Kirchhoff Graphs
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Joseph D. Fehribach
About this book
Kirchhoff graphs are a new type of graph, one whose edges are vectors. They depict the dependencies in sets of vectors, and in this regard, they are akin to matroids. Indeed every binary matroid is Kirchhoff graphic. If the vectors in the set represent the stoichiometry of a reaction network (chemical, electrochemical or otherwise), a Kirchhoff graph is a circuit diagram for that reaction network. This book discusses the basic definitions for Kirchhoff graphs, their connections to matroids and finite fields, their connections to reaction networks and use as circuit diagrams, Kirchhoff graph uniformity, prime, composite and fundamental Kirchhoff graphs, and the structure of families of Kirchhoff graphs. They been studied by the author and his collaborators since 2005, and this book presents what we have learned in the past twenty years.
- Provides a comprehensive introduction to Kirchhoff graphs
- Discusses the application of Kirchhoff Graphs to Reaction Networks and beyond.
- Explains how the Kirchhoff laws' duality relates to the row space and null space duality of a matrix.
Author / Editor information
Topics
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Frontmatter
I -
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Dedication
V -
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Foreword
VII -
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Notes to the reader
IX -
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Contents
XI -
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1 Introduction
1 -
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2 Basic results
24 -
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3 Kirchhoff graph uniformity
41 -
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4 Kirchhoff graph construction
50 -
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5 Matroids and Kirchhoff graphs over finite fields
76 -
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6 Equitable Kirchhoff graphs
93 -
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7 Kirchhoff graph duality and Maxwell reciprocal diagrams
109 -
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8 Kirchhoff graphs and reaction networks
133 -
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Bibliography
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Index
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