Search results for: network knowledge graph

Authors: Mahdi Jalili

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Functional connectivity in the human brain can be represented as a network using electroencephalography (EEG) signals. Network representation of EEG time series can be an efficient vehicle to understand the underlying mechanisms of brain function. Brain functional networks – whose nodes are brain regions and edges correspond to functional links between them – are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which graph theory metrics are sex dependent. To this end, EEGs from 24 healthy female subjects and 21 healthy male subjects were recorded in eyes-closed resting state conditions. The connectivity matrices were extracted using correlation analysis and were further binarized to obtain binary functional networks. Global and local efficiency measures – as graph theory metrics– were computed for the extracted networks. We found that male brains have a significantly greater global efficiency (i.e., global communicability of the network) across all frequency bands for a wide range of cost values in both hemispheres. Furthermore, for a range of cost values, female brains showed significantly greater right-hemispheric local efficiency (i.e., local connectivity) than male brains.

Keywords: EEG, brain, functional networks, network science, graph theory

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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

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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

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Authors: Lin Cheng, Zijiang Yang

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Program synthesis is the task to automatically generate programs based on user specification. In this paper, we present a framework that synthesizes programs from flow charts that serve as accurate and intuitive specification. In order doing so, we propose a deep neural network called GRCNN that recognizes graph structure from its image. GRCNN is trained end-to-end, which can predict edge and node information of the flow chart simultaneously. Experiments show that the accuracy rate to synthesize a program is 66.4%, and the accuracy rates to recognize edge and node are 94.1% and 67.9%, respectively. On average, it takes about 60 milliseconds to synthesize a program.

Keywords: program synthesis, flow chart, specification, graph recognition, CNN

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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: 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

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Authors: Cao Xiaopeng, Shi Linkai

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The practical Byzantine fault-tolerant algorithm does not add nodes dynamically. It is limited in practical application. In order to add nodes dynamically, Dynamic Practical Byzantine Fault Tolerance Algorithm (DPBFT) was proposed. Firstly, a new node sends request information to other nodes in the network. The nodes in the network decide their identities and requests. Then the nodes in the network reverse connect to the new node and send block information of the current network. The new node updates information. Finally, the new node participates in the next round of consensus, changes the view and selects the master node. This paper abstracts the decision of nodes into the undirected connected graph. The final consistency of the graph is used to prove that the proposed algorithm can adapt to the network dynamically. Compared with the PBFT algorithm, DPBFT has better fault tolerance and lower network bandwidth.

Keywords: practical byzantine, fault tolerance, blockchain, consensus algorithm, consistency analysis

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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

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Authors: Andrey Lebedev, Ilya Dmitrenok, JooYoung Lee, Leonard Johard

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Top-k shortest path routing problem is an extension of finding the shortest path in a given network. Shortest path is one of the most essential measures as it reveals the relations between two nodes in a network. However, in many real world networks, whose diameters are small, top-k shortest path is more interesting as it contains more information about the network topology. Many variations to compute top-k shortest paths have been studied. In this paper, we apply an efficient top-k shortest distance routing algorithm to the link prediction problem and test its efficacy. We compare the results with other base line and state-of-the-art methods as well as with the shortest path. Then, we also propose a top-k distance based graph matching algorithm.

Keywords: graph matching, link prediction, shortest path, similarity

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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

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Authors: Raghavi C. Janaswamy

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In the healthcare sector, heterogenous data elements such as patients, diagnosis, symptoms, conditions, observation text from physician notes, and prescriptions form the essentials of the Electronic Health Record (EHR). The data in the form of clear text and images are stored or processed in a relational format in most systems. However, the intrinsic structure restrictions and complex joins of relational databases limit the widespread utility. In this regard, the design and development of realistic mapping and deep connections as real-time objects offer unparallel advantages. Herein, a graph neural network-based classification of EHR data has been developed. The patient conditions have been predicted as a node classification task using a graph-based open source EHR data, Synthea Database, stored in Tigergraph. The Synthea DB dataset is leveraged due to its closer representation of the real-time data and being voluminous. The graph model is built from the EHR heterogeneous data using python modules, namely, pyTigerGraph to get nodes and edges from the Tigergraph database, PyTorch to tensorize the nodes and edges, PyTorch-Geometric (PyG) to train the Graph Neural Network (GNN) and adopt the self-supervised learning techniques with the AutoEncoders to generate the node embeddings and eventually perform the node classifications using the node embeddings. The model predicts patient conditions ranging from common to rare situations. The outcome is deemed to open up opportunities for data querying toward better predictions and accuracy.

