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Abstract A (1 , ≤ ℓ) -identifying code in digraph D is a dominating subset C of vertices of D , such that all distinct subsets of vertices of D with cardinality at most ℓ have distinct closed in-neighborhoods within C. As far as we know, it is the very first time that the spectral graph theory has been applied to the identifying codes. We give a new method to obtain an upper bound on ℓ for digraphs. The results obtained here can also be applied to graphs. [ABSTRACT FROM AUTHOR]

Graph coloring is an NP-hard problem. There is ample room to further reduce the number of colors being used under the strict constraints of the problem. This paper proposes an algorithm that stores the information of the vertices in the graph, together with the color and the next address field of a node in a singly linked list. The coloring of a particular vertex is decided on the content of color field of node corresponding to the searched vertex for coloring. The adjacency matrix of the graph was adopted to select the feasible color to be allocated to a vertex, without violating the constraints for coloring of the vertices in the graph. The proposed algorithm was tested on DIMACS benchmark graphs, using Python 3.6. The results show that our algorithm produced the result with the optimal number of colors required to solve the problem. This research provides a new strategy to find the optimal coloring solution for each type of graphs. [ABSTRACT FROM AUTHOR]

Hand Gestures Recognition (HGR) is one of the main areas of research for Human Computer Interaction applications. Most existing approaches are based on local or geometrical properties of pixels. Still, there are some serious challenges on HGR methods such as sensitivity to rotation, scale, illumination, perturbation, and occlusion. In this paper, we study HGR from graph viewpoints. We introduce a set of meaningful shape features based on a graph constructed by Growing Neural Gas (GNG) algorithm. These features are constructed from topological properties of this graph. Graph properties in conserving topological features improve stability against different deformations, scale, and noise. We evaluate our method on NTU Hand Digits dataset with state-of-the-art methods. We also prepared a comprehensive dataset (SBU-1) for different hand gestures containing 2170 images. This dataset includes many possible deformations and variations and some articulations. Most of the existing datasets don't capture these variations. We show the robustness of the algorithm to scale, rotation and noise, while preserving similar recognition rate in comparison with the state-of-the-art results. [ABSTRACT FROM AUTHOR]

Stable isotope based metabolic flux analysis is currently the unique methodology that allows the experimental study of the integrated responses of metabolic networks. This method primarily relies on isotope labeling and modeling, which could be a challenge in both experimental and computational biology. In particular, the algorithm implementation for isotope simulation is a critical step, limiting extensive usage of this powerful approach. Here, we introduce EMUlator a Python-based isotope simulator which is developed on Elementary Metabolite Unit (EMU) algorithm, an efficient and powerful algorithm for isotope modeling. We propose a novel adjacency matrix method to implement EMU modeling and exemplify it stepwise. This method is intuitively straightforward and can be conveniently mastered for various customized purposes. We apply this arithmetic pipeline to understand the phosphoketolase flux in the metabolic network of an industrial microbe Clostridium acetobutylicum. The resulting design enables a high-throughput and non-invasive approach for estimating phosphoketolase flux in vivo. Our computational insights allow the systematic design and prediction of isotope-based metabolic models and yield a comprehensive understanding of their limitations and potentials. [ABSTRACT FROM AUTHOR]

Abstract We investigate two Bruhat (partial) orders on graphs with vertices labeled 1 , 2 , ... , n and with a specified degree sequence R , equivalently, symmetric (0 , 1) -matrices with zero trace and a specified row sum vector R (adjacency matrices of such graphs). One is motivated by the classical Bruhat order on permutations while the other one, more restrictive, is defined by a switch of a pair of disjoint edges. In the Bruhat order, one seeks to concentrate the edges of a graph with a given degree sequence among the vertices with smallest labels, thereby producing a minimal graph in this order. We begin with a discussion of graphs whose isomorphism class does not change under a switch. Then we are interested in when the two Bruhat orders are identical. For labeled graphs of regular degree k , we show that the two orders are identical for k ≤ 2 but not for k = 3. [ABSTRACT FROM AUTHOR]

