Graph Theory Concepts Research Articles

Co‐optimising distribution network adequacy and security by simultaneous utilisation of network reconfiguration and distributed energy resources

With the evolution of smart grids, penetration of distributed energy resources (DERs) in the distribution networks has become ever-increasing problem. To improve network reliability, the complexity of the two important aspects of adequacy and security must be well assessed. There is a trade-off between adequacy of DERs, and the distribution network security, i.e. improving the adequacy can reduce the security. In this study, enhancement of the distribution network adequacy and security is proposed. In this regard, capacity of simultaneous reconfiguration and DERs sizing are utilised to improve the adequacy and security of an active distribution network. In the reconfiguration process, graph theory concept is adopted to implement a fast reconfiguration method. Since DERs are active, a combined bus and line security index is used to overcome security concerns of their existence. The IEEE 33-bus distribution network as a widely used standard test system in reconfiguration studies, and a practical 83-bus distribution network of Taiwan Power Company (TPC) which is a part of a real distribution network, are used to test the performance of the proposed method. The simulation results demonstrate the performance of the proposed framework.

Data Mining in Social Networks and its Application in Counterterrorism

Social Networks are best represented as complex interconnected graphs. Graph theory analysis can hence be used for insight into various aspects of these complex social networks. Privacy of such networks lately has been challenged and a detailed analysis of such networks is required. This paper applies key graph theory concepts to analyze such social networks. Moreover, it also discusses applications and proposal of a novel algorithm to analyze and gather key information from terrorist social networks. Investigative Data Mining is used for this which is defined as when Social Network Analysis (SNA) is applied to Terrorist Networks to gather useful insights about the network

Compressive System Identification for Multiple Line Outage Detection in Smart Grids

Real-time power line outage detection (POD) and localization is an important monitoring task for the modern smart grid. Reliable monitoring of power lines status plays a critical role in the system-wide blackout prevention. In this paper, the main aim is to address the multiple POD problems by exploiting the compressive system identification—a time-efficient approach in a complex network analysis. A typical power network is considered as a single graph, and the mathematical formulation of the POD problem is initialized using the dc power-flow model and graph theory concepts. Next, a sparse representation-based formulation for this problem (POD-SRP) is reported and further improved and generalized in case of multiple large-scale outages. Practical and technical challenges associated with this sparse recovery problem are partially addressed by developing new SRP solvers. Furthermore, a new sparse-based mathematical formulation for POD is introduced and termed as “Binary-POD-SRP,” which specifically deals with two particular issues, namely, the high coherence and the signal dynamic outrange. Finally, the identification performance of the proposed framework is evaluated by a variety of case studies, which are modeled using IEEE standard test-beds. We specifically discuss how the inherent challenges within large-scale multiple-outages can be solved by applying these new techniques and formulations.

Comparative Study of Formal Public Transport Network and Informal Public Transport Network of Nagpur, India

In the developing countries along with formal public transport network (FPTN), informal public transport network (IPTN) also plays an integral role by achieving high public transport ridership. IPTN caters effectively to the user’s expectations and appears to be highly integrated with urban fabric. IPTN either complements or compete with the existing FPTN, even though due credit is not given to IPTN and considered as unlawful entities. Efficiency and robustness of transport network is based on topological structure of network. To summarize which network is more efficient and robust, the study tests the network parameters of formal Public Transport Network and Informal Public Transport Network of Nagpur (India). A topological measure of network structure has tested based on elementary concepts of graph theory. We explore the network structure and their properties. The practical significance of the network parameters was then analysed. In the IPTN the degree of small-worldliness is smaller, as compared to FPTN, indicative of IPTN being more robust as compared to FPTN. This study provides an approach to understand the efficiency of an Informal public transport network in combination with Formal public transport network. The article identifies the importance of Informal public transport network to improve the Complementarity with the formal public transport network. Integrating formal and informal transportation network into a hybrid network has the potential to induce the desired relationships amongst FPTN and IPTN, i.e. competing or complimenting nature to improve the overall efficiency of FPTN.

Application of the graph cellular automaton in generating languages

The purpose of this research is to strengthen the core of Cellular Automaton using the concept of Graph theory and Automata theory. In this paper we introduce a new approach of defining the Graph Cellular Automaton GCA, V,I,δ consisting of set of vertices and input symbols along with the time evolution function δ. Using the Basic Linear Rules, we define the kth generation GCA. This method enables us to capture the complete characterization of the future generations. When the defined GCA is taken as a graph corresponding to a given finite automaton, then the language generated by the kth generation GCA is predicted corresponding to the fundamental basic linear rules. This enables us to predict the language of the kth generation automaton using all the 512 rules. All explained concepts are illustrated with suitable examples.

