Types Of Vertices Research Articles

On the Study of Structural Equivalency for Animal Conservation in Species-Habitat Network Form

Kerinci Seblat National Park is a combination of 17 forest groups located on the island of Sumatra. This study will discuss modeling the relationship between animals and their habitats in the form of an ecological network. The relationship between species and habitat is an essential topic in animal conservation. This relationship can be modeled as a graph called the habitat-species network, with two types of vertices: species (V^s ) or habitat (V^h ). The edge connecting a species vertex and a habitat vertex represents the species ever visiting the habitat. This study aimed to discuss three measures for describing the relationship between species and habitats: structural equivalence, Jaccard similarity, and Pearson’s correlation coefficient. Structural equivalence of a group of habitats represents the similarity of animals that visit the same habitat, the Jaccard similarity describes the percentage of habitats visited by a pair of different animals, and Pearson’s correlation coefficient shows the significance of the relationship between the two species.

Micromagnetic simulations of emergent monopole defects and magnetization reversal in connected and dipolar Square Artificial Spin Ice

Artificial spin ice (ASI) structures have garnered significant attention due to their unique properties including emergent magnetic monopoles, phase transitions, and collective switching dynamics. In this study, we employ micromagnetic simulations to investigate the magnetic microstates and magnetization reversal dynamics of square ASI with varying connectivity. In particular, we explore an intermediate or a quasi-connected system where the connectivity is altered without significantly changing the strength of dipolar interactions through the introduction of narrow gaps at the vertices. Our results reveal distinct differences in the populations of different vertex types during magnetic reversal for lattices with varying connectivity. These results suggest the possibility of engineering ASI systems in which specific vertex types can be repeatably accessed through adjustments in lattice connectivity.

Optimal Network Analysis through Vertex Order Coloring of Intuitionistic Fuzzy Graph Operations

Intuitionistic fuzzy graphs (IFGs) are a powerful tool for modeling uncertainty and complex relationships. They offer versatile frameworks for addressing real‐world challenges. In this research, we have introduced intuitionistic fuzzy vertex order coloring (IFVOC) and analyzed the alpha‐strong (), beta‐strong (), and gamma‐strong () vertices through their degree. We explored important theorems based on the types of strong vertices, broadening the scope of our study. We analyzed multiple IFG products to determine the most optimal network based on some important metrics, including the weight and total number of vertices, the chromatic number, and the weight of the graph’s minimum spanning tree. We systematically evaluate different types of IFG products, such as conormal, modular, residue, and maximal, and consider their implications for fuzzy graph structure and connectivity. We have investigated new metrics to measure the presence and importance of vertices in the graph, assessing both their frequency and overall impact. Additionally, we have investigated the impact of product operations on the significance of nodes and the resultant minimum spanning tree, providing insights into the overall robustness and efficiency of each product. We have explored how variations in product operations impact the distribution of vertices and the characteristics of the minimum spanning tree and chromatic number, elucidating the trade‐offs between different product options. We have modeled the product graph as a network to represent complex systems composed of interconnected entities. The outcomes of this research contribute to the advancement of IFG theory and its use in various fields, such as network design, strategic planning, and system analysis.

Certain Types of Vertices in m-Polar Fuzzy Graphs

In this study, we explore the concept of m-polar fuzzy (mPF) detour g-eccentric nodes within m-polar fuzzy graphs (mPFGs). We delve into the idea of mPF detour g-interior nodes and mPF detour g-boundary nodes, examining their significance and properties. Additionally, we establish the relationship between mPF detour g-boundary vertices and mPF cut vertices.

Coarsening effects on k-partite network classification

The growing data size poses challenges for storage and computational processing time in semi-supervised models, making their practical application difficult; researchers have explored the use of reduced network versions as a potential solution. Real-world networks contain diverse types of vertices and edges, leading to using k-partite network representation. However, the existing methods primarily reduce uni-partite networks with a single type of vertex and edge. We develop a new coarsening method applicable to the k-partite networks that maintain classification performance. The empirical analysis of hundreds of thousands of synthetically generated networks demonstrates the promise of coarsening techniques in solving large networks’ storage and processing problems. The findings indicate that the proposed coarsening algorithm achieved significant improvements in storage efficiency and classification runtime, even with modest reductions in the number of vertices, leading to over one-third savings in storage and twice faster classifications; furthermore, the classification performance metrics exhibited low variation on average.

