在這篇論文中，我們提出了一種具有隨機三元閉包的廣義網絡配置模型（簡稱GCTC）。該模型擁有5種基本網絡特性：大集聚係數，節點度呈現冪分佈，短路徑長度，非零點Pearson度相關係數和存在社區結構。我們分析推導了在特定条件下該模型的Pearson度相關係數和集聚係數的公式。我們選擇幾個真實世界網絡的資料集。我們用GCTC模型模擬真實網絡發現，在Pearson度相關係數和集聚係數這2種特性上，GCTC模型與真實網絡取值很接近。我們還選擇了3種著名的社區檢測演算法去對GCTC網絡、真實世界網絡和其他三個基準網絡模型進行社區檢測。結果發現，GCTC網絡在大多数情况下表现比其他三個基準網絡模型好。最後，我們使用獨立級聯模型和線性閾值模型在GCTC網絡上做影響力擴散模擬，我們發現GCTC模型在影響力擴散值上會比其他三種基準網絡模型更接近於真實世界網絡的取值。這些結果顯示，如果度相關係數和集聚係數對於網絡科學問題的解決起關鍵作用時，GCTC網絡模型會是一個研究此類問題的合適工具。

In this thesis we present a generalized configuration model with random triadic closure (GCTC). This model possesses five fundamental properties: large clustering coefficient, power law degree distribution, short path length, non-zero Pearson degree correlation, and existence of community structures. We analytically derive the Pearson degree correlation coefficient and the clustering coefficient of the proposed model. We select a few datasets of real-world networks. By simulation, we show that the GCTC model matches very well with the datasets in terms of Pearson degree correlations and clustering coefficients. We also test three well-known community detection algorithms on our model, the datasets and other three prevalent benchmark models. We show that the GCTC model performs equally well as the other three benchmark models. Finally, we perform influence diffusion on the GCTC model using the independent cascade model and the linear threshold model. We show that the influence spreads of the GCTC model are much closer to those of the datasets than the other benchmark models. This suggests that the GCTC model is a suitable tool to study network science problems where degree correlation or clustering plays an important role.

中 文摘 要 i
Abstract ii
Acknowledgements iii
List of Figures vi
List of Tables viii
1 Introduction 1
2 Construction Algorithm 6
3 Analyze the Pearson degree correlation Coeffi cient and the
Clustering Coeffi cient 11
3.1 Review of the Generalized Confi guration Model . . . . . 11
3.2 Pearson degree correlation Coeffi cient . . . . . . . . . . 16
3.3 Clustering Coeffi cient . . . . . . . . . . . . . . . . . . . 39
3.4 Numerical and Simulation Results . . . . . . . . . . . . 44
4 Real world applications of GCTC model 53
4.1 Modeling real-world networks . . . . . . . . . . . . . . 53
4.2 Community detection . . . . . . . . . . . . . . . . . . . 58
4.3 Infl uence diffusion . . . . . . . . . . . . . . . . . . . . 60
5 Conclusions 64
Bibliography 66

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