Some algebraic hyperstructures related to zero forcing sets and forcing digraphs

A zero forcing set is a new concept in Graph Theory which was introduced in recent years. In this paper, we investigate the relationship between zero forcing sets and algebraic hyperstructures. To this end, we present some new definitions by considering a zero forcing process on a graph [Formula: see text]. These definitions help us analyze the zero forcing process better and construct various hypergroups and join spaces on the vertex set of graph [Formula: see text]. Finally, we give some examples to clarify these hyperstructures.

The CASCADE toolbox for analyzing river sediment connectivity and management

Sediment connectivity in rivers directly links to fluvial processes and eco-system services. Modelling network-scale sediment connectivity and its response to anthropic alterations, such as dams or land-use changes, is key to better understanding river processes and to inform river basin management. This paper contributes a MatlabTM toolbox for network-scale sediment connectivity based on an implementation of the CASCADE (CAtchment Sediment Connectivity And DElivery) model. CASCADE combines concepts of graph theory with empirical sediment transport formulas to quantify sediment transfers between many connected sediment sources and sinks in a river network. Greater numerical efficiency compared to common hydrodynamic models enables application to large river networks, stochastic simulations of sediment connectivity, and screening impacts of many infrastructure portfolios. Input data requirements are flexible and basic functionality is available with globally available datasets to ensure applicability to data-scarce basins. The toolbox offers options for customization and interactive output visualization tools.

Determining Solvability in the Birds of a Feather Card Game

Birds of a Feather is a single-player card game in which cards are arranged in a grid. The player attempts to combine stacks of cards under certain rules, with the goal being to combine all cards into a single stack. This paper highlights several approaches for efficiently classifying whether a randomlychosen state has a single-stack solution. These approaches use graph theory and machine learning concepts to prune a state’s search space, resulting in significant reductions in runtime relative to a baseline search.

Supply chain network using 3rd dimensional product of vertex measurable graphs

Graph theory concepts applicable in more real life problems. The 3rd dimensional product of vertex measurable graph is applicable in supply chain network. Assigning secondary warehouses and maintaining the selling stores plays important role in supply chain network. In this paper, the mathematical model of 3rd dimensional product of vertex measurable graph is developed and the numerical example is taken to illustrate the model.

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

The purpose of this article is twofold. Firstly, combining concepts of graph theory and of fixed point theory, we will present a fixed point result for Kannan type mappings, in the framework of recently introduced, graphicalb-metric spaces. Appropriate examples of graphs validate the established theory. Secondly, our focus is to apply the proposed results to some nonlinear problems which are meaningful in engineering and science. Some open problems are proposed.

A Graph-Theoretic Approach to Capacity Benefit Margin Calculation for Large Multiarea Power Systems

In a deregulated power market, independent system operators exchange information related to the available transfer capability (ATC) of their respective areas for efficient power system operation. Accurate ATC calculation is important for efficient market operations. Among the parameters required to calculate ATC, the capacity benefit margin (CBM) is an important one. CBM represents the interarea tie-lines capacity reserved in order to have access to external generation in an event of power supply shortage. This paper proposes a new technique for CBM evaluation using graph theory concepts. The proposed technique can be used as an effective tool to solve the CBM problem for large multiarea power systems which are not fully connected and may have multiple deficient areas, unlike previous approaches which considered only fully connected areas with only one deficient area. The IEEE 24-bus reliability test system is employed to implement the proposed method. A performance analysis of the proposed technique shows that it can find a feasible solution efficiently.

A New Heuristic Clustering Algorithm Based on RSU for Internet of Vehicles

The emergence of the Internet of Things has led to the evolution of conventional Vehicular Ad-hoc NETworks (VANETs) toward a new paradigm called the Internet of Vehicles (IoV). This latter has recently received the attention of many researchers. In order to overcome the different challenges, such as high mobility, the number of connected vehicles and the big data, clustering, as an important technique used in a VANET, has significantly improved the performance of numerous applications. In this regard, the present work proposes a new heuristic clustering algorithm based on RSU called HCAR for IoV, which entails the centralization of a clustering algorithm at distributed RSUs. This latter is responsible for performing the cluster formation phase based on a simple heuristic algorithm, using graph theory concepts, such as node degree and adjacency matrix. In addition, HCAR uses a new mechanism to recover the problem of the unavailability of cluster head (CH), through the election of a secondary CH using a weighted mechanism. Moreover, HCAR takes care of the maintenance phase to keep clusters’ stability and structure. The efficiency of the proposed scheme is proven theoretically, and the simulation results, in the NS-2 and VanetMobiSim integrated environment, show its performance advantages.