A comparison of two groups of plane shooting targets (PSTs) characterizing the shooter-silhouette in different observation and rifle-firing positions was the starting point for this study. Selected infantry targets are used for shooting training in the Russian Federation and in the Swiss Confederation. The comparison results of two target groups (five PSTs in each of them) showed a significant similarity of their geometric shapes. To explain this fact, a targets design system (TDS) was developed. The TDS is based on attributing a certain number of simple geometric shapes - geometric primitives (GP). In our case, the number of GPs was equal to ten (five polygons for Russian and five polygons for Swiss targets). The TDS enabled building a human-like target silhouette. If two sides of two adjoining GPs or their parts become common for them, then such GPs can be combined into one common geometric figure whose area is equal to the sum of the two GPs. The TDS was further transformed into two isomorphic graphs. Their adjacency matrix (AM) was obtained. The AM matrices for the Russian PSTs and the Swiss PSTs were the same. To improve the estimation of the area and the coordinates of the target centroid, a matrix modification of Bourke’s formulas were proposed. The geometric areas for the Russian and Swiss PSTs and the location of their centroids were refined and compared. GNU Octave, GeoGebra and Mathcad were used as mathematical software for computer calculations and for graphic visualizations. [ABSTRACT FROM AUTHOR]

Information extraction from scanned document page images is an important issue in image analysis. The main objectives of this work are: vectorization of image of the digital logic-gate circuits as graph, and automatic generation of Boolean expression. We have employed a novel method for circuit component separation using morphological operators. Connecting wires (in the form of poly lines in the image) lead to adjacency matrix describing directed interconnection between logic gates. Logic gate symbols are recognized by support vector machine (SVM) based on the features obtained by deep convolutional neural network (DCNN). Finally, we exploit this abstract representation of digital logic circuit as a graph to determine the Boolean expression. The approach is tested on a dataset developed by us and the results are encouraging. [ABSTRACT FROM AUTHOR]

Let be a signed graph, where G is the underlying simple graph and is the sign function on the edges of G. The adjacency matrix of a signed graph has or for adjacent vertices, depending on the sign of the connecting edges. In this paper, the eigenvalues of signed complete graphs are investigated. We prove that and 1 are the eigenvalues of the signed complete graph with the multiplicity at least t if there are vertices whose all incident edges are positive or negative, respectively. We study the spectrum of a signed complete graph whose negative edges induce an r-regular subgraph H. We obtain a relation between the eigenvalues of this signed complete graph and the eigenvalues of H. [ABSTRACT FROM AUTHOR]

Invasion science is in a state of paradox, having low predictability despite strong, identifiable covariates of invasion performance. We propose shifting the foundation metaphor of biological invasions from a linear filtering scheme to one that invokes complex adaptive networks. We link invasion performance and invasibility directly to the loss of network stability and indirectly to network topology through constraints from the emergence of the stability criterion in complex systems. We propose the wind vane of an invaded network – the major axis of its adjacency matrix – which reveals how species respond dynamically to invasions. We suggest that invasion ecology should steer away from comparative macroecological studies, to rather explore the ecological network centred on the focal species. Highlights Invasion performance can be tentatively explained by the traits of alien species relative to those of natives, recipient site characteristics, and introduction pathways. The rush to identify invasive traits from comparative studies has not yet led to predictability at a satisfactory level. Synergies among invasion science, network ecology, and community ecology warrant increasing attention. Winners and losers in recipient ecosystems are the results of the multiplayer game between natives and aliens, as well as human factors. Statistical tools that can handle multispecies interactions are on the horizon. [ABSTRACT FROM AUTHOR]

Abstract Motivated by the study of genomes evolving by reversals, we consider pseudograph transformations known as "pressing sequences". In particular, we address the question of when a graph has precisely one pressing sequence resulting in the empty graph, thus answering an question from Cooper and Davis (2015) [13]. We characterize such "uniquely pressable" graphs, count the number of them on a given number of vertices, and provide a polynomial-time recognition algorithm. We conclude with several open questions. [ABSTRACT FROM AUTHOR]

