Discovering structures in large networks.

• Other Authors: Wang, Jia.
• Format: Others
• Language: English; Chinese
• Published: 2013
• Subjects: System analysis > Mathematical models
• Online Access: http://library.cuhk.edu.hk/record=b5549279; http://repository.lib.cuhk.edu.hk/en/item/cuhk-328774

本論文討論了幾個重要的用於網絡分析的圖結構以及相闋的算法設計問題，並著重討論了其中的組合結構及其在大規模網絡中之計算問題。根據這些結構在網絡所處之層次，我們將它們分成局部結構和全局結構來分別討論。 === 對於在大規模網絡中的緊密子圖探測問題和極大完全子圖枚舉問題，本論文提出了新概念和新算法。其一，對於一種名為k-truss的新型緊密子圖，提出了更快的內存算法和適用於在大規模網絡中尋找此種子圖的方法。其二，針對於傳統完全子圖枚舉算法的輸出過大的問題，提出了用於緊湊表示圖中一切極大完全子圖的新方法。采用此種方法，我們能夠在保證重要信息得到保留的情況下，顯著地減小輸出的體積同時提高計算速度。 === This thesis discusses a number of important structures for network analysis and their algorithmic results. Special attentions are paid to combinatorial structures and related computation problems in large networks. According to the granularity of the concepts, we shall distinguish between local and global objects and present them separately. === New algorithms and concepts are proposed for interesting arising problems in cohesive subgraph detection and maximal clique enumeration (MCE). Specifically, algorithms for k-truss, a new type of cohesive subgraphs, are proposed including a fast in-memory algorithm and techniques that handle large disk-resident networks. Motivated by the sheer size of output by classic MCE algorithms, a novel notion for a low-redundancy representation of the set of all maximal cliques is proposed, which enables effective use of maximal cliques and a faster computation of the reduced output. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Wang, Jia. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. === Includes bibliographical references (leaves 58-62). === Abstracts also in Chinese. === Chapter 1 --- Introduction --- p.1 === Chapter 2 --- Preliminaries --- p.2 === Chapter 3 --- Global Structures --- p.3 === Chapter 3.1 --- Component Decomposition --- p.4 === Chapter 3.2 --- Structures with Hierarchy --- p.6 === Chapter 3.2.1 --- k-cores --- p.6 === Chapter 3.2.2 --- k-trusses --- p.8 === Chapter 3.3 --- Improved Truss Computation [45] --- p.10 === Chapter 3.3.1 --- Notations --- p.11 === Chapter 3.3.2 --- Faster In-Memory Algorithm --- p.11 === Chapter 3.3.3 --- Handling Massive Graphs --- p.16 === Chapter 3.3.4 --- Bottom-Up Approach --- p.17 === Chapter 3.3.5 --- Top-k Trusses --- p.23 === Chapter 3.3.6 --- Empirical Study --- p.28 === Chapter 3.4 --- Summary --- p.33 === Chapter 4 --- Local Structures --- p.33 === Chapter 4.1 --- Small Cycles and Clustering Coefficients --- p.33 === Chapter 4.2 --- Maximal Cliques --- p.36 === Chapter 4.3 --- Redundancy-Aware MCE [46] --- p.36 === Chapter 4.3.1 --- Motivations --- p.38 === Chapter 4.3.2 --- τ-visible MCE --- p.41 === Chapter 4.3.3 --- Applications --- p.50 === Chapter 4.3.4 --- Empirical Study --- p.52 === Chapter 4.4 --- Summary --- p.56 === Chapter 5 --- Structures in Mid-Zone --- p.56 === Chapter 5.1 --- Densest Subgraph --- p.56 === Chapter 5.2 --- Relaxed Cliques --- p.57 === Chapter 6 --- Concluding Remarks --- p.58