Managing and Mining Graph Data

Transcription

1 Managing and Mining Graph Data by Charu C. Aggarwal IBM T.J. Watson Research Center Hawthorne, NY, USA Haixun Wang Microsoft Research Asia Beijing, China <ÖSp nneer

2 Contents List of Figures List of Tables Preface 1 An Introduction to Graph Data Charit С. Aggarwal and Haixun Wang 1. Introduction 2. Graph Management and Mining Applications 3. Summary References 2 Graph Data Management and Mining: A Survey of Algorithmsand Cham C. Aggarwal and Haixun Wang 1. Introduction 2. Graph Data Management Algorithms 2.1 Indexing and Query Processing Techniques 2.2 Reachability Queries 2.3 Graph Matching 2.4 Keyword Search 2.5 Synopsis Construction of Massive Graphs 3. Graph Mining Algorithms 3.1 Pattern Mining in Graphs 3.2 Clustering Algorithms for Graph Data 3.3 Classification Algorithms for Graph Data 3.4 The Dynamics of Time-Evolving Graphs 4. Graph Applications 4.1 Chemical and Biological Applications 4.2 Web Applications 4.3 Software Bug Localization 5. Conclusions and Future Research References 3 Graph Mining: Laws and Generators Deepaxan Chakrabarti, Christos Faloiitsos and Mary McGlohon 1. Introduction 2. Graph Patterns

3 VI MANAGING AND MINING GRAPH DATA 2.1 Power Laws and Heavy-Tailed Distributions Small Diameters Other Static Graph Patterns Patterns in Evolving Graphs The Structure of Specific Graphs Graph Generators Random Graph Models Preferential Attachment and Variants Optimization-based generators Tensor-based Generators for specific graphs Graph Generators: A summary Conclusions 115 References Query Language and Access Methods for Graph Databases 125 Hiiahai He and Ambuj K. Singh 1. Introduction Graphs-at-a-time Queries Graph Specific Optimizations GraphQL Operations on Graph Structures Concatenation Disjunction Repetition Graph Query Language Data Model Graph Patterns Graph Algebra FLWR Expressions Expressive Power Implementation of the Selection Operator Graph Pattern Matching Local Pruning and Retrieval of Feasible Mates Joint Reduction of Search Space Optimization of Search Order Experimental Study Biological Network Synthetic Graphs Related Work Graph Query Languages Graph Indexing Future Research Directions Conclusion 156 Appendix: Query Syntax of GraphQL 156 References Graph Indexing 161 Xifeng Yan and Jiawei Han 1. Introduction 161

4 Contents VII 2. Feature-Based Graph Index Paths Frequent Structures Discriminative Structures Closed Frequent Structures Trees Hierarchical Indexing Structure Similarity Search Feature-Based Structural Filtering Feature Miss Estimation Frequency Difference Feature Set Selection Structures with Gaps Reverse Substructure Search Conclusions 177 References Graph Reachability Queries: A Survey 181 Jeffrey Xu Yu and Jiefeng Cheng 1. Introduction Traversal Approaches Tree+SSPI GRIPP Dual-Labeling Tree Cover Chain Cover Computing the Optimal Chain Cover Path-Tree Cover HOP Cover A Heuristic Ranking A Geometrical-Based Approach Graph Partitioning Approaches Hop Cover Maintenance Hop Cover Distance-Aware 2-Hop Cover Graph Pattern Matching A Special Case: A^D The General Cases Conclusions and Summary 212 References Exact and Inexact Graph Matching: Methodology and Applications 217 Kaspar Riesen, Xiaoyi Jiang and Horst Blinke 1. Introduction Basic Notations Exact Graph Matching Inexact Graph Matching Graph Edit Distance Other Inexact Graph Matching Techniques Graph Matching for Data Mining and Information Retrieval 231

5 Vlll MANAGING AND MINING GRAPH DATA 6. Vector Space Embeddings of Graphs via Graph Matching Conclusions 239 References A Survey of Algorithms for Keyword Search on Graph Data 249 Hai.xun Wang and Cham С Aggarwal 1. Introduction Keyword Search on XML Data Query Semantics Answer Ranking Algorithms for LCA-based Keyword Search Keyword Search on Relational Data Query Semantics DBXplorer and DISCOVER Keyword Search on Schema-Free Graphs Query Semantics and Answer Ranking Graph Exploration by Backward Search Graph Exploration by Bidirectional Search Index-based Graph Exploration - the BLINKS Algorithm The ObjectRank Algorithm Conclusions and Future Research 271 References A Survey of Clustering Algorithms for Graph Data 275 Cham С Aggarwal and Haixun Wang 1. Introduction Node Clustering Algorithms The Minimum Cut Problem Multi-way Graph Partitioning Conventional Generalizations and Network Structure Indices The Girvan-Newman Algorithm The Spectral Clustering Method Determining Quasi-Cliques The Case of Massive Graphs Clustering Graphs as Objects Extending Classical Algorithms to Structural Data The XProj Approach Applications of Graph Clustering Algorithms Community Detection in Web Applications and Social Networks Telecommunication Networks Analysis Conclusions and Future Research 297 References A Survey of Algorithms for Dense Subgraph Discovery 303 Victor E. Lee. Ning Ruan, Ruoming Jin and Cham Aggarwal 1. Introduction 304

