scholarly journals Relating centralities in graphs and the principal eigenvector of its distance matrix

2021 ◽  
Vol 40 (1) ◽  
pp. 217-237
Author(s):  
Celso M. da Silva Jr. ◽  
Renata R. Del-Vecchio ◽  
Bruno B. Monteiro
Keyword(s):  
Graph Theory ◽  
Distance Matrix ◽  
Closeness Centrality ◽  
Spectral Graph Theory ◽  
Principal Eigenvector ◽  
Centrality Measure ◽  
Spectral Graph ◽  
Threshold Graphs

In this work a new centrality measure of graphs is presented, based on the principal eigenvector of the distance matrix: spectral closeness. Using spectral graph theory, we show some of its properties and we compare the results of this new centrality with closeness centrality. In particular, we prove that for threshold graphs these two centralities always coincide. In addition we construct an infinity family of graphs for which these centralities never coincide.

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

An Algorithm for Determining the Position and Orientation of 3-D Objects from Images Using Spectral Graph Theory

2015 ◽  
Vol 770 ◽  
pp. 585-591
Author(s):  
Alexey Barinov ◽  
Aleksey Zakharov
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Spectral Decomposition ◽  
Spectral Graph Theory ◽  
Feature Points ◽  
Image Comparison ◽  
Spectral Graph ◽  
Position And Orientation ◽  
Weighted Adjacency Matrix

This paper describes an algorithm for computing the position and orientation of 3-D objects by comparing graphs. The graphs are based on feature points of the image. Comparison is performed by a spectral decomposition with obtaining eigenvectors of weighted adjacency matrix of the graph.

Sign in / Sign up

Export Citation Format

Share Document