Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
Papers published on a yearly basis
Papers
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18 Sep 2018TL;DR: Wagner and Wang as mentioned in this paper presented a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices, including distance-based, degree-based and counting-based indices.
Abstract: Introduction to Chemical Graph Theory is a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices. These include distance-based, degree-based, and counting-based indices. The book covers some of the most commonly used mathematical approaches in the subject. It is also written with the knowledge that chemical graph theory has many connections to different branches of graph theory (such as extremal graph theory, spectral graph theory).
The authors wrote the book in an appealing way that attracts people to chemical graph theory. In doing so, the book is an excellent playground and general reference text on the subject, especially for young mathematicians with a special interest in graph theory.
Key Features:
A concise introduction to topological indices of graph theory
Appealing to specialists and non-specialists alike
Provides many techniques from current research
About the Authors:
Stephan Wagner grew up in Graz (Austria), where he also received his PhD from Graz University of Technology in 2006. Shortly afterwards, he moved to South Africa, where he started his career at Stellenbosch University as a lecturer in January 2007. His research interests lie mostly in combinatorics and related areas, including connections to other scientific fields such as physics, chemistry and computer science.
Hua Wang received his PhD from University of South Carolina in 2005. He held a Visiting Research Assistant Professor position at University of Florida before joining Georgia Southern University in 2008. His research interests include combinatorics and graph theory, elementary number theory, and related problems
34 citations
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34 citations
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28 Jun 2015TL;DR: This work presents a robust cerebral cortex parcellation method based on spectral graph theory and resting-state fMRI correlations that generates reliable parcellations at the single-subject level and across multiple subjects and can be reliably used to represent the population in network analyses.
Abstract: Identification of functional connections within the human brain has gained a lot of attention due to its potential to reveal neural mechanisms. In a whole-brain connectivity analysis, a critical stage is the computation of a set of network nodes that can effectively represent cortical regions. To address this problem, we present a robust cerebral cortex parcellation method based on spectral graph theory and resting-state fMRI correlations that generates reliable parcellations at the single-subject level and across multiple subjects. Our method models the cortical surface in each hemisphere as a mesh graph represented in the spectral domain with its eigenvectors. We connect cortices of different subjects with each other based on the similarity of their connectivity profiles and construct a multi-layer graph, which effectively captures the fundamental properties of the whole group as well as preserves individual subject characteristics. Spectral decomposition of this joint graph is used to cluster each cortical vertex into a subregion in order to obtain whole-brain parcellations. Using rs-fMRI data collected from 40 healthy subjects, we show that our proposed algorithm computes highly reproducible parcellations across different groups of subjects and at varying levels of detail with an average Dice score of 0.78, achieving up to 9\(\%\) better reproducibility compared to existing approaches. We also report that our group-wise parcellations are functionally more consistent, thus, can be reliably used to represent the population in network analyses.
33 citations
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TL;DR: A novel technique for indexing multimedia databases in which entries can be represented as graph structures in which the topological structure of a graph as well as that of its subgraphs are represented as vectors whose components correspond to the sorted laplacian eigenvalues of the graph or sub graphs.
33 citations
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TL;DR: An upper bound on the spectral radius of the adjacency matrix of a graph is obtained and graphs for which the bound is attained are characterized.
33 citations