Densest Multipartite Subgraph Search in Heterogeneous Information Networks

Cohesive multipartite subgraphs (CMS) in heterogeneous information networks (HINs) uncover closely connected vertex groups of multiple types, enhancing real applications like community search and anomaly detection. However, existing works for HINs pay less attention to searching CMS. In this paper, we leverage well-established concepts of meta-path and densest subgraph to propose a novel CMS model called the densest P -partite subgraph. Given a multipartite subgraph of an HIN induced by i =| P | types of vertices defined in a query meta-path P (i.e., a P -partite subgraph), we devise a novel density function which is the number of the instances of P over the geometric mean of the sizes of i different types of vertex sets in the subgraph. A P -partite subgraph with the highest density serves as the optimum result. To find the densest P -partite subgraph in an HIN with n vertices, we first design an exact algorithm with a runtime cost equivalent to solving Θ(|M|) instances of the min-cut problem where |M|= O (( n/i ) i ). Then, we attempt a more efficient approximation algorithm that achieves a ratio of 1/ i but still incurs the cost of solving Θ(|M|) instances of our proposed peeling problem. Both approaches struggle with scalability due to Θ(|M|). To overcome this bottleneck, we improve the exact algorithm with novel pruning rules that non-trivially reduce the number of min-cut problem instances to solve to O (|M|). Empirically, 70-90% instances are pruned, making the improved exact algorithm significantly faster than the approximation algorithm. Extensive experiments on real datasets demonstrate the effectiveness of the proposed model and the efficiency of our algorithms.

Influential Community Search over Large Heterogeneous Information Networks

Recently, the topic of influential community search has gained much attention. Given a graph, it aims to find communities of vertices with high importance values from it. Existing works mainly focus on conventional homogeneous networks, where vertices are of the same type. Thus, they cannot be applied to heterogeneous information networks (HINs) like bibliographic networks and knowledge graphs, where vertices are of multiple types and their importance values are of heterogeneity (i.e., for vertices of different types, their importance meanings are also different). In this paper, we study the problem of influential community search over large HINs. We introduce a novel community model, called heterogeneous influential community (HIC), or a set of closely connected vertices that are of the same type and high importance values, using the meta-path-based core model. An HIC not only captures the importance of vertices in a community, but also considers the influence on meta-paths connecting them. To search the HICs, we mainly consider meta-paths with two and three vertex types. Then, we develop basic algorithms by iteratively peeling vertices with low importance values, and further propose advanced algorithms by identifying the key vertices and designing pruning strategies that allow us to quickly eliminate vertices with low importance values. Extensive experiments on four real large HINs show that our solutions are effective for searching HICs, and the advanced algorithms significantly outperform baselines.

A large-deviations principle for all the components in a sparse inhomogeneous random graph

We study an inhomogeneous sparse random graph, {mathcal G }_N, on [N]={1,dots ,N} as introduced in a seminal paper by Bollobás et al. (Random Struct Algorithms 31(1):3–122, 2007): vertices have a type (here in a compact metric space {mathcal S }), and edges between different vertices occur randomly and independently over all vertex pairs, with a probability depending on the two vertex types. In the limit Nrightarrow infty , we consider the sparse regime, where the average degree is O(1). We prove a large-deviations principle with explicit rate function for the statistics of the collection of all the connected components, registered according to their vertex type sets, and distinguished according to being microscopic (of finite size) or macroscopic (of size asymp N). In doing so, we derive explicit logarithmic asymptotics for the probability that {mathcal G }_N is connected. We present a full analysis of the rate function including its minimizers. From this analysis we deduce a number of limit laws, conditional and unconditional, which provide comprehensive information about all the microscopic and macroscopic components of {mathcal G }_N. In particular, we recover the criterion for the existence of the phase transition given in Bollobás et al. (2007).

