# adjacency matrix

Published articles for adjacency matrix.

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## A Spectral Analysis of Moore Graphs

DevFeed: [A Spectral Analysis of Moore Graphs](<https://devfeed.tech/articles/a-spectral-analysis-of-moore-graphs-40406.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2016/11/03/a-spectral-analysis-of-moore-graphs/>)

Published: 2016-11-03T08:00:14Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [adjacency-matrix](<https://devfeed.tech/tags/adjacency-matrix.md>), [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [graph](<https://devfeed.tech/tags/graph.md>), [graphs](<https://devfeed.tech/tags/graphs.md>), [math](<https://devfeed.tech/tags/math.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [moore-graph](<https://devfeed.tech/tags/moore-graph.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [regular](<https://devfeed.tech/tags/regular.md>), [spectral-graph-theory](<https://devfeed.tech/tags/spectral-graph-theory.md>), [trace](<https://devfeed.tech/tags/trace.md>), [vertex](<https://devfeed.tech/tags/vertex.md>)

### AI overview

This mathematical article analyzes Moore graphs of girth 5 using the eigenvalues of their adjacency matrices. It derives the minimum vertex count and shows that the degree must be one of 3, 7, or 57.

### Source excerpt

For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$.

## Linear Algebra--A Primer

DevFeed: [Linear Algebra--A Primer](<https://devfeed.tech/articles/linear-algebra-a-primer-40204.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/06/19/linear-algebra-a-primer/>)

Published: 2011-06-19T18:39:40Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Matrix](<https://devfeed.tech/topics/matrix-org.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [adjacency-matrix](<https://devfeed.tech/tags/adjacency-matrix.md>), [algebra](<https://devfeed.tech/tags/algebra.md>), [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [eigenvectors](<https://devfeed.tech/tags/eigenvectors.md>), [graph](<https://devfeed.tech/tags/graph.md>), [history](<https://devfeed.tech/tags/history.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-independence](<https://devfeed.tech/tags/linear-independence.md>), [linear-maps](<https://devfeed.tech/tags/linear-maps.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrices](<https://devfeed.tech/tags/matrices.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [primer](<https://devfeed.tech/tags/primer.md>), [transformation](<https://devfeed.tech/tags/transformation.md>), [vector](<https://devfeed.tech/tags/vector.md>), [vector-spaces](<https://devfeed.tech/tags/vector-spaces.md>)

### AI overview

This primer introduces linear algebra through its historical origins in solving systems of linear equations. It explains determinants, matrices, vector algebra, and linear transformations, and shows how matrices can model graphs and compute path counts.

### Source excerpt

Story Time Linear algebra was founded around the same time as Calculus (think Leibniz, circa 1700) solely for the purpose of solving general systems of linear equations. The coefficients of a system were written in a grid form, with rows corresponding to equations and columns to the unknown variables. Using a computational tool called the determinant (an awkward, but computable formula involving only the coefficients of the equations in a system), researchers were able to solve these systems, opening a world of information about the positions of celestial bodies and large-scale measurements (of geodesic arcs) on the surface of the earth.