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On Treewidth of Social Networks

Liaee, Mehraneh | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43394 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Safari, Mohammad Ali; Habibi, Jafar
  7. Abstract:
  8. In this thesis, we study the treewidth of social networks. The importance of studding treewidth is for two reasons. The first is that for the graph with bounded treewidth, many optimization problems that are NP-hard in general, can be solved in polynomial or even linear time. The second is that the high value of treewidth in a graph, reflects some high degree of connectivity and robustness, which is an essential factor in designing many networks. But the problem is that determining the value of treewidth in a graph is NP-complete so, computing the treewidth of real complex networks is not feasible. We first review the related works and mention the weakness of the past works, then introduce a lower bound for treewidth that not only can be applied for models of social networks but also can be generalized to real complex networks. Because the lower bound is a function of the second smallest eigenvalue of Laplacian matrix (), by setting some experiments we show that in Barabasi-Albert random graph, which is a famous model for social networks, the value of is Ω(1) and finally using this result, we prove that the treewidth of these graphs is at least Ω(√n)
  9. Keywords:
  10. Lower Bound ; Social Networks ; Tree Width ; Barabasi-Albert Model ; The Second Smallest Eigenvalue of Laplacian Matrix

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  • مقدمه
  • شبکه‌های اجتماعی
    • مقدمه
    • ویژگی‌های ساختاری
      • پدیده‌ی جهان کوچک
      • تراکم یال‌ها
      • مقیاس آزاد
      • بستار سه‌تایی
      • ضریب خوشه‌بندی
      • مقاومت شبکه
    • مدل‌ها
      • گراف‌های تصادفی Missing left brace has been substituted= Erdős-Rényi
      • گراف‌های تصادفی Missing left brace has been substituted= Watts-Strogatz
      • گراف‌های تصادفی Missing left brace has been substituted= Barabási-Albert
  • عرض درختی و تجزیه‌ی ‌درختی
    • مقدمه
    • تعریف
      • تعاریف معادل
    • الگوریتم‌های دقیق و مکاشفه‌ای
    • الگوریتم‌های تقریبی
    • کران‌های پایین
  • کارهای مرتبط
    • کران پایین عرض درختی در گراف‌های تصادفی
    • عرض درختیِ گراف اینترنت
  • کارهای انجام شده و نتایج آن
    • رابطه‌ی عرض درختی با بسط رأسی گراف
    • بسط رأسی
    • مقدار ویژه‌ی دوم ماتریس لاپلاسی
  • جمع‌بندی و کارهای آینده
  • مراجع
    • گراف تصادفی هندسی
    • درجه‌ی اتصال گراف
    • ماتریس لاپلاسی گراف
...see more