Wiener index of a directed rough fuzzy graph and application to human trafficking

In this paper, we introduced Wiener index ( WI ) and average Wiener index ( AWI ) of directed rough fuzzy graph (DRFG). WI is the most extensively used index in graph theory. This index is based on the geodesic distance between two vertices. If there is no directed path from vertex x to vertex y in DRFG, we assume that the weight of geodesic from vertex x to vertex y is zero. In this paper, we investigate the connection between WI and connectivity index ( CI ), which is one of the most prominent index, by presenting several examples and results. We introduced the concept of complete directed rough fuzzy graph (CDRFG) along with some useful results like CDRFG have no weak edges. We also compute the WI for CDRFG. Moreover, we discussed three types of vertices: Wiener enhancing vertex (WEV), Wiener reducing vertex (WRV), and Wiener neutral vertex (WNV). The proposed study of DRFG is suitable for modeling uncertainties and unclear data information in the real life circumstances. In the end, we proposed an application of the WI in the human trafficking network. We also presented a detailed comparative analysis and comparison table by comparing our result for both CI and WI for the same human trafficking network.

Approach to reduce the communication cost when partitioning a big graph

While several graph mining systems have been developed to run different graph mining algorithms on such large networks, they have difficulty processing Web-scale graphs owing to the significant communication and I/O expenses incurred when workers connect with one another and frequently read subgraphs. In this study, we provide a cost-effective, scalable, distributed method for mining real-world graphs by exploiting graph properties. Our technique drastically decreases the communication cost, the main bottleneck of distributed systems, by using alternate edge placement criteria depending on the types of vertices.

Molecular network analysis of hormonal contraceptives side effects via database integration

Hormonal contraceptives (HCs) have been shown to be safe and effective when used correctly and consistently, however, as other classes of drugs, they are also associated with adverse health outcomes. In this study, we aim to explain the occurrence of common and unexpected HCs side effects (SEs) integrating drug-target, drug-SE and protein-protein interaction (PPI) public databases. We created a tripartite network that includes three types of vertices: SEs, drugs, and targets. The three layers are linked by means of the inter-layer associations drug-target and drug-SE, whereas only the target layer is characterized also by intra-layer links (PPIs). We exploited the drug-mediated association SE-target to identify the side effect modules defined as a network connected component composed of target proteins plus the proteins needed to connect them. We found that module proteins are associated with diseases/phenotypes and/or KEGG pathways related to the SEs. In particular, in many cases, targets are not enriched in SE features, whereas investigating their neighborhood (here defined as the proteins that allow the targets' connection) we found SE-related pathways. These results show that HCs action can perturb the targets’ neighborhood inducing unwanted reaction and that the proposed approach can help to understand how, and through which molecular mechanisms, side effects can occur. The approach is general in its nature: it can be applied to other drugs categories providing a support in identifying a subject-specific therapy that takes into account comorbidities and lifestyle to reduce or avoid the most undesired side effects.

Demand and influencing factors of Ice-Snow sports tourism products using heterogeneous network

<abstract> <p>Heterogeneous networks are complex directed graphs that incorporate multiple types of vertices and edges, enabling the representation of diverse structural and semantic information, and facilitating the abstraction of real-world phenomena. In the context of modern-day societal demands and pressures, individuals seek emotional solace and physical well-being. Notably, China has witnessed a surge in winter sports tourism, with outdoor activities such as skiing gaining increased attention. However, research in this field is sporadic and lacks a comprehensive analysis of the distinctive features of snow and ice sports tourism. Hence, this paper proposes to investigate the demand for ice and snow sports tourism products and its underlying factors using a heterogeneous network model. Drawing upon relevant theories and content, the study analyzes the primary drivers of the development of ice and snow sports tourism. Furthermore, based on the evaluation of ice and snow sports attractions across five major cities, the research synthesizes various product requirements that affect both existing and potential consumers of ice and snow sports tourism. The ultimate aim is to provide practical insights to guide the development and design of ice and snow sports tourism products and ensure the sustainable development of tourism destinations. The final experimental results reveal that the three most crucial aspects of ice and snow sports tourism products are entertainment, stimulation, and safety, with respective effective rates of 64.0%, 62.1%, and 58.9%.</p> </abstract>

Connectivity indices of m-polar fuzzy network model, with an application to a product manufacturing problem

