Search results for: graph representation of circuit networks

Authors: Kay Thi Yar, Khin Mar Lar Tun

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Nowadays, social networks are so popular and widely used in all over the world. In addition, searching personal information of each person and searching connection between them (peoples’ relation in real world) becomes interesting issue in our society. In this paper, we propose a framework with three portions for exploring peoples’ relations from their connected information. The first portion focuses on the Graph database structure to store the connected data of peoples’ information. The second one proposes the graph database searching algorithm, the Modified-SoS-ACO (Sense of Smell-Ant Colony Optimization). The last portion proposes the Deductive Reasoning Algorithm to define two persons’ relationship. This study reveals the proper storage structure for connected information, graph searching algorithm and deductive reasoning algorithm to predict and analyze the personnel relationship from peoples’ relation in their connected information.

Keywords: personnel information, graph storage structure, graph searching algorithm, deductive reasoning algorithm

Procedia PDF Downloads 416

Authors: Nileshkumar Vishnav, Aditya Tatu

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A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

Procedia PDF Downloads 319

Authors: Manuel Meranza-Castillon, Rolando Diaz-Castillo, Adrian Arellano-Delgado, Cesar Cruz-Hernandez, Rosa Martha Lopez-Gutierrez

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In this work, we deal with experimental network synchronization of chaotic nodes with different topologies. Our approach is based on complex system theory, and we use a master-slave configuration to couple the nodes in the networks. In particular, we design and implement electronically complex dynamical networks composed by nine coupled chaotic Chua’s circuits with topologies: in nearest-neighbor, small-world, open ring, star, and global. Also, network synchronization is evaluated according to a particular coupling strength for each topology. This study is important by the possible applications to private transmission of information in a chaotic communication network of multiple users.

Keywords: complex networks, Chua's circuit, experimental synchronization, multiple users

Procedia PDF Downloads 317

Authors: Robert Gold

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Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modelled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyse the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: control flow graph, graph reduction, software engineering, software applications

Procedia PDF Downloads 517

Authors: Qiuyi Lyu, Bin Gong

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Breadth-First Search(BFS) is a core graph algorithm that is widely used for graph analysis. As it is frequently used in many graph applications, improve the BFS performance is essential. In this paper, we present a graph ordering method that could reorder the graph nodes to achieve better data locality, thus, improving the BFS performance. Our method is based on an observation that the sibling relationships will dominate the cache access pattern during the BFS traversal. Therefore, we propose a frequency-based model to construct the graph order. First, we optimize the graph order according to the nodes’ visit frequency. Nodes with high visit frequency will be processed in priority. Second, we try to maximize the child nodes overlap layer by layer. As it is proved to be NP-hard, we propose a heuristic method that could greatly reduce the preprocessing overheads. We conduct extensive experiments on 16 real-world datasets. The result shows that our method could achieve comparable performance with the state-of-the-art methods while the graph ordering overheads are only about 1/15.

Keywords: breadth-first search, BFS, graph ordering, graph algorithm

Procedia PDF Downloads 107

Authors: Gowtham Kalkere Jayanna, Mohamad Nazri Husin

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Graph theory, chemistry, and technology are all combined in cheminformatics. The structure and physiochemical properties of organic substances are linked using some useful graph invariants and the corresponding molecular graph. In this paper, we study specific reverse topological indices such as the reverse sum-connectivity index, the reverse Zagreb index, the reverse arithmetic-geometric, and the geometric-arithmetic, the reverse Sombor, the reverse Nirmala indices for the bistar graphs B (n: m) and the corona product Kₘ∘Kₙ', where Kₙ' Represent the complement of a complete graph Kₙ.

Keywords: reverse topological indices, bistar graph, the corona product, graph

Procedia PDF Downloads 58

Authors: S. R. Nayaka, Putta Swamy

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Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