Link prediction for complex networks is a research hotspot. The main purpose is to predict the unknown edge according to the structure of the existing network. However, the edges in realworld networks are often sparsely distributed, and the number of unobserved edges is usually far greater than that of observed ones. Considering the weak performance of traditional link prediction algorithms under the above situation, this paper puts forward a novel link prediction algorithm called network adjacency matrix blocked-compressive sensing (BCS). Firstly, the diagonal blocks were subjected to sparse transformation with the network adjacency matrix; Next, the measurement matrix was rearranged into a new measurement matrix using the sorting operator; Finally, the subspace pursuit (SP) algorithm was introduced to solve the proposed algorithm. Experiments on ten real networks show that the proposed method achieved higher accuracy and consumed less time than the baseline methods. [ABSTRACT FROM AUTHOR]

A three-phase unbalanced power flow method can provide a more realistic scenario of how distribution networks operate. The backward/forward sweep-based power flow method (BF-PF) has been used for many years as an important computational tool to solve the power flow for unbalanced and radial power systems. However, some of the few available research tools produce many errors when they are used for network reconfiguration because the topology changes after multiple switch actions and the nodes are disorganized continually. This paper presents a modified BF-PF for three-phase unbalanced radial distribution networks that is capable of arranging the system topology when reconfiguration changes the branch connections. A binary search is used to determine the connections between nodes, allowing the algorithm to avoid those problems when reconfiguration is carried out, regardless of node numbers. Tests are made to verify the usefulness of the proposed algorithm in both the IEEE 13-node test feeder and the 123-node test feeder, converging in every run where constraints are accomplished. This approach can be used easily for a large-scale feeder network reconfiguration. The full version of this modified backward/forward sweep algorithm is available for research at MathWorks. [ABSTRACT FROM AUTHOR]

An innovative automatic modulation classification via graph-based constellation analysis for ${M}$ -ary QAM signals is presented. In our framework, a unified mesh model for the constellation diagrams of the ${M}$ -QAM signals within the modulation candidate set is first constructed and exploited to transform the received ${M}$ -QAM signal into graph domain. The concise graph representation of the received ${M}$ -QAM signal is established from its constellation according to the positions of the recovered symbols in the mesh model. Then, the modulation feature vector is built from the eigenvector(s) corresponding to the maximum eigenvalue of its adjacency matrix. The modulation type can be identified by measuring the angle between the feature vectors resulting from the training data and the test data. Monte Carlo simulation results and theoretical analysis demonstrate that the proposed method with lower computational complexity can provide superior performance to the existing subtractive clustering technique, and is robust to the residual phase and timing offsets. [ABSTRACT FROM AUTHOR]

Abstract This paper adopts network analysis to investigate the feasibility of recruiting nearby fishing vessels as the initial rescue force for search-and-rescue operations. Network analysis was conducted to analyze the proximity among fishing vessels according to the type of fishing. The results were used as input to an adjacency matrix and schematized by applying the network. Given that fish species tend to travel together, fishing vessels in pursuit of them also operate in the same waters, essentially forming a network. It is thus desirable to secure a search-and-rescue system among fishing vessels of the same fishing type for prompt rescue. Specifically, network analysis confirmed that fishing vessels of the same type within 10 nautical miles can become vigilant, and a system of prompt rescue support can thus be secured; this approach improves the overall speed of rescue operations. These findings can be used as baseline data for developing a practical search-and-rescue system through a network of fishing vessels of the same fishing type. Highlights • Network analysis to evaluate the proximity among fishing vessels by fishing type. • Study utilized the fishing vessel location data for a 1 month span. • Intensity of the connection between two vessels by relative weight. • Network analysis can be applied to developing a rescue system. [ABSTRACT FROM AUTHOR]

For a sequence of adjacency matrices, describing the unfolding of a network from the graph of a star, through graphs of a broom, to the graph of a link with constant vertices and edges, we show that the leading eigenvalue (the spectral radius) satisfies a simple algebraic equation. The equation allows easy numerical computation of the leading eigenvalue as well as a direct proof of its monotonicity in terms of the maximal degree of vertices. [ABSTRACT FROM AUTHOR]