Connectivity is among the most essential concerns in graph theory and its applications. We consider this issue in a framework that stems from the combination of m-polar fuzzy set theory with graphs. We introduce two measurements of connectedness of m-polar fuzzy graphs that we call their connectivity and average connectivity indices. Examples are given, and the theoretical performance of these concepts is investigated. Particularly, we are concerned with the effect of deleting a vertex or an edge from an m-polar fuzzy graph, on its connectivity and average connectivity indices. We also establish bounding expressions for the connectivity index in complete m-polar fuzzy graphs, complete bipartite m-polar fuzzy graphs, and wheel m-polar fuzzy graphs. Moreover, we introduce some special types of vertices called m-polar fuzzy connectivity reducing vertices, m-polar fuzzy connectivity enhancing vertices, and m-polar fuzzy connectivity neutral vertices. Our theoretical contribution is applied to a product manufacturing problem that takes advantage of multi-polar uncertain information. The justification for our application is systematized using an algorithm. Finally, we compare the proposed method to existing methodologies to demonstrate its feasibility and applicability.

Directed rough fuzzy graph with application to trade networking

In the realm of linking networks to the real world, connectivity (strength of connectedness) plays a crucial role. In this article, we introduce three types of vertices based on the indegree and outdegree of the vertices of directed rough fuzzy networks (DRFNs). We also define the concept of strength-reducing sets (mathcal {SRS}s) of DRF-vertices, DRF-edges, and important related results using the strongest path in directed rough fuzzy graphs (DRFGs). We generalize the idea of Menger’s theorem of vertices and edges in directed fuzzy graphs to directed rough fuzzy graphs which are appropriate for dealing with uncertainty in information systems. Furthermore, we use alpha strong DRF-edges, beta strong DRF-edges and delta DRF-edges to identify developing countries most affected by trade deficits during COVID-19. Finally, our research results are compared with existing methods to demonstrate their applicability and productivity.

Graph optimization algorithm using symmetry and host bias for low-latency indirect network

It is known that an indirect network with a small host-to-host Average Shortest Path Length (h-ASPL) improves overall system performance in a parallel computer system. As a means to discuss such indirect networks in graph theory, the Order/Radix Problem (ORP) has been proposed. ORP involves finding a graph with a minimum h-ASPL that satisfies a given number of hosts and radix. A graph in ORP represents an indirect network and has two types of vertices: host and switch. We propose an optimization algorithm to generate graphs with a sufficiently small h-ASPL. The primary features of the proposed algorithm are the symmetry of the graph and the bias of the hosts adjacent to each switch. These features reduce the computational time to calculate the h-ASPL and improve the search performance of the algorithm. The performance of the proposed algorithm is evaluated using problems presented by Graph Golf, an international ORP competition. Our results show that the proposed algorithm can generate graphs with a smaller h-ASPL than the existing algorithm. To evaluate the performance of the graphs generated by the proposed algorithm, we use the parallel simulation framework SimGrid and the parallel benchmark collection NAS Parallel Benchmarks. Our results also show that the graphs generated by the proposed algorithm have higher performance than those generated by the existing algorithm.

Business processes monitoring based on fuzzy cognitive maps

The subject matter of the article is a toolkit and monitoring processes of weakly structured business processes using fuzzy cognitive maps (FCMs). The goal is to create a model for monitoring and forecasting the course of business processes based on the FCMs, which provide flexibility and the ability to adapt to the conditions of changing circumstances in the process to be monitored, as well as insurance of the possibility of applying unstable FCM.s The task is to develop a formal monitoring system model; develop a computational FCM model; develop a method of using unstable FCMs: to develop a method for creating and using an FCM model. The methods used are graph modeling methods and computational experiment methods. The following results were obtained. A formal model of the system of monitoring and coordination of decisions regarding the course of business processes has been developed. A model of a weighted semantic graph was developed, which includes three types of vertices, namely, input vertices that will receive subjective evaluations of users regarding the course of the process, intermediate vertices that correspond to factors important from the perspective of the decision-maker, and final vertices that reflect integral evaluations of the quality of business process execution. A computational FCM model has been developed, which can adapt to the specifics of business logic due to the flexible adjustment of memory parameters and connections between FCM nodes. A method of using unstable FCMs has been developed. A methodology for creating and using FCMs designed for monitoring weakly structured business processes has been developed. Conclusions. The scientific novelty of the work is as follows: the model for monitoring and forecasting the course of business processes due to the use of a fuzzy cognitive map, in which the parameters of the importance and node memory and connections provide additional flexibility and the possibility of coordination and adaptation in the conditions of changing circumstances in the process to be monitored has been improved; a method of using unstable FCMs by setting limits on the values of the nodes excitation and using as a measure of excitation not only stable excitation values of FCM nodes but also the rate of growth of excitation values as an indicator of trends, which allows monitoring and forecasting the course of business processes has been proposed.