Procedia PDF Downloads 216

Authors: Stefan K. Behfar

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The rapid growth of the Ethereum network has brought forth the urgent need for scalable analysis methods to handle the increasing volume of blockchain data. In this research, we propose efficient methodologies for making Ethereum network analysis scalable. Our approach leverages a combination of graph-based data representation, probabilistic sampling, and parallel processing techniques to achieve unprecedented scalability while preserving critical network insights. Data Representation: We develop a graph-based data representation that captures the underlying structure of the Ethereum network. Each block transaction is represented as a node in the graph, while the edges signify temporal relationships. This representation ensures efficient querying and traversal of the blockchain data. Probabilistic Sampling: To cope with the vastness of the Ethereum blockchain, we introduce a probabilistic sampling technique. This method strategically selects a representative subset of transactions and blocks, allowing for concise yet statistically significant analysis. The sampling approach maintains the integrity of the network properties while significantly reducing the computational burden. Graph Convolutional Networks (GCNs): We incorporate GCNs to process the graph-based data representation efficiently. The GCN architecture enables the extraction of complex spatial and temporal patterns from the sampled data. This combination of graph representation and GCNs facilitates parallel processing and scalable analysis. Distributed Computing: To further enhance scalability, we adopt distributed computing frameworks such as Apache Hadoop and Apache Spark. By distributing computation across multiple nodes, we achieve a significant reduction in processing time and enhanced memory utilization. Our methodology harnesses the power of parallelism, making it well-suited for large-scale Ethereum network analysis. Evaluation and Results: We extensively evaluate our methodology on real-world Ethereum datasets covering diverse time periods and transaction volumes. The results demonstrate its superior scalability, outperforming traditional analysis methods. Our approach successfully handles the ever-growing Ethereum data, empowering researchers and developers with actionable insights from the blockchain. Case Studies: We apply our methodology to real-world Ethereum use cases, including detecting transaction patterns, analyzing smart contract interactions, and predicting network congestion. The results showcase the accuracy and efficiency of our approach, emphasizing its practical applicability in real-world scenarios. Security and Robustness: To ensure the reliability of our methodology, we conduct thorough security and robustness evaluations. Our approach demonstrates high resilience against adversarial attacks and perturbations, reaffirming its suitability for security-critical blockchain applications. Conclusion: By integrating graph-based data representation, GCNs, probabilistic sampling, and distributed computing, we achieve network scalability without compromising analytical precision. This approach addresses the pressing challenges posed by the expanding Ethereum network, opening new avenues for research and enabling real-time insights into decentralized ecosystems. Our work contributes to the development of scalable blockchain analytics, laying the foundation for sustainable growth and advancement in the domain of blockchain research and application.

Keywords: Ethereum, scalable network, GCN, probabilistic sampling, distributed computing

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Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

Procedia PDF Downloads 39

Authors: Somayeh Sadat Hashemi Kamangar, Fatemeh Bakouie, Shahriar Gharibzadeh

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In this study, we target to exploit Maximum Spanning Trees (MST) of children's semantic networks to investigate their language development. To do so, we examine the graph-theoretic properties of word-embedding networks. The networks are made of words children learn prior to the age of 30 months as the nodes and the links which are built from the cosine vector similarity of words normatively acquired by children prior to two and a half years of age. These networks are weighted graphs and the strength of each link is determined by the numerical similarities of the two words (nodes) on the sides of the link. To avoid changing the weighted networks to the binaries by setting a threshold, constructing MSTs might present a solution. MST is a unique sub-graph that connects all the nodes in such a way that the sum of all the link weights is maximized without forming cycles. MSTs as the backbone of the semantic networks are suitable to examine developmental changes in semantic network topology in children. From these trees, several parameters were calculated to characterize the developmental change in network organization. We showed that MSTs provides an elegant method sensitive to capture subtle developmental changes in semantic network organization.

Keywords: maximum spanning trees, word-embedding, semantic networks, language development

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Authors: Lee Myung-Won, Kwak Keun-Chang

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This paper is concerned with knowledge representation and extraction of fuzzy if-then rules using Interval Type-2 Context-based Fuzzy C-Means clustering (IT2-CFCM) with the aid of fuzzy granulation. This proposed clustering algorithm is based on information granulation in the form of IT2 based Fuzzy C-Means (IT2-FCM) clustering and estimates the cluster centers by preserving the homogeneity between the clustered patterns from the IT2 contexts produced in the output space. Furthermore, we can obtain the automatic knowledge representation in the design of Radial Basis Function Networks (RBFN), Linguistic Model (LM), and Adaptive Neuro-Fuzzy Networks (ANFN) from the numerical input-output data pairs. We shall focus on a design of ANFN in this paper. The experimental results on an estimation problem of energy performance reveal that the proposed method showed a good knowledge representation and performance in comparison with the previous works.

Keywords: IT2-FCM, IT2-CFCM, context-based fuzzy clustering, adaptive neuro-fuzzy network, knowledge representation

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Authors: Hend Alrasheed

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Due to their different properties that have led to avoid several limitations of classic client/server systems, there has been a great interest in the development and the improvement of different peer to peer systems. Understanding the properties of complex peer to peer networks is essential for their future improvements. It was shown that the performances of peer to peer protocols are directly related to their underlying topologies. Therefore, multiple efforts have analyzed the topologies of different peer to peer systems. This study presents an overview of major findings of close experimental analyses to different topologies of three unstructured peer to peer systems: BitTorrent, Gnutella, and FreeNet.