An Efficient Coloring Algorithm for Time Detraction of Sign Image Segmentation Based on Fuzzy Graph Theory

Graph theory has various applications but sometimes it provides uncertain solutions and hence in order to overcome this, fuzzy graph theory is adopted. Fuzzy graph for any application will be processed by applying the concept of graph coloring because it is one of the most vital concepts in graph theory and it is exploited in many real time applications like scheduling, network security, map coloring, and Global System for Mobile (GSM) mobile phone networks, and so forth. Here, graph coloring is adapted for acquiring proper segmented image and the proper coloring of graph is coloring of the vertices with minimal number of colors such that no any adjacent vertices have the identical color. The graph coloring is based on adaptive Welsh-Powell coloring algorithm. In this article, image segmentation is done for Indian Sign Language (ISL) images and here the image is considered as a fuzzy graph defined on the set of pixels where fuzzy edges represent the distance between pixels.

A Network-Topology-Based Approach for the Load-Flow Solution of AC–DC Distribution System With Distributed Generations

The ac–dc distribution systems have recently gained huge popularity due to advancements in power converters, high penetration of renewable energy resources, and wide usages of dc loads. However, load flow in such systems is a challenging task due to nonlinear characteristics of power converters. This paper presents a novel load-flow algorithm for ac–dc distribution systems, utilizing the concept of graph theory and matrix algebra. Four developed matrices, loads beyond branch matrix, the path impedance matrix, the path drop matrix, and the slack bus to other buses drop matrix, and simple matrix operations are utilized to obtain load-flow solutions. These matrices reveal the network topology and relevant information about the behavior of ac–dc distribution network during load-flow studies. In contrast with traditional load-flow methods for HVDC systems, the proposed technique does not require any lower–upper decomposition, matrix inversion, and forward–backward substitution of the Jacobian matrix. Because of the aforementioned reasons, the developed technique is computationally efficient. The proposed method has been tested using several case studies of ac–dc distribution network, which includes different operating modes of various power converters. Results show the feasibility and authenticity of the proposed method.

Consensus and Eigenvalue Estimation in Dynamic Consensus Networks with Strictly Positive Real Systems

The use of consensus networks in networking has received great attention due to its wide array of applications in fields such as robotics, transportation, sensor networking, communication networking, biology, and physics. The focus of this paper is to study a generalization of consensus problems whereby the weights of network edges are no longer static gains, but instead are dynamic systems, leading to the notion of dynamic consensus networks. Specifically, we consider networks whose nodes are transfer functions (typically integrators) and whose edges are strictly positive real transfer functions representing dynamical systems that couple the nodes. We transform each concept of static graph theory into dynamic terms, out of which a generalized dynamic graph theory naturally emerges. We present a framework for dynamic graphs and dynamic consensus networks. This framework introduces the idea of dynamic degree, adjacency, incident, and Laplacian matrices in a way that naturally extends these concepts from the static case. We show that strictly positive realness of the edges is a sufficient condition for dynamic networks to be stable (i.e., to reach consensus). To study the spectral properties of dynamic networks, we introduce the Dynamic Grounded Laplacian matrix, which is used to estimate lower and upper bounds for the real parts of the smallest and largest non-zero eigenvalues of the dynamic Laplacian matrix. These bounds can be used to obtain stability conditions using the Nyquist graphical stability test for undirected dynamic networks controlled using distributed controllers. Numerical simulations are provided to verify the effectiveness of the results.

Computation in Causal Graphs

The goal of this paper is to introduce some of the important concepts in causal graph theory and examine them from combinatorial and computational perspectives. Of fundamental importance in applications of causal models that use graphs are dependence-separators or, simply, $d$-separators. A vertex set $Z$ is a $d$-separator for a pair of disjoint vertex sets $(X,Y)$ if $X$ and $Y$ are independent conditioned on $Z$. For the case of a single-setpair it is known that $d$-separators can be found efficiently by elegant network flow techniques. In this paper, we consider $d$-separators for a collection $\{(X_1,Y_1),(X_2,Y_2),\dots,(X_k,Y_k)\}$ of setpairs. We focus on two classes of combinatorial objects in this multiple-setpair framework: $d$-separators and $d$-super-separators. We say that $Z$ is a $d$-separator for multiple setpairs if, for each $i$, $X_i$ and $Y_i$ are independent conditioned on $Z$; we say that $Z$ is a $d$-super-separator if, for each $i$, there exists $Z_i\subseteq Z$, such that $X_i$ and $Y_i$ are independent conditioned on $Z_i$. For the latter object, we give an $O(\log^2k)$-approximation algorithm for the problem of finding a minimum cost $d$-super-separator. The focus on approximation algorithms is necessary as we show this problem is NP-complete. For the former object, we show it is hard to determine whether a $d$-separator exists, even when there are just five setpairs. This problem remains hard even if each setpair consists of singleton vertices, provided the number of setpairs is large. On the positive side, we show that if there are a fixed number of singleton setpairs then a $d$-separator for multiple setpairs can be found in polynomial time, if one exists.

