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Volume 152007
Metagraphs and Their ApplicationsAuthors:
- Amit Basu,
- Robert W. Blanning
- …show all 2hide
ISBN: 978-0-387-37233-4 (Print) 978-0-387-37234-1 (Online)
Metagraphs and Their ApplicationsSeries: Integrated Series in Information Systems, Vol. 15
Basu, Amit, Blanning, Robert W.
2007, VIII, 172 p.
ISBN 978-0-387-37234-1
Immediately available per PDF-download (no DRM, watermarked)
About this book
The graph is a critical and useful concept in designing many information processing systems. Systems such as transaction processing systems, decision support systems, and workflow systems are all helped immensely by a graphical structure. Simple graphs and digraphs allow for the construction of a variety of system design tools that provide a convenient and appealing format for illustrating information infrastructures, while allowing any subsequent analyses to be performed by the user. However, the metagraph, a new graphical structure that is developed in this book, goes beyond the representational and provides Information Systems with a robust, analytical modeling graphic tool.
METAGRAPHS AND THEIR APPLICATIONS is a presentation of metagraph theory and its applications that begins by defining a metagraph and its uses. They are more complex than a simple graph structure, but they allow for representation and analysis of more complex systems. The material contained in this book is presented in two parts. The first develops the theoretical results with the emphasis on the development of a metagraph algebra. In the second part of the book, four promising applications of metagraphs are examined: 1) modeling of data relations, 2) the modeling of decision models, 3) the modeling of decision rules, and 4) the modeling of workflow tasks. Hence, the theoretical results in the initial chapters lay the foundation for the application areas in the second part of the book.
The book concludes by examining several possible extensions of this work. Of special interest is the structuring of the metagraphs modeling process, which may enhance the body of work on systems analysis and design (including software engineering), the development of a metagraphs workbench to support such a process, and the possible application of the results presented here, suitably enhanced, to social networks.
CONTENTS
Preface vii
Chapter 1: Graphs, Hypergraphs, and Metagraphs 1
1. Graphs and Data Visualization 1
2. Graph Structures 4
3. Metagraph Theory (Part I) 9
4. Applications of Metagraphs (Part II) 11
Part I. Metagraph Theory 13
Chapter 2: The Algebraic Structure of Metagraphs 15
1. Formal Representation of a Metagraph 15
2. The Incidence and Adjacency Matrices 17
3. Identifying Metapaths 23
Chapter 3: Connectivity Properties of Metagraphs 27
1. Dominant Metapaths 27
2. Cutsets and Bridges 29
Chapter 4: Metagraph Transformations 33
1. Hierarchical Abstraction Using Projection 33
2. The Inverse Metagraph 46
3. The Element Flow Metagraph 48
Chapter 5: Attributed Metagraphs 53
1. Qualitative Attributes 53
2. Quantitative Attributes 55
3. Conditional Metagraphs 55
3.1. Projections in Conditional Metagraphs 58
3.2. Connectivity and Redundancy 61
Chapter 6: Independent Sub-Metagraphs 65
Part II. Applications of Metagraphs 69
Chapter 7: Metagraphs in Model Management 71
1. Models as Metagraphs 72
2. Model Selection and Integration 74
vi Contents
3. Hierarchical Modeling 76
4. Assumptions in Model Bases 86
Chapter 8: Metagraphs in Data and Rule Management 97
1. Representing Rule Bases as Metagraphs 99
2. Integrating Rules, Models and Data 105
3. Discovering Implicit Integrity Constraints 111
4. Metagraph Models of Decision Support Systems 115
Chapter 9: Metagraphs in Workflow and Process Analysis 117
1. Representing Workflows and Processes with Metagraphs 118
2. Views of Workflows 123
3. Analysis of Information Interactions 128
4. Analysis of Task Interactions 131
5. Analysis of Resource Interactions 133
6. Interactions among Different Types of Components 136
7. Synthesis of Processes 137
8. Decomposition of Processes and Implications for Organizational Design 143
9. Representing Time-Critical Workflows with Attributed Metagraphs 146
Chapter 10: Conclusion 153
1. The Metagraph Modeling Process 153
2. Towards a Metagraph Workbench 156
3. Metagraphs and Social Networks 158
4. And Finally 160
References 161
Index of Definitions 165
Index 167
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