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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 l.jpg

Graph Algebra I: An Introduction

Courtney Brown, Ph.D.

Emory University


The origin of graph algebra l.jpg
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.


Rule 1 things on the same path get multiplied l.jpg
Rule #1: Things on the same path get multiplied.

pC(t) = V(t), where p is a parameter of proportional transformation.


Rule 2 things that meet at an intersection get added l.jpg
Rule #2: Things that meet at an intersection get added.

C(t) + R(t) = V(t)

C(t)

+

V(t)

R(t)




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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)]


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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.


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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.


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The Keynesian Multiplier

  • Economic outputt = Investmentt[1/(1-c)]


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