Keywords: peer to peer networks, network topology, graph diameter, clustering coefficient, small-world property, random graph, degree distribution

Procedia PDF Downloads 354

Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

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This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

Procedia PDF Downloads 185

Authors: A. Boulanoir, B. Ould Bouamama, A. Debiane, N. Achour

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The paper deals with robust Fault Detection and isolation with respect to parameter uncertainties based on linear fractional transformation form (LFT) Bond graph. The innovative interest of the proposed methodology is the use only one representation for systematic generation of robust analytical redundancy relations and adaptive residual thresholds for sensibility analysis. Furthermore, the parameter uncertainties are introduced graphically in the bond graph model. The methodology applied to the nonlinear industrial Electro-Mechanical Actuators (EMA) used in avionic systems, has determined first the structural monitorability analysis (which component can be monitored) with given instrumentation architecture with any need of complex calculation and secondly robust fault indicators for online supervision.

Keywords: bond graph (BG), electro mechanical actuators (EMA), fault detection and isolation (FDI), linear fractional transformation (LFT), mechatronic systems, parameter uncertainties, avionic system

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Authors: Tamas Madl

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Sudden cardiac death (SCD) constitutes a large proportion of cardiovascular mortalities, provides little advance warning, and the risk is difficult to recognize based on ubiquitous, low cost medical equipment such as the standard, 12-lead, ten second ECG. Autonomic abnormalities have been shown to be strongly predictive of SCD risk; yet current methods are not trivially applicable to the brevity and low temporal and electrical resolution of standard ECGs. Here, we build horizontal visibility graph representations of very short inter-beat interval time series, and perform unsuper- vised representation learning in order to convert these variable size objects into fixed-length vectors preserving similarity rela- tions. We show that such representations facilitate classification into healthy vs. at-risk patients on two different datasets, the Mul- tiparameter Intelligent Monitoring in Intensive Care II and the PhysioNet Sudden Cardiac Death Holter Database. Our results suggest that graph representation learning of heartbeat interval time series facilitates robust classification even in sequences as short as ten seconds.

Keywords: sudden cardiac death, heart rate variability, ECG analysis, time series classification

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Authors: Vadim E. Levit, Eugen Mandrescu

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A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered.

Keywords: maximum independent set, corona, concatenation, join, well-covered graph

Procedia PDF Downloads 174

Authors: Jiajun Wang, Xiaoge Li

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The purpose of the aspect-level sentiment analysis task is to identify the sentiment polarity of aspects in a sentence. Currently, most methods mainly focus on using neural networks and attention mechanisms to model the relationship between aspects and context, but they ignore the dependence of words in different ranges in the sentence, resulting in deviation when assigning relationship weight to other words other than aspect words. To solve these problems, we propose a new aspect-level sentiment analysis model that combines a multi-channel convolutional network and graph convolutional network (GCN). Firstly, the context and the degree of association between words are characterized by Long Short-Term Memory (LSTM) and self-attention mechanism. Besides, a multi-channel convolutional network is used to extract the features of words in different ranges. Finally, a convolutional graph network is used to associate the node information of the dependency tree structure. We conduct experiments on four benchmark datasets. The experimental results are compared with those of other models, which shows that our model is better and more effective.

Keywords: aspect-level sentiment analysis, attention, multi-channel convolution network, graph convolution network, dependency tree

Procedia PDF Downloads 171

Authors: Yasmeen A. S. Essawy, Khaled Nassar

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With the rapid increase of complexity in the building industry, professionals in the A/E/C industry were forced to adopt Building Information Modeling (BIM) in order to enhance the communication between the different project stakeholders throughout the project life cycle and create a semantic object-oriented building model that can support geometric-topological analysis of building elements during design and construction. This paper presents a model that extracts topological relationships and geometrical properties of building elements from an existing fully designed BIM, and maps this information into a directed acyclic Elemental Graph Data Model (EGDM). The model incorporates BIM-based search algorithms for automatic deduction of geometrical data and topological relationships for each building element type. Using graph search algorithms, such as Depth First Search (DFS) and topological sortings, all possible construction sequences can be generated and compared against production and construction rules to generate an optimized construction sequence and its associated schedule. The model is implemented in a C# platform.

