Spectral graph theory examines the structural and dynamical properties of graphs by analysing the spectra of associated matrices such as the adjacency matrix, Laplacian, normalised Laplacian and ...

Abstract: Spectral graph theory is the study of the eigenvalues and eigenvectors of matrices associated with graphs. In this tutorial, we will try to provide some intuition as to why these ...

Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They ...

During the 18th century the denizens of the Prussian city of Königsberg wrestled with a puzzle: How could they find a walking path through the city that crossed each of its storied seven bridges ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

Abstract: Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ...

Crystal structures have a decisive impact on the properties of materials, and research on crystal structures often serves as a starting point for material studies. Crystal structure prediction is a ...