scholarly journals Maximal and minimal entry in the principal eigenvector for the distance matrix of a graph

2011 ◽  
Vol 311 (22) ◽  
pp. 2593-2600 ◽  
Author(s):  
Kinkar Ch. Das
Keyword(s):  
Distance Matrix ◽  
Principal Eigenvector

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 On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals The normalized distance Laplacian

2021 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
Carolyn Reinhart
Keyword(s):  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

scholarly journals The Diversity, Composition, and Metabolic Pathways of Archaea in Pigs

Animals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 2139
Author(s):  
Feilong Deng ◽  
Yushan Li ◽  
Yunjuan Peng ◽  
Xiaoyuan Wei ◽  
Xiaofan Wang ◽  
...  
Keyword(s):  
Relative Abundance ◽  
Antibiotic Resistance Genes ◽  
Alpha Diversity ◽  
Distance Matrix ◽  
Archaeal Community ◽  
Gene Families ◽  
Shannon Index ◽  
Metabolic Potential ◽  
Substantial Progress ◽  
Archaeal Communities

Archaea are an essential class of gut microorganisms in humans and animals. Despite the substantial progress in gut microbiome research in the last decade, most studies have focused on bacteria, and little is known about archaea in mammals. In this study, we investigated the composition, diversity, and functional potential of gut archaeal communities in pigs by re-analyzing a published metagenomic dataset including a total of 276 fecal samples from three countries: China (n = 76), Denmark (n = 100), and France (n = 100). For alpha diversity (Shannon Index) of the archaeal communities, Chinese pigs were less diverse than Danish and French pigs (p < 0.001). Consistently, Chinese pigs also possessed different archaeal community structures from the other two groups based on the Bray–Curtis distance matrix. Methanobrevibacter was the most dominant archaeal genus in Chinese pigs (44.94%) and French pigs (15.41%), while Candidatus methanomethylophilus was the most predominant in Danish pigs (15.71%). At the species level, the relative abundance of Candidatus methanomethylophilus alvus, Natrialbaceae archaeon XQ INN 246, and Methanobrevibacter gottschalkii were greatest in Danish, French, and Chinese pigs with a relative abundance of 14.32, 11.67, and 16.28%, respectively. In terms of metabolic potential, the top three pathways in the archaeal communities included the MetaCyc pathway related to the biosynthesis of L-valine, L-isoleucine, and isobutanol. Interestingly, the pathway related to hydrogen consumption (METHANOGENESIS-PWY) was only observed in archaeal reads, while the pathways participating in hydrogen production (FERMENTATION-PWY and PWY4LZ-257) were only detected in bacterial reads. Archaeal communities also possessed CAZyme gene families, with the top five being AA3, GH43, GT2, AA6, and CE9. In terms of antibiotic resistance genes (ARGs), the class of multidrug resistance was the most abundant ARG, accounting for 87.41% of archaeal ARG hits. Our study reveals the diverse composition and metabolic functions of archaea in pigs, suggesting that archaea might play important roles in swine nutrition and metabolism.

Precise clustering analysis of Internet financial credit reporting dependent on multidimensional attribute sparse large data

2021 ◽  
pp. 002072092110020
Author(s):  
Lingling Chen ◽  
Yuanyuan Zhang ◽  
Min Zeng
Keyword(s):  
Clustering Analysis ◽  
Large Data ◽  
Distance Matrix ◽  
The Internet ◽  
Relationship Matrix ◽  
Clustering Methods ◽  
Correlation Relationship ◽  
Credit Reporting ◽  
Financial Credit ◽  
Approximate Distance

Given that the traditional methods cannot perform clustering analysis on the Internet financial credit reporting directly and effectively, a kind of precise clustering analysis of internet financial credit reporting dependent on multidimensional attribute sparse large data is proposed. By measuring the overall distance between Internet financial credit reporting through the sparse large data with multidimensional attributes, the multidimensional attribute sparse large data are used to perform clustering analysis on the overall distance matrix and the component approximate distance matrix between the data, respectively. The correlation relationship between the Internet financial credit reporting under these two perspectives is taken into comprehensive consideration. Multidimensional attribute sparse large data pairs are used to reflect the comprehensive relationship matrix of the original Internet financial credit reporting to achieve clustering with relatively high quality. Numerical experiments show that compared with the traditional clustering methods, the method proposed in this paper can not only reflect the overall data features effectively, but also improve the clustering effect of the original Internet financial credit reporting data through the analysis of the correlation relationship between the important component attribute sequences.

scholarly journals Chatbot to improve learning punctuation in Spanish and to enhance open and flexible learning environments

