Graph Algebra I: An Introduction

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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

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 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.

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

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