Stochastic symplectic ice

In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term “stochastic symplectic ice”. The models consist of alternating rows of two types of vertices. The probabilistic interpretation of the models leads to novel interacting particle systems where particles alternately jump to the right and then to the left. Two colored versions of the models and related stochastic dynamics are also introduced. Using the Yang–Baxter equations, we establish functional equations and recursive relations for the partition functions of these models. In particular, the recursive relations satisfied by the partition function of one of the colored models are closely related to Demazure–Lusztig operators of type C.

An ensemble model to optimize modularity in dynamic bipartite networks

Distinct non-random quantitative interactions at diverse timestamps formulate real-world dynamic complex networks. The most frequently used class of methods for discovering communities in dynamic networks is modularity optimization that evaluates the quality of the partition of network nodes into distinct communities. The bipartite networks have bipartite modularity and bipartite modularity optimization respectively. Newman's modularity is a consistently used algorithm to evaluate modules of unipartite networks yet it is ineffective for assessing the division of bipartite networks with two types of vertices. Many community detection methods suggest bipartite modularity to accommodate this issue. They usually employ information about the existence or lack of interactions between nodes. In quantitative networks, weighted modularity is a potential approach for measuring the quality of community partitions (Lu et al. IEEE, 179–184, 2013). This study offers an ensemble model for detecting one-mode communities and optimizing modularity in dynamic bipartite weighted networks. By using collaborative weighted projection, bipartite networks get projected into two weighted one-mode networks. The results of experiments both on real-world dynamic network data and synthetic data demonstrate that the modularity of the method is significantly greater than that of current techniques and the communities discovered contain vertices of comparable kinds exhibiting the suggested algorithm's performance is ample.

GIS-Analysis Of The Ural Power Grid Vulnerability To The Impact Of Sleet And Wind

In this paper, we describe an experiment of complex power grid structure and wind and sleet mapping of territory using two different network indices: standard edge betweenness centrality and new author’s index – electrical grid centrality. Such analysis of the network allows to identify power lines with high load which could be vulnerable elements of the power grid. It is very important for strategic planning of power grids to reduce the risk of accidents by distributing loads across several lines so that they will be able to reserve each other. As a case territory for this research, we took the Ural united power system in Russia which is greatly exposed to different sleet and wind according to the statistics of the power grid operator. The degree of natural hazard consequences could be compensated by the network structure through alternative paths of energy supply or vice versa – increased if they are absent. At the same time, in this paper we consider that power grids have their own features from the graph theory point of view, for example multiple (parallel) edges, branches, different types of vertices. The existing index of edge betweenness centrality does not perfectly cope with them. We compare two indices characterizing power line importance within the system – betweenness centrality and electrical grid centrality and analyze the network structure features together with the spatial distribution of sleet and wind. As a result, we could identify bottlenecks in the study network. According to this study the most vulnerable power lines were detected, for example 500 kV Iriklinskaya CHP – Gazovaya and 500 kV Yuzhnouralskaya CHP-2 – Shagol power lines, that supply big cities such as Chelyabinsk and Orenburg and a bunch of industries around them.

Motifs, coherent configurations and second order network generation

In this paper we illuminate some algebraic-combinatorial structure underlying the second order networks (SONETS) random graph model of Zhao, Beverlin, Netoff and Nykamp and collaborators (Fuller, 2016; Zhao, 2012; Zhao et al. 2011). In particular we show that this algorithm is deeply connected with a certain homogeneous coherent configuration, a non-commuting generalization of the classical Johnson scheme. This algebraic structure underlies certain surprising, previously unobserved, identities satisfied by the covariance matrices in the SONETS model. We show that an understanding of this algebraic structure leads to simplified numerical methods for carrying out the linear algebra required to implement the SONETS algorithm. We also show that the SONETS method can be substantially generalized to allow different types of vertices and/or edges, and that these generalizations enjoy similar algebraic structure.