Vertices In Network Research Articles

Target Controllability: a Feed-Forward Greedy Algorithm in Complex Networks, Meeting Kalman's Rank Condition.

The concept of controllability within complex networks is pivotal in determining the minimal set of driver vertices required for the exertion of external signals, thereby enabling control over the entire network's vertices. Target controllability further refines this concept by focusing on a subset of vertices within the network as the specific targets for control, both of which are known to be NP-hard problems. Crucially, the effectiveness of the driver set in achieving control of the network is contingent upon satisfying a specific rank condition, as introduced by Kalman. On the other hand, structural controllability provides a complementary approach to understanding network control, emphasizing the identification of driver vertices based on the network's structural properties. However, in structural controllability approaches, the Kalman condition may not always be satisfied. In this study, we address the challenge of target controllability by proposing a feed-forward greedy algorithm designed to efficiently handle large networks while meeting the Kalman controllability rank condition. We further enhance our method's efficacy by integrating it with Barabasi et al.'s structural controllability approach. This integration allows for a more comprehensive control strategy, leveraging both the dynamical requirements specified by Kalman's rank condition and the structural properties of the network. Empirical evaluation across various network topologies demonstrates the superior performance of our algorithms compared to existing methods, consistently requiring fewer driver vertices for effective control. Additionally, our method's application to protein-protein interaction networks associated with breast cancer reveals potential drug repurposing candidates, underscoring its biomedical relevance. This study highlights the importance of addressing both structural and dynamical aspects of network controllability for advancing control strategies in complex systems. The source code is available for free at: Https://github.com/fatemeKhezry/targetControllability. Supplementary data are available at Bioinformatics online.

Multi-Level Sum of Product (SOP) Network Power Optimization Based on Switching Graph

The article presents the methodology of optimization of technology mapping of a multi-output function implemented in the form of sum of product (SOP) networks. The optimization is based on the concept of reducing the switching activity of combinational circuits. The aim of reducing network switching is to limit the consumption of dynamic power. Since dynamic power is one of the components of the total power consumed by digital systems, this leads to an optimization focused on the energy efficiency of digital systems. The basis of the proposed method is the technology mapping using a modified output graph describing the result of minimizing the multi-output function. The modified output graph, in terms of parameters associated with dynamic power, is defined as a switching graph. It was assumed that the key parameter associated with dynamic power is the switching activity of individual nodes of the logic network. The article presents elements of switching graph optimization which lead to the improvement of parameters associated with the dynamic power of the circuit. The essence of the proposed optimization methods is the appropriate movement of products and connections occurring in the logic network. Reducing the number of logic network vertices is also extremely important. The effectiveness of the proposed method was confirmed by the results of experiments performed on selected benchmarks. A significant reduction in the total value of switching activity was obtained for the optimized structures.

The choice of algorithms for solving a multi-agent routing problem based on solving related problems

The paper considers the problem of reducing the complexity of $NP$-hard problems by using related problems for which an optimal or acceptable solution is already known. For multi-agent routing tasks, a technique is used based on network clustering consistent with traveling salesman routes on each cluster and constructing routes that take into account the limitation of delivery time windows. A mathematical model is presented that corresponds to a block of pseudo-Boolean conditional optimization with constraints in the form of disjunctive normal forms that allows polynomial solvability and a block of time constraints. The results of choosing metaheuristics based on related problems are used in a program for the delivery of goods by many agents to consumers located at the vertices of the regional infrastructure road network.

On physical analysis of topological indices for iron disulfide network via curve fitting model

In this study, we conduct a comprehensive physical analysis of topological indices for the Iron Disulfide (FeS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2}$$\\end{document}) network using a curve-fitting model. Iron Disulfide is a cubic compound. In metamorphic rock, sedimentary rock, and quartz veins, it is typically found in combination with other sulfides or oxides. The numerical properties of molecular structures are referred to as topological indices. There are several different kinds of topological indices, including those that are based on distance, degree, or counting, among other factors. The real process of creating a topological index involves turning a chemical structure into a numerical value. In this paper, we calculate the iron disulfide network topological indices using the degrees of vertices in a chemical network of Iron Disulfide (FeS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2}$$\\end{document}). Thereafter, we discovered the physical parameters of FeS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{2}$$\\end{document} production, such as heat of formation. We then fitted curves between the thermodynamic properties and several indices. Several techniques based on rationality, linearity, and nonlinearity were used to fit curves in MATLAB. These quantitative results imply that a variety of thermodynamic characteristics of semiconducting materials may be accurately predicted by topological indices. These findings have significant ramifications as they provide the groundwork for the application of topological indices in semiconducting network design and optimization, which might result in more effective and economical material creation.

