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
More filters
01 May 2018
TL;DR: A transmission network clustering method based on spectral graph theory, which is applied to Transmission Network Expansion Planning (TEP), allows to identify sub-systems in an efficient way by applying both topological and system criteria.
Abstract: This paper presents a transmission network clustering method based on spectral graph theory, which is applied to Transmission Network Expansion Planning (TEP). This novel method allows to identify sub-systems in an efficient way by applying both topological and system criteria. The identified subsystems are used to solve the TEP problem in a distributed way: by combining a Reduced Linear Disjunctive Model with an active power injection mechanism based on the minium effort network criterium. Results show a significant improvement in execution times without sacrificing the quality of the expansion plan.
TL;DR: It is shown that graph matching methods based on relaxation labeling, spectral graph theory and tensor theory have the same mathematical form by employing power iteration technique and a fast compatibility building procedure is proposed to accelerate the preprocessing speed.
01 Jan 2012
TL;DR: An interactive toolbox application is presented to enable users to gain an intuitive understanding of the “meaning” of eigenvalues and eigenvectors of graph-related matrices and proves a logarithmic upper bound for zmax, the largest distance from any vertex to its nearest MIS vertex after one round of Luby's algorithm.
Abstract: We present an interactive toolbox application we have developed to enable users to gain an intuitive understanding of the “meaning” of eigenvalues and eigenvectors of graph-related matrices. In addition, we explore spectral embeddings and the effects of graph altering algorithms on the eigenvalues of a graph. Furthermore, we examine Luby’s fast distributed randomized algorithm for finding a maximal independent set (MIS) of a network of nodes. We compare different graph classes with respect to how many rounds the algorithm takes to complete on them on average. We suggest that certain graph classes exhibit a logarithmic lower bound for this number of rounds. Lastly, we prove a logarithmic upper bound for zmax, the largest distance from any vertex to its nearest MIS vertex after one round of Luby’s algorithm, once for path graphs and then for all graphs in general.