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Graph Algebra I: An Introduction

Graph Algebra I: An Introduction. Courtney Brown, Ph.D. Emory University. The Origin of Graph Algebra. The language of graph algebra was derived from the engineering literature, and was developed by Fernando Cort é s, Adam Przeworski, and John Sprague.

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Graph Algebra I: An Introduction

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  1. Graph Algebra I: An Introduction Courtney Brown, Ph.D. Emory University

  2. The Origin of Graph Algebra • The language of graph algebra was derived from the engineering literature, and was developed by Fernando Cortés, Adam Przeworski, and John Sprague. • See Systems Analysis for Social Scientists, by F. Cortés, A. Przeworski, and J. Sprague. 1974. New York: John Wiley & Sons.

  3. Rule #1: Things on the same path get multiplied. pC(t) = V(t), where p is a parameter of proportional transformation.

  4. Rule #2: Things that meet at an intersection get added. C(t) + R(t) = V(t) C(t) + V(t) R(t)

  5. Linear Regression Model Using Graph Algebra

  6. Overview of Graph Algebra Rules #1 and #2

  7. Positive Feedback Loop • The Xs are states of the system. • X1 = Input + X3; X2 = pX1; X3 = mX2. • Since Output=X2, substitution yields • Output = p(Input + mOutput), or re-arranging • Output = Input[p/(1 – pm)]

  8. Mason’s Rule • This derives Mason’s Rule. • The function of a single feedback loop is Forward Path/[1 – (Forward Path)(Feedback Path)] • This gets multiplied by the Input to equal the Output.

  9. Negative Feedback Loop • From Mason’s Rule, Output = Input[p/(1+pm)] • Note the positive sign in the denominator. This is because of the sign of –m.

  10. The Keynesian Multiplier • Economic outputt = Investmentt[1/(1-c)]

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