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Graph Algebra
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Graph Algebra
Mathematical Modeling With a Systems Approach



September 2007 | 104 pages | SAGE Publications, Inc
Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modelling that offers social scientists a variety of tools that are both sophisticated and easily applied.
 
Series Editor's Introduction
 
Acknowledgments
 
1. Systems Analysis
Structure and Function

 
An Overview of the Substantive Examples Found in Subsequent Chapters

 
 
2. Graph Algebra Basics
Inputs, Outputs, and the Forward Path

 
Feedback Loops and Mason's Rule

 
An Example From Economics: The Keynesian Multiplier

 
 
3. Graph Algebra and Discrete-Time Linear Operators
Delay and Advance Operators for Discrete Time

 
Including an Additive Constant With Graph Algebra

 
Difference and Summation Operators for Discrete Time

 
An Estimated Example: Labor Union Membership

 
 
4. Working With Systems of Equations
Richardson's Arms Race Model Using Graph Algebra

 
Variations of Richardson's Arms Race Model

 
An Estimated Example of a Multiple-Equation System With Nonlinear or Embedded Parameters: Richardson's Arms Race

 
 
5. Applying Graph Algebra to Continuous Time
Using Graph Algebra With Continuous-Time Operators

 
 
6. Graph Algebra and Nonlinearity
Nonlinear Filters

 
The Logistic Function

 
Placement Rules for Operators in Nonlinear Models

 
Graph Algebra and Chaos

 
Forced Oscillators

 
 
7. Working With Conditional Paths
Logical and Decision Systems

 
An Example of Democratic Transition

 
 
8. Systems, Shocks, and Stochasticity
 
9. Graph Algebra and Social Theory
Systems and Equilibria

 
 
References
 
Index
 
About the Author

"Brown is well known for research on mathematical modeling in the social sciences.  His book introduces the graph algebra approach to modeling systems in the social sciences."

—CHOICE

B. Borchers
New Mexico Institute of Mining and Technology
CHOICE

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