6 Contents ix 2. Types of Dense Components Absolute vs. Relative Density Graph Terminology Definitions of Dense Components Dense Component Selection Relationship between Clusters and Dense Components Algorithms for Detecting Dense Components in a Single Graph 31 I 3.1 Exact Enumeration Approach Heuristic Approach Exact and Approximation Algorithms for Discovering Densest Components Frequent Dense Components Frequent Patterns with Density Constraints Dense Components with Frequency Constraint Enumerating Cross-Graph Quasi-Cliques Applications of Dense Component Analysis Conclusions and Future Research 331 References Graph Classification 337 Koji Tsuda and Hiroto Saigo 1. Introduction Graph Kernels Random Walks on Graphs Label Sequence Kernel Efficient Computation of Label Sequence Kernels Extensions Graph Boosting Formulation of Graph Boosting Optimal Pattern Search Computational Experiments Related Work Applications of Graph Classification Label Propagation Concluding Remarks 359 References Mining Graph Patterns 365 Hong Cheng, Xifeng Yan and Jiawei Han 1. Introduction Frequent Subgraph Mining Problem Definition Apriori-based Approach Pattern-Growth Approach Closed and Maximal Subgraphs Mining Subgraphs in a Single Graph The Computational Bottleneck Mining Significant Graph Patterns Problem Definition gboost: A Branch-and-Bound Approach 373

7 X MANAGING AND MINING GRAPH DATA 3.3 gpls: A Partial Least Squares Regression Approach LEAP: A Structural Leap Search Approach GraphSig: A Feature Representation Approach Mining Representative Orthogonal Graphs Problem Definition Randomized Maximal Subgraph Mining Orthogonal Representative Set Generation Conclusions 389 References A Survey on Streaming Algorithms for Massive Graphs 393 Jian Zhang 1. Introduction Streaming Model for Massive Graphs Statistics and Counting Triangles Graph Matching Unweighted Matching Weighted Matching Graph Distance Distance Approximation using Multiple Passes Distance Approximation in One Pass Random Walks on Graphs Conclusions 416 References A Survey of Privacy-Preservation of Graphs and Social Networks 421 Xintao Wit. Xiaowei Ying, Kim Liu and Lei Chen 1. Introduction Privacy in Publishing Social Networks Background Knowledge Utility Preservation Anonymization Approaches Notations Privacy Attacks on Naive Anonymized Networks Active Attacks and Passive Attacks Structural Queries Other Attacks Л -Anonymity Privacy Preservation via Edge Modification Л-Degree Generalization Tv'-Neighborhood Anonymity Л'-Automorphism Anonymity Privacy Preservation via Randomization Resilience to Structural Attacks Link Disclosure Analysis Reconstruction Feature Preserving Randomization Privacy Preservation via Generalization Anonymixing Rich Graphs 441

8 Contents XI 6.1 Link Protection in Rich Graphs Anonymizing Bipartite Graphs Anonymizing Rich Interaction Graphs Anonymizing Edge-Weighted Graphs Other Privacy Issues in Online Social Networks Deriving Link Structure of the Entire Network Deriving Personal Identifying Information from Social Networking Sites Conclusion and Future Work 448 Acknowledgments 449 References A Survey of Graph Mining for Web Applications 455 Debora Donato and Aristides Gionis 1. Introduction Preliminaries 2.1 Link Analysis Ranking Algorithms Mining High-Quality Items Prediction of Successful Items in a Co-citation Network Finding High-Quality Content in Question-Answering Portals Mining Query Logs Description of Query Logs Query Log Graphs Query Recommendations Conclusions 480 References Graph Mining Applications to Social Network Analysis 487 Lei Tang and Huan Liu 1. Introduction Graph Patterns in Large-Scale Networks Scale-Free Networks Small-World Effect Community Structures Graph Generators Community Detection 3.1 Node-Centric Community Detection Group-Centric Community Detection Network-Centric Community Detection Hierarchy-Centric Community Detection Community Structure Evaluation Research Issues 507 References Software-Bug Localization with Graph Mining 515 Frank Eichinger and Klemens Behm 1. Introduction Basics of Call Graph Based Bug Localization 517

9 Xll MANAGING AND MINING GRAPH DATA Acknowledgments References 2.1 Dynamic Call Graphs 2.2 Bugs in Software 2.3 Bug Localization with Call Graphs 2.4 Graph and Tree Mining Related Work Call-Graph Reduction 4.1 Total Reduction Iterations Temporal Order Recursion Comparison Call Graph Based Bug Localization 5.1 Structural Approaches 5.2 Frequency-based Approach 5.3 Combined Approaches 5.4 Comparison Conclusions and Future Directions A Survey of Graph Mining Techniques for Biological Datasets 547 S. Parthasarathy, S. Tatikonda and D. Ucar 1. Introduction Mining Trees Frequent Subtree Mining Tree Alignment and Comparison Statistical Models Mining Graphs for the Discovery of Frequent Substructures Frequent Subgraph Mining Motif Discovery in Biological Networks Mining Graphs for the Discovery of Modules Extracting Communities Clustering Discussion 569 References Trends in Chemical Graph Data Mining 581 Nikil Wale, Xia Ning and George Karypis 1. Introduction Topological Descriptors for Chemical Compounds Hashed Fingerprints (FP) Maces Keys (MK) Extended Connectivity Fingerprints (ECFP) Frequent Subgraphs (FS) Bounded-Size Graph Fragments (GF) Comparison of Descriptors Classification Algorithms for Chemical Compounds Approaches based on Descriptors Approaches based on Graph Kernels Searching Compound Libraries 590

10 Contents xin Methods Based on Direct Similarity Methods Based on Indirect Similarity Performance oflndirect Similarity Methods Identifying Potential Targets for Compounds Model-based Methods For Target Fishing Performance of Target Fishing Strategies Future Research Directions 600 References 602 Index 607