Keywords: building information modeling (BIM), elemental graph data model (EGDM), geometric and topological data models, graph theory

Procedia PDF Downloads 345

Authors: Dimitra Alexiou

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In an urban area the allocation placement of an emergency service mobile units, such as ambulances, police patrol must be designed so as to achieve a prompt response to demand locations. In this paper, a partition of a given urban network into distinct sub-networks is performed such that; the vertices in each component are close and simultaneously the difference of the sums of the corresponding population in the sub-networks is almost uniform. The objective here is to position appropriately in each sub-network a mobile emergency unit in order to reduce the response time to the demands. A mathematical model in the framework of graph theory is developed. In order to clarify the corresponding method a relevant numerical example is presented on a small network.

Keywords: graph partition, emergency service, distances, location

Procedia PDF Downloads 459

Authors: Khidir R. Sharaf, Didar A. Ali

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The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: graph theory, graph spectra, nullity of graphs, statistic

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Authors: Skiker Kaoutar, Mounir Maouene

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Neuroimaging studies have shown that animal and tool concepts rely on distinct networks of brain areas. Animal concepts depend predominantly on temporal areas while tool concepts rely on fronto-temporo-parietal areas. However, the origin of this neurofunctional distinction for processing animal and tool concepts remains still unclear. Here, we address this question from a network perspective suggesting that the neural distinction between animals and tools might reflect the differences in their structural semantic networks. We build semantic networks for animal and tool concepts derived from Mc Rae and colleagues’s behavioral study conducted on a large number of participants. These two networks are thus analyzed through a large number of graph theoretical measures for small-worldness: centrality, clustering coefficient, average shortest path length, as well as resistance to random and targeted attacks. The results indicate that both animal and tool networks have small-world properties. More importantly, the animal network is more vulnerable to targeted attacks compared to the tool network a result that correlates with brain lesions studies.

Keywords: animals, tools, network, semantics, small-world, resilience to damage

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Authors: Hanlin Liu, Hua Li, Yintan AI

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Network performance prediction (NPP) is essential for the management and optimization of software-defined networking (SDN) and contributes to improving the quality of service (QoS) in SDN to meet the requirements of users. Although current deep learning-based methods can achieve high effectiveness, they still suffer from some problems, such as difficulty in capturing global information of the network, inefficiency in modeling end-to-end network performance, and inadequate graph feature extraction. To cope with these issues, our proposed Graphormer-based architecture for NPP leverages the powerful graph representation ability of Graphormer to effectively model the graph structure data, and a node-edge transformation algorithm is designed to transfer the feature extraction object from nodes to edges, thereby effectively extracting the end-to-end performance characteristics of the network. Moreover, routing oriented centrality measure coefficient for nodes and edges is proposed respectively to assess their importance and influence within the graph. Based on this coefficient, an enhanced feature extraction method and an advanced centrality encoding strategy are derived to fully extract the structural information of the graph. Experimental results on three public datasets demonstrate that the proposed GraphNPP architecture can achieve state-of-the-art results compared to current NPP methods.

Keywords: software-defined networking, network performance prediction, Graphormer, graph neural network

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Authors: Yong Seo Koo, Jong Ho Nam, Yong Nam Choi, Dae Yeol Yoo, Jung Woo Han

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This paper presents a silicon controller rectifier (SCR) based ESD protection circuit for IC. The proposed ESD protection circuit has low trigger voltage and high holding voltage compared with conventional SCR ESD protection circuit. Electrical characteristics of the proposed ESD protection circuit are simulated and analyzed using TCAD simulator. The proposed ESD protection circuit verified effective low voltage ESD characteristics with low trigger voltage and high holding voltage.

Keywords: electro-static discharge (ESD), silicon controlled rectifier (SCR), holding voltage, protection circuit

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Authors: Asraful Islam

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Extended dependency graph (EDG) is a state-of-the-art isomorphic graph to represent normal logic programs (NLPs) that can characterize the consistency of NLPs by graph analysis. To construct the vertices and arcs of an EDG, additional renaming atoms and rules besides those the given program provides are used, resulting in higher space complexity compared to the corresponding traditional dependency graph (TDG). In this article, we propose an extended labeled dependency graph (ELDG) to represent an NLP that shares an equal number of nodes and arcs with TDG and prove that it is isomorphic to the domain program. The number of nodes and arcs used in the underlying dependency graphs are formulated to compare the space complexity. Results show that ELDG uses less memory to store nodes, arcs, and cycles compared to EDG. To exhibit the desirability of ELDG, firstly, the stable models of the kernel form of NLP are characterized by the admissible coloring of ELDG; secondly, a relation of the stable models of a kernel program with the handles of the minimal, odd cycles appearing in the corresponding ELDG has been established; thirdly, to our best knowledge, for the first time an inverse transformation from a dependency graph to the representing NLP w.r.t. ELDG has been defined that enables transferring analytical results from the graph to the program straightforwardly.

