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.
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07 Sep 2022
TL;DR: In this paper , the authors provide an introductory review of some topics in spectral theory of Laplacians on metric graphs, focusing on three different aspects: the trace formula, the self-adjointness problem, and connections between L 1 and L 2.
Abstract: We provide an introductory review of some topics in spectral theory of Laplacians on metric graphs. We focus on three different aspects: the trace formula, the self-adjointness problem and connections between Laplacians on metric graphs and discrete graph Laplacians.
TL;DR: In this paper, the authors focus on the problem of creating graphs that balance high modularity and low mixing time, and show how "liaisons" rather than brokers maximize this objective.
Abstract: By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for the specific features of social networks, such as the notion of teams. We fill this gap by demonstrating how desirable aspects of organizational structure can be mapped parsimoniously onto the spectrum of the graph Laplacian allowing the specification of structural objectives and build on recent advances in non-convex programming to optimize them. This design framework is general, but we focus here on the problem of creating graphs that balance high modularity and low mixing time, and show how "liaisons" rather than brokers maximize this objective.
01 Jan 2014
TL;DR: This is a collection of references for a series of lectures that I gave in the “boot camp” of the semester on spectral graph theory at the Simons Institute in August, 2014.
Abstract: This is a collection of references for a series of lectures that I gave in the “boot camp” of the semester on spectral graph theory at the Simons Institute in August, 2014. To keep this document focused, I only refer to results related to the lectures in question, which means that my own work is disproportionally represented. I plan to post a better version of this document in the future, so please send me corrections and additions.
TL;DR: Based on the characteristic polynomial coefficients (CPCs) of the adjacency matrix A′ of heterogeneous molecular graphs of the molecules containing a tetravalent heteroatom >Si Ge Sn<), a 13-constant additive scheme for the calculation of their physicochemical properties is obtained.
Abstract: Based on the characteristic polynomial coefficients (CPCs) of the adjacency matrix A′ of heterogeneous molecular graphs of the molecules containing a tetravalent heteroatom >Si Ge Sn<), etc. in the chain, a 13-constant additive scheme for the calculation of their physicochemical properties is obtained. The structural meaning of CPCs of the adjacency matrix A′ is established. By the formula obtained the formation enthalpies ΔfHgas, 298K0 of SiCnH2n+2 alkylsilanes not studied experimentally are calculated.