weights before deletion.

  5. 5.

    Minimum outgoing weights before deletion.

  6. 6.

    Maximum outgoing weights before deletion.

  7. 7.

    PageRank of the node before deletion.

  8. 8.

    Transitivity of the node before deletion.

  9. 9.

    Indegree of the node before deletion.

  10. 10.

    Outdegree of the node before deletion.

  11. 11.

    Degree centrality before deletion.

  12. 12.

    Betweenness centrality of the node before deletion.

  13. 13.

    Closeness centrality of the node before deletion.

  14. 14.

    Eigenvalue of the node before deletion.

  15. 15.

    Coreness value of the node before deletion.

  16. 16.

    Hub value of the node before deletion.

  17. 17.

    Authority value of the node before deletion.

  18. 18.

    Eccentricity value of the node before deletion.

  19. 19.

    Number of community membership of a node before deletion.

  20. 20.

    Average size of community membership of a node before deletion.

  21. 21.

    Minimum size of community membership of a node before deletion.

  22. 22.

    Maximum size of community membership of a node before deletion.

  23. 23.

    If the node is a deleted one.

  24. 24.

    Number of neighbors of deleted nodes.

  25. 25.

    Average incoming weights of all neighbors of deleted nodes.

  26. 26.

    Minimum incoming weights of all neighbors of deleted nodes.

  27. 27.

    Maximum incoming weights of all neighbors of deleted nodes.

  28. 28.

    Average outgoing weights of all neighbors of deleted nodes.

  29. 29.

    Minimum outgoing weights of all neighbors of deleted nodes.

  30. 30.

    Maximum outgoing weights of all neighbors of deleted nodes.

  31. 31.

    Average PageRank of neighbors of deleted nodes.

  32. 32.

    Minimum PageRank of neighbors of deleted nodes.

  33. 33.

    Maximum PageRank of neighbors of deleted nodes.

  34. 34.

    Average transitivity of neighbors of deleted nodes.

  35. 35.

    Minimum transitivity of neighbors of deleted nodes.

  36. 36.

    Maximum transitivity of neighbors of deleted nodes.

  37. 37.

    Average degree of neighbors of deleted nodes.

  38. 38.

    Minimum degree of neighbors of deleted nodes.

  39. 39.

    Maximum degree of neighbors of deleted nodes.

  40. 40.

    Average degree centrality of the neighbors of deleted nodes.

  41. 41.

    Minimum degree centrality of the neighbors of deleted nodes.

  42. 42.

    Maximum degree centrality of the neighbors of deleted nodes.

  43. 43.

    Average betweenness centrality of the neighbors of deleted nodes.

  44. 44.

    Minimum betweenness centrality of the neighbors of deleted nodes.

  45. 45.

    Maximum betweenness centrality of the neighbors of deleted nodes.

  46. 46.

    Average closeness centrality of the neighbors of deleted nodes.

  47. 47.

    Minimum closeness centrality of the neighbors of deleted nodes.

  48. 48.

    Maximum closeness centrality of the neighbors of deleted nodes.

  49. 49.

    Average eigenvalues of the neighbors of deleted nodes.

  50. 50.

    Minimum eigenvalues of the neighbors of deleted nodes.

  51. 51.

    Maximum eigenvalues of the neighbors of deleted nodes.

  52. 52.

    Average coreness values of the neighbors of deleted nodes.

  53. 53.

    Minimum coreness values of the neighbors of deleted nodes.

  54. 54.

    Maximum coreness values of the neighbors of deleted nodes.

  55. 55.

    Average hub values of the neighbors of deleted nodes.

  56. 56.

    Minimum hub values of the neighbors of deleted nodes.

  57. 57.

    Maximum hub values of the neighbors of deleted nodes.

  58. 58.

    Average authority values of the neighbors of deleted nodes.

  59. 59.

    Minimum authority values of the neighbors of deleted nodes.

  60. 60.

    Maximum authority values of the neighbors of deleted nodes.

  61. 61.

    Average eccentricity values of the neighbors of deleted nodes.

  62. 62.

    Minimum eccentricity values of the neighbors of deleted nodes.

  63. 63.

    Maximum eccentricity values of the neighbors of deleted nodes.

  64. 64.

    Average number of common neighbors among the neighbors of deleted nodes.

  65. 65.

    Minimum number of common neighbors among the neighbors of deleted nodes.

  66. 66.

    Maximum number of common neighbors among the neighbors of deleted nodes.

  67. 67.

    Average number of common communities with the neighbors of deleted nodes.

  68. 68.

    Minimum number of common communities with the neighbors of deleted nodes.

  69. 69.

    Maximum number of common communities with the neighbors of deleted nodes.

  70. 70.

    Average size of common communities with the neighbors of deleted nodes.

  71. 71.

    Minimum size of common communities with the neighbors of deleted nodes.

  72. 72.

    Maximum size of common communities with the neighbors of deleted nodes.

  73. 73.

    Average incoming similarity with the neighbors of deleted nodes.

  74. 74.

    Minimum incoming similarity with the neighbors of deleted nodes.

  75. 75.

    Maximum incoming similarity with the neighbors of deleted nodes.

  76. 76.

    Average outgoing similarity with the neighbors of deleted nodes.

  77. 77.

    Minimum outgoing similarity with the neighbors of deleted nodes.

  78. 78.

    Maximum outgoing similarity with the neighbors of deleted nodes.

  79. 79.

    Average incoming weights after deletion.

  80. 80.

    Minimum incoming weights after deletion.

  81. 81.

    Maximum incoming weights after deletion.

  82. 82.

    Average outgoing weights after deletion.

  83. 83.

    Minimum outgoing weights after deletion.

  84. 84.

    Maximum outgoing weights after deletion.

  85. 85.

    PageRank of the node after deletion.

  86. 86.

    Transitivity of the node after deletion.

  87. 87.

    Indegree of the node after deletion.

  88. 88.

    Outdegree of the node after deletion.

  89. 89.

    Degree centrality after deletion.

  90. 90.

    Betweenness centrality of the node after deletion.

  91. 91.

    Closeness centrality of the node after deletion.

  92. 92.

    Eigenvalue of the node after deletion.

  93. 93.

    Coreness value of the node after deletion.

  94. 94.

    Hub value of the node after deletion.

  95. 95.

    Authority value of the node after deletion.

  96. 96.

    Eccentricity value of the node after deletion.

  97. 97.

    Number of community membership of a node after deletion.

  98. 98.

    Average size of community membership of a node after deletion.

  99. 99.

    Minimum size of community membership of a node after deletion.

  100. 100.

    Maximum size of community membership of a node after deletion.

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Razavi, A.H., Anggraini, D., Missaoui, R. et al. Modeling and predicting cascading removal phenomenon over social networks. Soc. Netw. Anal. Min. 4, 233 (2014). https://doi.org/10.1007/s13278-014-0233-1

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  • DOI: https://doi.org/10.1007/s13278-014-0233-1

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