A Note on Wiener and Hyper-Wiener Indices of Abid-Waheed Graph

A Hosoya polynomial is a polynomial connected to a molecular graph, which is a graph representation of a chemical compound with atoms as vertices and chemical bonds as edges. A graph invariant is the Hosoya polynomial; it is a graph attribute that does not change under graph isomorphism. It provides information about the number of unique non-empty subgraphs in a given graph. A molecular graph's size and branching complexity are determined by a topological metric known as the Wiener index. The Wiener index of each pair of vertices in a molecular network is the sum of those distances. The topological index, one of the various classes of graph invariants, is a real number related to a connected graph's structure .The goal of this article is to compute the Hosoya polynomial of some class of Abid-Waheed graph. Further, this research focused on a C++ algorithm to calculate the wiener index of and . The Wiener index (W∗I) and Hyper-Wiener index (H∗W∗I) are calculated using Hosoya polynomial (H∗-polynomial) of some family of Abid-Waheed graphs and . Illustrations and applications are given to enhance the research work.

Precise Push Study of Sci-tech Journals Based on Knowledge Graph Reasoning

To effectively promote the efficient dissemination of sci-tech journals and improve the influence of sci-tech journals, a precise push method of sci-tech journals based on knowledge graph reasoning is proposed, using knowledge graph to build network to realize push reasoning of scientific and Technological Journals. Based on the one-way author relationship network diagram and the two-way keyword network diagram, the PageRank algorithm is used to calculate the weight of network vertices, quantitatively and accurately identify the research direction of push customers and predict customers, and realize the accurate push management of content, so as to obtain the basis for the construction of network diagram. Based on the previous article in the Journal of the information society of science and technology of China, this paper constructs a knowledge reasoning diagram, mines 52 co-author cases and 60 related papers as experimental data, and verifies the progressiveness method through customer value. According to the network diagram, the progressiveness of this method is verified. The experimental results show that the knowledge map network reasoning method proposed in this paper has high accuracy in identifying the push objects of scientific and technological journals and accurately predicting the research direction. The matching degree between the number of customers and the pushed content. Using knowledge map network can ensure the timeliness and accuracy of pushing scientific and technological journals.

Hosoya polynomial and wiener index of Abid-Waheed graph (AW)a8 and (AW)a10

Molecular structures are characterised by the Hosoya polynomial and Wiener index, ideas from mathematical chemistry and graph theory. The graph representation of a chemical compound that has atoms as vertices and chemical bonds as edges is called a molecular graph, and the Hosoya polynomial is a polynomial related to this graph. As a graph attribute that remains unchanged under graph isomorphism, the Hosoya polynomial is known as a graph invariant. It offers details regarding the quantity of distinct non-empty subgraphs within a specified graph. A topological metric called the Wiener index is employed to measure the branching complexity and size of a molecular graph. For every pair of vertices in a molecular network, the Wiener index is the total of those distances. In this paper, discussed the Hosoya polynomial, Wiener index and Hyper-Wiener index of the Abid-Waheed graphs (AW)a8 and (AW)a10. This graph is similar to Jahangir’s graph. Further, we have extended the research work on the applications of the described graphs.

Reliability of [formula omitted]-ary [formula omitted]-dimensional hypercubes under embedded restriction

The topological structure of a recursive interconnection network can be modeled by an n-dimensional graph Gn. A faulty vertex set (resp. edge set) of Gn is called a t-embedded vertex (resp. edge) cut if the remaining network is disconnected and each vertex in the residual network is in a copy of fault-free t-dimensional graph Gt. The t-embedded vertex connectivity ζt(Gn) (resp. the t-embedded edge connectivity ηt(Gn)) is defined as the minimum cardinality over all t-embedded vertex (resp. edge) cuts of Gn. The m-ary n-dimensional hypercube G(n,m) has an elegant recursive structure and is also a generalized variant of the classical hypercube. This paper studies the reliability of the G(n,m) and generalizes some known results in ternary n-cubes. Specifically, we prove that ζt(G(n,m))=(m−1)(n−t)mt for t≤n−2 and ηt(G(n,m))=(m−1)(n−t)mt for t≤n−1.