In recent time graphical analytics of uncertainty and indeterminacy has become major concern for data analytics researchers. In this direction, the mathematical algebra of neutrosophic graph is extended to interval-valued neutrosophic graph. However, building the interval-valued neutrosophic graphs, its spectrum and energy computation is addressed as another issues by research community of neutrosophic environment. To resolve this issue the current paper proposed some related mathematical notations to compute the spectrum and energy of interval-valued neutrosophic graph using the MATAB. [ABSTRACT FROM AUTHOR]

Abstract Finding a diagonal matrix congruent to A − c I for constants c , where A is the adjacency matrix of a graph G allows us to quickly tell the number of eigenvalues in a given interval. If G has clique-width k and a corresponding k -expression is known, then diagonalization can be done in time O (poly (k) n) where n is the order of G. [ABSTRACT FROM AUTHOR]

For a simple graph G with n vertices and m edges having adjacency eigenvalues λ1;λ2,...,λn, the energy E (G) of G is defined as E (G) = Σni=1 |λi|. We obtain the upper bounds for E (G) in terms of the vertex covering number t, the number of edges m, maximum vertex degree d1 and second maximum vertex degree d2 of the connected graph G. These upper bounds improve some recently known upper bounds for E (G). Further, these upper bounds for E (G) imply a natural extension to other energies like distance energy and Randic energy associated to a connected graph G. [ABSTRACT FROM AUTHOR]

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Abstract In this paper we introduce a new graph matrix, named the anti-adjacency matrix or eccentricity matrix, which is constructed from the distance matrix of a graph by keeping for each row and each column only the largest distances. This matrix can be interpreted as the opposite of the adjacency matrix, which is instead constructed from the distance matrix of a graph by keeping for each row and each column only the distances equal to 1. We show that the eccentricity matrix of trees is irreducible, and we investigate the relations between the eigenvalues of the adjacency and eccentricity matrices. Finally, we give some applications of this new matrix in terms of molecular descriptors, and we conclude by proposing some further research problems. [ABSTRACT FROM AUTHOR]

Abstract An expression of the coefficient of immanantal polynomial of an n × n matrix is present. Moreover, we give expressions of the coefficient of immanantal polynomials of combinatorial matrices (adjacency matrix, Laplacian matrix, signless Laplacian matrix). As applications, we show that the immanantal polynomials for Laplacian matrix and signless Laplacian matrix of bipartite graphs are the same. This is a generalization of the characteristic polynomial for Laplacian matrix and signless Laplacian matrix of bipartite graphs. Furthermore, we consider the relations between the characteristic polynomial and the immanantal polynomial for trees. [ABSTRACT FROM AUTHOR]

Abstract Let μ be an eigenvalue of a simple graph G with multiplicity k ≥ 1. A star complement for μ in G is an induced subgraph of G of order n − k with no eigenvalue μ. In this paper, we study the maximal graphs with the star S m as a star complement for −2. The maximal graphs with S 3 , S 4 , S 13 and S 21 as a star complement for −2 are described. We also describe the regular graphs with K 2 , s (s ≥ 2) as a star complement for an eigenvalue μ. [ABSTRACT FROM AUTHOR]

Let G 1 , G 2 and H be three graphs on disjoint sets of vertices and G 1 has m 1 edges. Let S (G 1 , H) be the graph obtained from G 1 and H in the following way: (1) Delete all the edges of G 1 and consider m 1 disjoint copies of H. (2) Join each vertex of the i th copy of H to the end vertices of the i th edge of G 1 . Let G 1 (∨ H) G 2 be the graph obtained from S (G 1 , H) by joining each vertex of G 1 with each vertex of G 2. In this paper, we determine the adjacency (respectively, Laplacian, signless Laplacian) spectrum of G 1 (∨ H) G 2 in terms of those of G 1 , G 2 and H. As an application, we construct infinite pairs of cospectral graphs. [ABSTRACT FROM AUTHOR]

