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1. Raymond A. Sorensen, “ The random walk method for dc circuit analysis,” Am. J. Phys. 58(11), 10561059 (1990).
2. David A. Giltinan, “ Multiloop dc circuits by source conversion and nodal analysis,” Am. J. Phys. 62(7), 645647 (1994).
3. D. A. Van Baak, “ Variational alternatives to Kirchhoff's loop theorem in dc circuits,” Am. J. Phys. 67(1), 3644 (1999).
4. Henry G. Booker, An Approach to Electrical Science ( McGraw-Hill, New York, 1959).
5. Gemunu H. Gunaratne, Preethi H. Gunaratne, Lars Seemann, and Andrei Török, “ Using effective subnetworks to predict selected properties of gene networks,” PLoS ONE 5(10), e13080 (2010).
6. Jason Shulman, Lars Seemann, and Gemunu H. Gunaratne, “ Effective models of periodically driven networks,” Biophys. J. 101(11), 25632571 (2011).
7. Jason Shulman, Lars Seemann, Gregg W. Roman, and Gemunu H. Gunaratne, “ Effective models for gene networks and their applications,” Biophys. Rev. Lett. 7, 4170 (2012).
8. Timothy S. Gardner, Diego di Bernardo, David Lorenz, and James J. Collins, “ Inferring genetic networks and identifying compound mode of action via expression profiling,” Science 301, 102105 (2003).
9. Jason Shulman, Alexander Mo, Killian Ryan, and Gemunu H. Gunaratne, “ Controlling nonlinear networks using response surfaces,” (unpublished).
10. Timothy S. Gardner and Jeremiah J. Faith, “ Reverse-engineering transcription control networks,” Phys. Life Rev. 2, 6588 (2005).
11. It should be noted that condition 1 is sufficient to produce an exact model of the network. Condition 2 is necessary to produce an exact and complete model. Without this condition, the effect of node 3 on nodes 1 and 2 would not be included. See Eqs. (2) for an example.
12. Marc Timme, “ Revealing network connectivity from response dynamics,” Phys. Rev. Lett. 98, 224101-14 (2007).
13.See supplementary material at (algorithm description and implementation in MATLAB).[Supplementary Material]
14. Anant Agarwal and Jeffrey Lang, Foundations of Analog and Digital Electronic Circuits ( Morgan Kaufmann, San Francisco, 2005).
15. The coefficient between the ith and jth nodes, Gij, is often called the mutual conductance between the two nodes.
16.This is rather obvious from Eq. (10) and its generalization; however, to the best of the authors' knowledge, the most recent mention of this fact is from a textbook published in 1966, and reiteration seems appropriate. The textbook is Charles Close, The Analysis of Linear Circuits ( Harcourt, Brace & World, New York, 1966).
17. The network approach can be used in alternating current circuits with nonlinear components as well. In such a case, the resulting equations will be approximations (see Sec. V B).
18.Simulations were performed with 5spice software, which can be found at <>.
19. Donald Johnson, “ Solution of linear algebraic equations by means of equivalent electrical circuits,” Masters thesis in Electrical Engineering ( University of Wisconsin–Madison, 1953).

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Kirchhoff's laws offer a general, straightforward approach to circuit analysis. Unfortunately, their application becomes impractical for all but the simplest of circuits. This work presents an alternative procedure, based on an approach developed to analyze complex networks, thus making it appropriate for use on large, complicated circuits. The procedure is unusual in that it is not an analytic method but is based on experiment. Yet, this approach produces the same circuit equations obtained by more traditional means.


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