Fault-tolerant unicast paths constructive algorithms in a family of recursive networks

ABSTRACT In parallel and distributed systems, interconnection networks and data center networks are two crucial networks. They are also crucial parts of high-performance computing and cloud computing services. With the rapid growth of high-performance computing and cloud computing, both networks are growing in size. At the same time, vertex faults are unavoidable. In computer/communication networks, unicast refers to one-to-one communication between the source vertex and the destination vertex. Fault-tolerant routing of vertices in networks is an important problem that has been widely discussed. In this paper, for a class of recursive networks with less than g -restrict connectivity fault vertices and each fault-free vertex having at least g fault-free neighbors, we provide a fault-tolerant unicast path design algorithm in this study. The algorithm’s correctness is then demonstrated and its time complexity is analyzed. In addition, the results obtained can be used for unknown and known networks, including the dragonfly network, DCell, and generalized DCell.

Identification of influential vertices in complex networks: A hitting time‐based approach

AbstractUnravelling the dynamics of network vertices is pivotal, and traditional centrality measures have limitations in adapting to structural changes, directed and weighted networks, and temporal analyses. This paper introduces a ground breaking approach ‐ hitting time‐based centrality. Utilizing network matrix notations and a random walk model on a connected network , we establish a Markov chain to quantify the hitting time, hitting distance, and hitting centrality, providing a nuanced measure prioritizing central vertices. Through extensive experiments using Kendall's tau coefficient, the paper evaluates the method's correlation with actual influence in the Susceptible‐Infectious (SI) model, showcasing superior performance across diverse network sizes and structures. The hitting centrality method exhibits sensitivity to connectivity dynamics, effective incorporation of temporal dynamics, and robust handling of weighted and directed networks. Positive Kendall's tau coefficients underline the method's proficiency in prioritizing influential vertices by correlating hitting centrality values with actual infection ability. The demonstrated robustness to structural changes enhances its utility for dynamic network analysis. In conclusion, our hitting time‐based centrality approach emerges as a promising method, mitigating the shortcomings of traditional measures. By integrating information propagation speed, accommodating network dynamics, and enabling time‐dependent analyses, it offers a comprehensive tool for evaluating vertex importance and influence in complex networks.

Communicability cosine distance: similarity and symmetry in graphs/networks

A distance based on the exponential kernel of the adjacency matrix of a graph and representing how well two vertices connect to each other in a graph is defined and studied. This communicability cosine distance (CCD) is a Euclidean spherical distance accounting for the cosine of the angles spanned by the position vectors of the graph vertices in this space. The Euclidean distance matrix (EDM) of CCD is used to quantify the similarity between vertices in graphs and networks as well as to define a local vertex invariant—a closeness centrality measure, which discriminate very well vertices in small graphs. It allows to distinguish all nonidentical vertices, also characterizing all identity (asymmetric) graphs–those having only the identity automorphism–among all connected graphs of up to 9 vertices. It also characterizes several other classes of identity graphs. We also study real-world networks in term of both the discriminating power of the new centrality on their vertices as well as in ranking their vertices. We analyze some dictionary networks as well as the network of copurshasing of political books, remarking some of the main advantages of the new approaches studied here.

Temporal Network Embedding Enhanced With Long-Range Dynamics and Self-Supervised Learning.

Temporal network embedding (TNE) has promoted the research of knowledge discovery and reasoning on networks. It aims to embed vertices of temporal networks into a low-dimensional vector space while preserving network structures and temporal properties. However, most existing methods have limitations in capturing dynamics over long distances, which makes it difficult to explore multihop topological associations among vertices. To tackle this challenge, we propose LongTNE, which learns the long-range dynamics of vertices to endow TNE with the ability to capture high-order proximity (HP) of networks. In LongTNE, we employ graph self-supervised learning (Graph SSL) to optimize the establishment probability of deep links in each network snapshot. We also present an accumulated forward update (AFU) module to fathom global temporal evolution among multiple network snapshots. The empirical results on six temporal networks demonstrate that, in addition to achieving state-of-the-art performance on network mining tasks, LongTNE can be handily extended to existing TNE methods.