Keywords: normal logic program, isomorphism of graph, extended labelled dependency graph, inverse graph transforma-tion, graph colouring

Procedia PDF Downloads 182

Authors: Guiheng Zhang, Wei Zhang, Jun Fu, Yudong Wang

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A 900 MHz three-stage SiGe power amplifier (PA) with high power gain is presented in this paper. Volterra Series is applied to analyze nonlinearity sources of SiGe HBT device model clearly. Meanwhile, the influence of operating current to IMD3 is discussed. Then a β-helper current mirror bias circuit is applied to improve linearity, since the β-helper current mirror bias circuit can offer stable base biasing voltage. Meanwhile, it can also work as predistortion circuit when biasing voltages of three bias circuits are fine-tuned, by this way, the power gain and operating current of PA are optimized for best linearity. The three power stages which fabricated by 0.18 μm SiGe technology are bonded to the printed circuit board (PCB) to obtain impedances by Load-Pull system, then matching networks are done for best linearity with discrete passive components on PCB. The final measured three-stage PA exhibits 21.1 dBm of output power at 1 dB compression point (OP1dB) with power added efficiency (PAE) of 20.6% and 33 dB power gain under 3.3 V power supply voltage.

Keywords: high gain power amplifier, linearization bias circuit, SiGe HBT model, Volterra series

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Authors: Ahmed Hamida Boudinar, Noureddine Benouzza, Azeddine Bendiabdellah, Mohamed El Amine Khodja

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This paper describes a new diagnosis approach for identification of the progressive stator winding inter-turn short-circuit fault in induction motor. This approach is based on a simple monitoring of the combined information related to both magnitude and phase-angle obtained from the fundamental by the three line currents frequency analysis. In addition, to simplify the interpretation and analysis of the data; a new graphical tool based on a triangular representation is suggested. This representation, depending on its size, enables to visualize in a simple and clear manner, the existence of the stator inter-turn short-circuit fault and its discrimination with respect to a healthy stator. Experimental results show well the benefit and effectiveness of the proposed approach.

Keywords: induction motor, magnitude, phase-angle, spectral analysis, stator fault

Procedia PDF Downloads 334

Authors: A. Kulandai Therese

Abstract:

The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs.

Keywords: corona graph, degree, eccentricity, eccentric connectivity index, first zagreb index, second zagreb index, subdivision graphs

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

Procedia PDF Downloads 366

Authors: Gaye Ibrahima, Mendy Gervais, Seck Diaraf, Ouya Samuel

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In this paper, we consider the influence maximization in social networks. Here we give importance to initial diffuser called the seeds. The goal is to find efficiently a subset of k elements in the social network that will begin and maximize the information diffusion process. A new approach which treats the social network before to determine the seeds, is proposed. This treatment eliminates the information feedback toward a considered element as seed by extracting an acyclic spanning social network. At first, we propose two algorithm versions called SCG − algoritm (v1 and v2) (Spanning Connected Graphalgorithm). This algorithm takes as input data a connected social network directed or no. And finally, a generalization of the SCG − algoritm is proposed. It is called SG − algoritm (Spanning Graph-algorithm) and takes as input data any graph. These two algorithms are effective and have each one a polynomial complexity. To show the pertinence of our approach, two seeds set are determined and those given by our approach give a better results. The performances of this approach are very perceptible through the simulation carried out by the R software and the igraph package.

Keywords: acyclic spanning graph, centrality measures, information feedback, influence maximization, social network

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Authors: Tribhuvan N. Soorya

Abstract:

Charging and discharging of a capacitor through a resistor can be shown as exponential curve. Theoretically, it takes infinite time to fully charge or discharge a capacitor. The flow of charge is due to electrons having finite and fixed value of charge. If we carefully examine the charging and discharging process after several time constants, the points on q vs t graph become discrete and curve become discontinuous. Moreover for all practical purposes capacitor with charge (q0-e) can be taken as fully charged, as it introduces an error less than one part per million. Similar is the case for discharge of a capacitor, where the capacitor with the last electron (charge e) can be taken as fully discharged. With this, we can estimate the finite value of time for fully charging and discharging a capacitor.

Keywords: charging, discharging, RC Circuit, capacitor

Procedia PDF Downloads 417