On Treewidth of Social Networks

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Liaee, Mehraneh | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43394 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Safari, Mohammad Ali; Habibi, Jafar
Abstract:
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)
Keywords:
Lower Bound ; Social Networks ; Tree Width ; Barabasi-Albert Model ; The Second Smallest Eigenvalue of Laplacian Matrix