Interactive experience of sculpture design based on virtual reality technology

Abstract The application of computer technology provides new ideas for the design of sculpture works. In this paper, with the support of virtual reality technology, the pixel set of each color block is extracted from the actual image to determine the location of the center point of the color block. Based on the extracted information, a visual color marking method is used to realize the 3D registration of the sculpture scene. In the virtual scene, through the virtual modeling of the sculpture work, a spline surface model was generated by applying sparse image sequences and optimally adjusted to transform the surface piece control point problem into a quadratic function of the network vertices. The mathematical logic properties of the virtual reality sculpture work wind direction improved by 22.5 points, the mathematical logic properties of the light design improved by 25.8 points, and the mathematical logic properties of the shadow design improved by 23.1 points. The virtual reality technology provides an interactive experience for the design of sculpture works.

Route Planning Based on Parallel Optimization in the Air-Ground Integrated Network

Recent advancement in propulsion technologies to reduce the need for travel or increase the share of sustainable unmanned devices has accelerated the shift toward sustainable transport. To achieve the optimization of route planning in the air-ground integrated network (AGIN), we design an optimization strategy of accompanying graph navigation for unmanned devices, which aims to reduce the power consumption and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CO_2$</tex-math> </inline-formula> gas emissions. The optimization of accompanying graph navigation is composed of three strategies, namely, the navigation based on the complete maps, the navigation based on the partitioned maps, and the navigation without maps. We propose a Two-tiered Grid (TG) index and Distributed AGIN Navigation (DAN) to navigate on partitioned maps. The top layer of the TG-index is composed of the border vertices of the global road network, which reflects the overall traffic conditions of the global road network and provides coarse-grained navigation routes. The bottom layer is a grid index composed of subgraphs, which reflects traffic conditions in local areas and provides fine-grained navigation routes. The navigation optimization is implemented in several segments, which can be run by multi-processors and realize rapid response to a large number of concurrent queries.

Statistics of remote regions of networks

We delve into the statistical properties of regions within complex networks that are distant from vertices with high centralities, such as hubs or highly connected clusters. These remote regions play a pivotal role in shaping the asymptotic behaviours of various spreading processes and the features of associated spectra. We investigate the probability distribution P≥m(s) of the number s of vertices located at distance m or beyond from a randomly chosen vertex in an undirected network. Earlier, this distribution and its large m asymptotics 1/s2 were obtained theoretically for undirected uncorrelated networks (Dorogovtsev et al., 2003). Employing numerical simulations and analysing empirical data, we explore a wide range of real undirected networks and their models, including trees and loopy networks, and reveal that the inverse square law is valid even for networks with strong correlations. We observe this law in the networks demonstrating the small-world effect and containing vertices with degree 1 (so-called leaves or dead ends). We find the specific classes of networks for which this law is not valid. Such networks include the finite-dimensional networks and the networks embedded in finite-dimensional spaces. We notice that long chains of nodes in networks reduce the range of m for which the inverse square law can be spotted. Interestingly, we detect such long chains in the remote regions of the undirected projection of a large Web domain.

CDBRA: Community Detection Based on Random Algorithm in Social Networks

Understanding the topology and functions of complex networks allows us to derive valuable information from them. There are various types of these networks. Community detection is a significant research area that involves dividing a network graph into subsets of nodes, known as communities. Each community consists of nodes that have dense communication with each other and sparse communication with nodes outside the community. This work proposes the use of Community Detection based on random Algorithm (CDBRA) to identify novel communities with low complexity and high accuracy by using both local and global network information. The proposed method consists of four components: Pre-Processing, Node Identification, Intra-Community Structure, and Inter-Community Structure. In the initial component, the task involves recognizing and saving similarity measures. Additionally, it requires assigning suitable weights to network vertex and edges, taking into the account of local and global network information. The next level involves using a random algorithm enhanced by nodes' weights to determine similarity measures for Node Identification. The third level, Intra-Community Structure, aims to achieve various community structures. The fourth level ultimately chooses the optimal community structure by taking into account the Inter-Community Structure and the evaluation functions derived from network’s local and global information. To assess the proposed method on various scenarios involving real and artificial networks. The proposed method outperforms existing methods in detecting community structures similar to real communities and provides efficient evaluation functions for all types and sizes of networks.