Representing a set of vertices in a graph means of a matrix was introduced by E. Sampath Kumar. Let G(V,E) be a graph and S ⊆ V be a set of vertices. We can represent the set S by means of a matrix as follows, in the adjacency matrix A(G) of G replace the aii element by 1 if and only if, vi ∈ S. In this paper we study the special case of set S being dominating set and corresponding domination energy of some class of graphs. [ABSTRACT FROM AUTHOR]

In this paper we develop the concept of energy of a vertex introduced in Arizmendi and Juarez-Romero (2018). We derive basic inequalities, continuity properties, give examples and extend the definition to locally finite graphs. [ABSTRACT FROM AUTHOR]

We study the eigenvalues of the unique connected anti-regular graph A n . Using Chebyshev polynomials of the second kind, we obtain a trigonometric equation whose roots are the eigenvalues and perform elementary analysis to obtain an almost complete characterization of the eigenvalues. In particular, we show that the interval Ω = [ − 1 − 2 2 , − 1 + 2 2 ] contains only the trivial eigenvalues λ = − 1 or λ = 0 , and any closed interval strictly larger than Ω will contain eigenvalues of A n for all n sufficiently large. We also obtain bounds for the maximum and minimum eigenvalues, and for all other eigenvalues we obtain interval bounds that improve as n increases. Moreover, our approach reveals a more complete picture of the bipartite character of the eigenvalues of A n , namely, as n increases the eigenvalues are (approximately) symmetric about the number − 1 2 . We also obtain an asymptotic distribution of the eigenvalues as n → ∞ . Finally, the relationship between the eigenvalues of A n and the eigenvalues of a general threshold graph is discussed. [ABSTRACT FROM AUTHOR]

In this manuscript we continue the investigations related to the wreath product of graphs by considering the compound graph of a clique with a circuit. This product shows nice combinatorial and algebraic properties which permit with reasonable effort to compute some topological indices and the (adjacency) spectrum. [ABSTRACT FROM AUTHOR]

An oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure. In this paper we obtain a combinatorial characterization of the coefficients of the characteristic polynomials of oriented hypergraphic Laplacian and adjacency matrices via a signed hypergraphic generalization of basic figures of graphs. Additionally, we provide bounds on the determinant and permanent of the Laplacian matrix, characterize the oriented hypergraphs in which the upper bound is sharp, and demonstrate that the lower bound is never achieved. [ABSTRACT FROM AUTHOR]

Let G = ( V , E ) , V = { 1 , 2 , … , n } , be a simple connected graph with n vertices, m edges, and sequence of vertex degrees d 1  ≥  d 2  ≥ ⋅⋅⋅ ≥  d n  > 0, d i = d ( i ) . A large number of vertex–degree-based topological indices is of the form T I = T I ( G ) = ∑ i ∼ j F ( d i , d j ) , where F is pertinently chosen function with the property F ( x , y ) = F ( y , x ) . To each of such topological indices a corresponding adjacency matrix A = ( a i j ) , of order n  ×  n , can be associated. The trace of matrix A is denoted as t r ( A ) . For F ( d i , d j ) = 2 d i d j d i + d j , the geometric–arithmetic topological index, GA 1 , is obtained. Upper and lower bounds for GA 1 in terms of t r ( A 2 ) are determined. Also, we generalize a number of results reported in the literature and obtain some new bounds for the indices of the form TI . [ABSTRACT FROM AUTHOR]

Connected planar graphs are of interest to a variety of scholars. Being able to simulate a database of such graphs with selected properties would support specific types of inference for spatial analysis and other network-based disciplines. This paper presents a simple, efficient, and flexible connected planar graph generator for this purpose. It also summarizes a comparison between an empirical set of specimen graphs and their simulated counterpart set, and establishes evidence for positing a conjecture about the principal eigenvalue of connected planar graphs. Finally, it summarizes a probability assessment of the algorithm’s outcomes as well as a comparison between the new algorithm and selected existing planar graph generators. [ABSTRACT FROM AUTHOR]

