Algorithms and Models for the Web Graph - Info and Reading Options

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Intro -- Preface -- Organization -- Contents -- Correcting for Granularity Bias in Modularity-Based Community Detection Methods -- 1 Introduction -- 2 Hyperspherical Geometry -- 3 The Heuristic -- 4 Derivation of the Heuristic -- 5 Experiments -- 6 Discussion -- References -- The Emergence of a Giant Component in One-Dimensional Inhomogeneous Networks with Long-Range Effects -- 1 Introduction and Statement of Result -- 1.1 The Weight-Dependent Random Connection Model -- 1.2 Main Result -- 1.3 Examples -- 2 Proof of the Main Theorem -- 2.1 Some Construction and Notation -- 2.2 Connecting Far Apart Vertex Sets -- 2.3 Existence of a Giant Component -- 2.4 Absence of an Infinite Component -- References -- Unsupervised Framework for Evaluating Structural Node Embeddings of Graphs -- 1 Introduction -- 2 Framework -- 2.1 Input/Output -- 2.2 Formal Description of the Algorithm -- 2.3 Properties -- 3 Experimentation -- 3.1 Synthetic Graphs Design -- 3.2 Algorithmic Properties of the Framework -- 3.3 Role Classification Case Study -- 4 Conclusion -- References -- Modularity Based Community Detection in Hypergraphs -- 1 Introduction -- 2 Modularity Functions -- 3 Hypergraph Modularity Optimization Algorithm -- 3.1 Louvain Algorithm -- 3.2 Challenges with Adjusting the Algorithm to Hypergraphs -- 3.3 Our Approach to Hypergraph Modularity Optimization: h-Louvain -- 4 Results -- 4.1 Synthetic Hypergraph Model: h-ABCD -- 4.2 Exhaustive Search for the Best Strategy -- 4.3 Comparing Basic Policies for Different Modularity Functions -- 5 Conclusions -- References -- Establishing Herd Immunity is Hard Even in Simple Geometric Networks -- 1 Introduction -- 2 Preliminaries -- 3 Unanimous Thresholds -- 4 Constant Thresholds -- 5 Majority Thresholds -- 6 Conclusions -- References -- Multilayer Hypergraph Clustering Using the Aggregate Similarity Matrix

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