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Esteban Vázquez-Cano ◽  
Santiago Mengual-Andrés ◽  
Eloy López-Meneses
Keyword(s):  
Learning Process ◽  
Latent Dirichlet Allocation ◽  
Distance Matrix ◽  
Ease Of Use ◽  
Three Dimensions ◽  
Pairwise Distance ◽  
Control Group ◽  
Quantitative Methodology ◽  
Quasi Experimental ◽  
Experimental Group

AbstractThe objective of this article is to analyze the didactic functionality of a chatbot to improve the results of the students of the National University of Distance Education (UNED / Spain) in accessing the university in the subject of Spanish Language. For this, a quasi-experimental experiment was designed, and a quantitative methodology was used through pretest and posttest in a control and experimental group in which the effectiveness of two teaching models was compared, one more traditional based on exercises written on paper and another based on interaction with a chatbot. Subsequently, the perception of the experimental group in an academic forum about the educational use of the chatbot was analyzed through text mining with tests of Latent Dirichlet Allocation (LDA), pairwise distance matrix and bigrams. The quantitative results showed that the students in the experimental group substantially improved the results compared to the students with a more traditional methodology (experimental group / mean: 32.1346 / control group / mean: 28.4706). Punctuation correctness has been improved mainly in the usage of comma, colon and periods in different syntactic patterns. Furthermore, the perception of the students in the experimental group showed that they positively value chatbots in their teaching–learning process in three dimensions: greater “support” and companionship in the learning process, as they perceive greater interactivity due to their conversational nature; greater “feedback” and interaction compared to the more traditional methodology and, lastly, they especially value the ease of use and the possibility of interacting and learning anywhere and anytime.

Empirical Estimation of Shortest Route Length along U.S. Interstate Highways Based on Great Circle Distance

2021 ◽  
pp. 036119812110152
Author(s):  
Nawei Liu ◽  
Fei Xie ◽  
Zhenhong Lin ◽  
Mingzhou Jin
Keyword(s):  
Linear Regression ◽  
State Level ◽  
Distance Matrix ◽  
Great Circle ◽  
The State ◽  
Empirical Estimation ◽  
Interstate Highways ◽  
Shortest Route ◽  
Route Length ◽  
Great Circle Distance

In this study, 98 regression models were specified for easily estimating shortest distances based on great circle distances along the U.S. interstate highways nationwide and for each of the continental 48 states. This allows transportation professionals to quickly generate distance, or even distance matrix, without expending significant efforts on complicated shortest path calculations. For simple usage by all professionals, all models are present in the simple linear regression form. Only one explanatory variable, the great circle distance, is considered to calculate the route distance. For each geographic scope (i.e., the national or one of the states), two different models were considered, with and without the intercept. Based on the adjusted R-squared, it was observed that models without intercepts generally have better fitness. All these models generally have good fitness with the linear regression relationship between the great circle distance and route distance. At the state level, significant variations in the slope coefficients between the state-level models were also observed. Furthermore, a preliminary analysis of the effect of highway density on this variation was conducted.

Methods for Studying Morphological Integration and Modularity

2010 ◽  
Vol 16 ◽  
pp. 213-243 ◽  
Author(s):  
Anjali Goswami ◽  
P. David Polly
Keyword(s):  
Distance Matrix ◽  
Japanese Macaques ◽  
Morphological Integration ◽  
Matrix Analysis ◽  
Euclidean Distance Matrix ◽  
Phenotypic Data ◽  
Graphical Modelling ◽  
Landmark Data ◽  
Competing Models ◽  
Matrix Correlation

Morphological integration and modularity are closely related concepts about how different traits of an organism are correlated. Integration is the overall pattern of intercorrelation; modularity is the partitioning of integration into evolutionarily or developmentally independent blocks of traits. Modularity and integration are usually studied using quantitative phenotypic data, which can be obtained either from extant or fossil organisms. Many methods are now available to study integration and modularity, all of which involve the analysis of patterns found in trait correlation or covariance matrices. We review matrix correlation, random skewers, fluctuating asymmetry, cluster analysis, Euclidean distance matrix analysis (EDMA), graphical modelling, two-block partial least squares, RV coefficients, and theoretical matrix modelling and discuss their similarities and differences. We also review different coefficients that are used to measure correlations. We apply all the methods to cranial landmark data from and ontogenetic series of Japanese macaques,Macaca fuscatato illustrate the methods and their individual strengths and weaknesses. We conclude that the exploratory approaches (cluster analyses of various sorts) were less informative and less consistent with one another than were the results of model testing or comparative approaches. Nevertheless, we found that competing models of modularity and integration are often similar enough that they are not statistically distinguishable; we expect, therefore, that several models will often be significantly correlated with observed data.

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