The numerical range of a simple graph G, named F(G), is the numerical range of its adjacency matrix A(G). The main purpose of this paper is to approximate F(G). Then, using this approximation, bounds for the largest and the smallest eigenvalues of G are proposed. In fact, lower bounds for the largest eigenvalues of G are presented in terms of disjoint induced subgraphs of G and the numerical range of the square of A(G). [ABSTRACT FROM AUTHOR]

We derive an inequality that includes the largest eigenvalue of the adjacency matrix and walks of an arbitrary length of a signed graph. We also consider certain particular cases. [ABSTRACT FROM AUTHOR]

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in the literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several metrics of the graph. However, it is not always clear whether this representation is unique, as the permutation of rows and columns in the matrix can represent the same graph. To address this issue, the proposed methodology employs a sorting algorithm to rearrange the elements of the adjacency matrix of a complex graph in a specific order. The resulting sorted adjacency matrix is then used as input for feature extraction and machine learning algorithms to classify the networks. The results indicate that the proposed methodology outperforms previous literature results on synthetic and real-world data. • This work presents a new technique for extracting important features of complex networks to improve machine learning performance. • The proposed methodology employs sorting algorithm to rearrange the elements of adjacency matrix of complex graph. • The resulting sorted adjacency matrix is then used as input for feature extraction and machine learning classification. • Results indicate that the proposed methodology outperforms previous literature results in synthetic and real-world data. [ABSTRACT FROM AUTHOR]

Let Φ = (G , φ) be a connected complex unit gain graph (T -gain graph) of n vertices with largest vertex degree Δ, adjacency matrix A (Φ) , and degree matrix D (Φ). Let m α (Φ , λ) be the multiplicity of λ as an eigenvalue of A α (Φ) : = α D (Φ) + (1 − α) A (Φ) , for α ∈ [ 0 , 1). In this article, we establish that m α (Φ , λ) ≤ (Δ − 2) n + 2 Δ − 1 and characterize the sharpness. Then, we obtain some lower bounds for the rank r (Φ) in terms of n and Δ including r (Φ) ≥ n − 2 Δ − 1 and characterize their sharpness. Besides, we introduce zero-2-walk gain graphs and study their properties. It is shown that a zero-2-walk gain graph is always regular. Furthermore, we prove that Φ has exactly two distinct eigenvalues with equal magnitude if and only if it is a zero-2-walk gain graph. Using this, we establish a lower bound of r (Φ) in terms of the number of edges and characterize the sharpness. Result about m α (Φ , λ) extends the corresponding known result for undirected graphs and simplifies the existing proof, and other bounds of r (Φ) obtained in this article work better than the bounds given elsewhere. [ABSTRACT FROM AUTHOR]

• More citations. • Clarified research question and hypotheses. • Reorganized methods section for improved clarity. • Added more experimental results for findings not included in original manuscript. • Improved overall writing style and grammar. Mild Cognitive Impairment (MCI) is an early stage of Alzheimer's Disease (AD), often mistaken for natural aging. Early detection and treatment of MCI are crucial for effective treatment, but the condition can be difficult to diagnose. In recent years, multi-modal data and deep learning methods have shown promise in this field. The objective of this study is to develop a computer-aided MCI diagnosis system that effectively processes multi-modal data using deep learning methods. We proposed a Dual Fusion Cluster Graph Convolution Network (DFCGCN) model, which combines two channels of feature extraction, one adjacency matrix, and the Cluster GCN in series. Brain imaging is downsampled using graph pooling and flattened into sparse vectors, from which advanced features are extracted. Similarity between connectivity matrices is calculated using the Gaussian kernel function and combined with non-imaging details to construct a population graph that better represents inter-subject variability. Finally, features are assigned to subjects in the population graph, and node embeddings are learned using Cluster GCN to output diagnostic results. We tested the proposed algorithm on the public Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, achieving an accuracy, sensitivity, and specificity of 90.7%, 91.1%, and 94.0%, respectively. The DFCGCN model presented in this study enhances the diagnosis of MCI and outperforms other state-of-the-art algorithms. This approach has potential to be a valuable tool for early detection and treatment of MCI. [ABSTRACT FROM AUTHOR]