Research on the information dissemination method of Chinese culture education based on information dissemination datasetResearch on the information dissemination method of Chinese culture education based on information dissemination dataset

Abstract This paper proposes an evolutionary model of information dissemination based on information exposure states and the underlying topology of social networks. Based on the definition of similarity, the K-means method is used to cluster the categories of information based on the activation of information at the network vertices and to model the “category-category” interactions. The evolution of information dissemination is then explored, and the EGT model is fitted to obtain a gain matrix that reveals the interaction of information, and the quantitative evolution of information is then analyzed. Finally, the information dissemination media of Chinese language and culture education are explored, and the analysis of the dissemination of Chinese language and culture education under various media, comparing the feedback effects of traditional and modern media as representatives of Chinese language and culture classes. Among the feedback results of each medium, the traditional medium’s positive and active feedback indices ranged from 5 to 17, while the modern medium ranged from 12 to 27. The traditional media’s negative and passive feedback indices ranged from 2-3, while the modern media ranged from 3-4. In the field research on the informatization of the Chinese language and culture, the total score for the informatization of the Chinese language and culture curriculum in Yucai Middle School was 0.45, and the total score for Guangming Middle School was 0.65. Modern media can facilitate the spread of the Chinese language and culture to a certain extent.

Defective vertex and stable connectivity of a fuzzy graph and their application to identify the chickenpox

A new concept of vertices in a fuzzy graph known as defective vertices is introduced here. A vertex in a fuzzy network is called defective if no edges incident with it are strong. Defective vertex cannot be ignored when determining dominance in a fuzzy network because they are a part of the network. Finding defective vertices in a network is not much difficult when the adjacency matrix is given. In this paper, the novel concept of defective vertices of a fuzzy graph is introduced. Based on this idea a stable domination set and a stable domination number are defined. This also optimised the network by establishing minimal connectivity. We have proposed three algorithms for finding the defective vertices, establishing stable connectivity, and determining the stable domination number for a given graph. An application of stable domination in the diagnosis of chickenpox disease is demonstrated to show the effectiveness of the proposed algorithms.

Clustering of Multilayer Networks Using Joint Learning Algorithm With Orthogonality and Specificity of Features.

Complex systems in nature and society consist of various types of interactions, where each type of interaction belongs to a layer, resulting in the so-called multilayer networks. Identifying specific modules for each layer is of great significance for revealing the structure-function relations in multilayer networks. However, the available approaches are criticized undesirable because they fail to explicitly the specificity of modules, and balance the specificity and connectivity of modules. To overcome these drawbacks, we propose an accurate and flexible algorithm by joint learning matrix factorization and sparse representation (jMFSR) for specific modules in multilayer networks, where matrix factorization extracts features of vertices and sparse representation discovers specific modules. To exploit the discriminative latent features of vertices in multilayer networks, jMFSR incorporates linear discriminant analysis (LDA) into non-negative matrix factorization (NMF) to learn features of vertices that distinguish the categories. To explicitly measure the specificity of features, jMFSR decomposes features of vertices into common and specific parts, thereby enhancing the quality of features. Then, jMFSR jointly learns feature extraction, common-specific feature factorization, and clustering of multilayer networks. The experiments on 11 datasets indicate that jMFSR significantly outperforms state-of-the-art baselines in terms of various measurements.

Analysis on evolution characteristics and influencing factors of global energy pattern under anti-globalization background

With the rapid development of international energy trade, its structure has shown a trend toward complexity and network development. The traditional unilateral or bilateral perspective of causal analysis can no longer explain the changes in the international energy trade network at this stage. This paper constructs the world energy trade network from 2000 to 2020, analyzes the structural characteristics of the network, and adopts the quadratic assignment procedure method to deconstruct and explain the structural evolution of the world energy trade network. The study shows that the global energy trade network is increasingly connected and has small-world characteristics; the growing global energy demand coexists with the increasing energy monopoly; GDP difference and geographical distance are the decisive factors in forming an international energy trade network. It is suggested that countries should strengthen the integrated development of energy trade; formulate differentiated regional policies according to the structure and economic development characteristics of national and regional energy trade; pay more attention to the hub vertexes in the international energy trade network; and formulate differentiated energy strategies for countries and regions with different development levels, taking into account their development situations.