Tinnitus Identification based on Brain Network Analysis of EEG Functional Connectivity

Introduction: Tinnitus known as a central nervous system disorder is correlated with specific oscillatory activities within auditory and non-auditory brain areas. Several studies in the past few years have revealed that in the most tinnitus cases, the response pattern of neurons in auditory system is changed due to auditory deafferentation, which leads to variation of the brain networks. According to neuroimaging studies, the human brain is assumed as an organization with the different degree of small-worldness, which is a concept in graph theory. Such organization is able to optimize the functional integration and segregation and therefore efficiently transfer the information among its different pairs of nodes. Materials and Methods: In this paper, we introduce an approach to automatically distinguish tinnitus individuals from healthy controls based on whole-brain functional connectivity and network analysis. Eight participants with tinnitus and eight healthy individuals were included in the study. Resting state electroencephalographic (EEG) data were recorded using a 64-channel recorder. The functional connectivity analysis was applied to the EEG data using Weighted Phase Lag Index (WPLI) for various frequency bands in 2-44 Hz frequency range. The classification was performed on graph theoretical measures using support vector machine (SVM) as a robust classification method. Results: Experimental results showed that the variations of connectivity patterns in tinnitus group were observed within the frontal, temporal and parietal regions. Further, promising classification performance was achieved with a high accuracy, sensitivity, and specificity in all frequency bands. The best classification performance was observed in the beta2 frequency band with accuracy, sensitivity, and specificity of 100%. The results demonstrate that four graph theory based network measures i.e. node strength, clustering coefficient, local efficiency and characteristic path length could successfully discriminate tinnitus from healthy group. Conclusion: The results would be interpreted that the tinnitus network is more segregated but has weaker global efficiency compared to healthy group in high frequencies. In addition, tinnitus individuls presented lower segregation and greater integration relative to the healthy group in the theta frequency domain. As a conclusion, the tinnitus group shows a reduction of small-worldness as well as network integration in high-frequency bands. In general, our study provides substantial evidence that the tinnitus network can be successfully detected by consistent measures of the brain networks based on EEG functional connectivity.

Visibility Graph Feature Model of Vibration Signals: A Novel Bearing Fault Diagnosis Approach.

Reliable fault diagnosis of rolling bearings is an important issue for the normal operation of many rotating machines. Information about the structure dynamics is always hidden in the vibration response of the bearings, and it is often very difficult to extract them correctly due to the nonlinear/chaotic nature of the vibration signal. This paper proposes a new feature extraction model of vibration signals for bearing fault diagnosis by employing a recently-developed concept in graph theory, the visibility graph (VG). The VG approach is used to convert the vibration signals into a binary matrix. We extract 15 VG features from the binary matrix by using the network analysis and image processing methods. The three global VG features are proposed based on the complex network theory to describe the global characteristics of the binary matrix. The 12 local VG features are proposed based on the texture analysis method of images, Gaussian Markov random fields, to describe the local characteristics of the binary matrix. The feature selection algorithm is applied to select the VG feature subsets with the best performance. Experimental results are shown for the Case Western Reserve University Bearing Data. The efficiency of the visibility graph feature model is verified by the higher diagnosis accuracy compared to the statistical and wavelet package feature model. The VG features can be used to recognize the fault of rolling bearings under variable working conditions.

Modeling and control of mine main fan switchover system

Mine main fan switchover system (MMFSS) is crucial for the mine safe production. MMFSS consists of two main fans (one working and one on standby), and each main fan is equipped with a vertical air door and a horizontal air door. The main purpose of MMFSS is to ensure the stability of the underground airflow quantity and achieve the satisfactory ventilation during the switchover. Moreover, the safe and economic operation of mine production should be ensured. In this paper, the modeling and control problem of MMFSS is considered. First, based on the theory of fluid flow network, the minimal model of MMFSS is built by combining the branch fluid dynamics with the concept of graph theory. Then, a decentralized controller that fully considers the pressure head regulation of two main fans is developed by the Lyapunov stability theory. The controller can ensure that the four air doors can meet with the technological requirements. Finally, the proposed results are conformed using simulations on a semi-physical simulation platform for MMFSS.

A Study on Slope Number of Certain Classes of Bipartite Graphs

Graph drawing is the most important area of mathematics and computer science which combines methods from geometric graph theory and information visualization. Generally, graphs are represented to explore some intellectual ideas. Graph drawing is the familiar concept of graph theory. It has many quality measures and one among them is the slope number. Slope number problem is an optimization problem and is NP-hard to determine the slope number of any arbitrary graph. In the present paper, the investigation on slope number of bipartite graph is studied elaborately. Since the bipartite graphs creates one of the most intensively investigated classes of graphs, we consider few classes of graphs and discussed structural behavior of such graphs.