Kolmogorov-barzdin and Spacial Realizations of Expander Graphs
نویسنده
چکیده
One application of graph theory is to analyze connectivity of neurons and axons in the brain. We begin with basic definitions from graph theory including the Cheeger constant, a measure of connectivity of a graph. In Section 2, we will examine expander graphs, which are very sparse yet highly connected. Surprisingly, not only do expander graphs exist, but most random graphs have the expander property. Section 3 discusses the KolmogorovBarzdin realization of graphs in a sphere in R3. This can be used to model neurons and axons in the brain and yields the smallest possible radius for the sphere for any graph with the expander property.
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