Graph Algebra

Courtney Brown - Emory University, USA

Volume: 151

Series:
Quantitative Applications in the Social Sciences

July 2007 | 104 pages | SAGE Publications, Inc

"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

Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied.

Key Features:

Designed for readers in the social sciences with minimal mathematical training: In this volume, the author assists readers in developing their own difference and differential equation model specifications
Incorporates Social Theory: This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated algebraic statements of social and political phenomena. Graph algebra can be used to algebraically "flesh-out" even the most complicated and sophisticated of theories.
Contains social science examples of graph algebra models: Social science readers can see many examples of how graph algebra can be used to model theories from a wide variety of substantive areas and disciplines. The book also describes how to estimate such models, and two examples are fully worked out.
Explains linear and nonlinear model specifications using graph algebra from a social science perspective: Readers can move beyond simple linear regression models by using graph algebra.

This text is ideal for use in graduate courses such as Statistical Modeling, Quantitative Methods, and Applied Mathematics.

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Available Formats

ISBN: 9781412941099	Paperback	Suggested Retail Price: $46.00	Bookstore Price: $36.80
ISBN: 9781452213361	Electronic Version	Suggested Retail Price: $38.00	Bookstore Price: $30.40

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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

Key features

This text is geared towards readers in the social sciences with minimal mathematical training.
In this volume, the author assists readers in developing their own difference and differential equation model specifications
Social Theory: This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated algebraic statements of social and political phenomena. Graph algebra can be used to algebraically "flesh-out" even the most complicated and sophisticated of theories.
Social science examples of graph algebra models: Social science readers can see many examples of how graph algebra can be used to model theories from a wide variety of substantive areas and disciplines. The book also describes how to estimate such models, and two examples are fully worked out.
Linear and nonlinear model specifications using graph algebra are explained from a social science perspective: Readers can move beyond simple linear regression models by using graph algebra.