Kirchhoff Graphs – Joseph D Fehribach

The algorithm and the original version of this code was developed by Gietzmann-Sanders [→12] (2017) as a part of his MQP (senior thesis) under the supervision of the author. It was later refined by Venkatraman Varatharajan as a summer undergraduate research project. The current version of this code can be found on GitHub: →https://github.com/vaakash1/kirky The Python package in the GitHub repository provides users with a Kirchhoff object that can be used to find and investigate Kirchhoff graphs and with a drawing function to produce images.

The README file and examples in the repository provide an overview of how to install and use the code, but some of these refer to an earlier version of the code. An example here may be helpful. Example 4.5. Consider the row matrix of the form R = [qI|C]: Notice that here q = 1. Constructing a Kirchhoff graph by hand for this row matrix would be at best time consuming, but our linear programming code can find a Kirchhoff graph for it with little difficulty.

Once the code is downloaded from the repository, kirky can be installed using python setup.py install from a command line inside the kirky directory. Then kirky will attempt to find and draw a Kirchhoff graph corresponding to the row matrix R in (→4.7) when the following lines are entered in Python: from kirky import Kirchhoff from kirky.block_q import * from kirky.imagine import draw_graph, draw3d import numpy as np matrix = np.array([[2,1,1], [1,2,1], [1,1,2]]) k = Kirchhoff(matrix,q=1) k.draw_solution(np.array([1, 0, 0.707]), np.array([0, 1, 0.707])) Notice that kirky expects the integer values from the coefficient block C given as matrix and the integer value of q given in the line following the definition of matrix.

These entries must be integers because our solutions must be computed using exact arithmetic.

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de.

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

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