Transforming an adjacency matrix into a planar graph

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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Bounds for the Eigen Values and Energy of Degree Product Adjacency Matrix of A Graph

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/1038 ◽

2019 ◽

Vol 10 (3) ◽

pp. 565-573

Author(s):

Keerthi G. Mirajkar ◽

Bhagyashri R. Doddamani

Keyword(s):

Adjacency Matrix ◽

Eigen Values

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Energy of spherical fuzzy graphs

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.26 ◽

2020 ◽

pp. 321-332

Author(s):

S. Yahya Mohamed ◽

A. Mohamed Ali

Keyword(s):

Adjacency Matrix ◽

Upper Bounds ◽

Fuzzy Graph ◽

Lower And Upper Bounds ◽

Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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Mathematics of networks

10.1093/oso/9780198805090.003.0006 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Random Walks ◽

Adjacency Matrix ◽

Graph Partitioning ◽

Dynamic Networks ◽

Graph Laplacian ◽

Network Visualization ◽

Final Part ◽

Bipartite Networks ◽

Component Structure ◽

Basic Properties

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

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A Note on the Estrada Index of the Aα-Matrix

Mathematics ◽

10.3390/math9080811 ◽

2021 ◽

Vol 9 (8) ◽

pp. 811

Author(s):

Jonnathan Rodríguez ◽

Hans Nina

Keyword(s):

Lower Bounds ◽

Adjacency Matrix ◽

Estrada Index

Let G be a graph on n vertices. The Estrada index of G is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. V. Nikiforov studied hybrids of A(G) and D(G) and defined the Aα-matrix for every real α∈[0,1] as: Aα(G)=αD(G)+(1−α)A(G). In this paper, using a different demonstration technique, we present a way to compare the Estrada index of the Aα-matrix with the Estrada index of the adjacency matrix of the graph G. Furthermore, lower bounds for the Estrada index are established.

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Properties of adjacency matrix of the directed cyclic friendship graph

10.1063/5.0042158 ◽

2021 ◽

Author(s):

Nanda Anzana ◽

Siti Aminah ◽

Suarsih Utama

Keyword(s):

Adjacency Matrix

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Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽

10.3390/e23080976 ◽

2021 ◽

Vol 23 (8) ◽

pp. 976

Author(s):

R. Aguilar-Sánchez ◽

J. Méndez-Bermúdez ◽

José Rodríguez ◽

José Sigarreta

Keyword(s):

Random Matrix ◽

Adjacency Matrix ◽

Matrix Theory ◽

Computational Study ◽

Random Networks ◽

Geometric Graphs ◽

Theory Approach ◽

Complexity Measures ◽

Random Geometric Graphs ◽

Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

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