Keywords: electronic health record, graph neural network, heterogeneous data, prediction

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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

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Authors: Scott N. Gerard, Aliza Heching, Susann M. Keohane, Samuel S. Adams

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The world-wide population of people over 60 years of age is growing rapidly. The explosion is placing increasingly onerous demands on individual families, multiple industries and entire countries. Current, human-intensive approaches to eldercare are not sustainable, but IoT and AI technologies can help. The Knowledge Reactor (KR) is a contextual, data fusion engine built to address this and other similar problems. It fuses and centralizes IoT and System of Record/Engagement data into a reactive knowledge graph. Cognitive applications and services are constructed with its multiagent architecture. The KR can scale-up and scaledown, because it exploits container-based, horizontally scalable services for graph store (JanusGraph) and pub-sub (Kafka) technologies. While the KR can be applied to many domains that require IoT and AI technologies, this paper describes how the KR specifically supports the challenging domain of cognitive eldercare. Rule- and machine learning-based analytics infer activities of daily living from IoT sensor readings. KR scalability, adaptability, flexibility and usability are demonstrated.

Keywords: ambient sensing, AI, artificial intelligence, eldercare, IoT, internet of things, knowledge graph

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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: Shin-Shin Kao, Hsiu-Chunj Pan

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Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3-ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered [1]. Furthermore, based on computer experimental results in [1], it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

Keywords: Hamiltonian cycle, 4-ordered, Chordal rings, 3-regular

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Authors: Margarita Mayoral-Villa, J. Klapp, L. Di G. Sigalotti, J. E. V. Guzmán

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Automated learning techniques are widely applied in the energy sector to address challenging problems from a practical point of view. To this end, we discuss the implementation of a Message Passing algorithm (MPNN)within a Graph Neural Network(GNN)to leverage the neighborhood of a set of nodes during the aggregation process. This approach enables the characterization of multiphase diffusion processes in the reservoir, such that the flow paths underlying the interconnections between multiple wells may be inferred from previously available data on flow rates and bottomhole pressures. The results thus obtained compare favorably with the predictions produced by the Reduced Order Capacitance-Resistance Models (CRM) and suggest the potential of MPNNs to enhance the robustness of the forecasts while improving the computational efficiency.

Keywords: multiphase diffusion, message passing neural network, well interconnection, interwell connectivity, graph neural network, capacitance-resistance models

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Authors: Krishnendra Shekhawat

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Given a graph G = (V, E), a rectangular dual of G represents the vertices of G by a set of interior-disjoint rectangles such that two rectangles touch if and only if there is an edge between the two corresponding vertices in G. Rectangular duals do not exist for every graph, so we can define maximal rectangular duals. A maximal rectangular dual is a rectangular dual of a graph G such that there exists no graph G ′ with a rectangular dual where G is a subgraph of G ′. In this paper, we enumerate all maximal rectangular duals (or, to be precise, the corresponding planar graphs) up to six nodes and presents a necessary condition for the existence of a rectangular dual. This work allegedly has applications in integrated circuit design and architectural floor plans.

Keywords: adjacency, degree sequence, dual graph, rectangular dual

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Authors: Pallavi Bhogaram, Xiaolong Wu, Min He, Onyedikachi Okenwa

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A transportation network is a realization of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity. Examples include road networks, railways, air routes, pipelines, and many more. The transportation network plays a vital role in maintaining the vigor of the nation’s economy. Hence, ensuring the network stays resilient all the time, especially in the face of challenges such as heavy traffic loads and large scale natural disasters, is of utmost importance. In this paper, we used the Neo4j application to develop the graph. Neo4j is the world's leading open-source, NoSQL, a native graph database that implements an ACID-compliant transactional backend to applications. The Southern California network model is developed using the Neo4j application and obtained the most critical and optimal nodes and paths in the network using centrality algorithms. The edge betweenness centrality algorithm calculates the critical or optimal paths using Yen's k-shortest paths algorithm, and the node betweenness centrality algorithm calculates the amount of influence a node has over the network. The preliminary study results confirm that the Neo4j application can be a suitable tool to study the important nodes and the critical paths for the major congested metropolitan area.

Keywords: critical path, transportation network, connectivity reliability, network model, Neo4j application, edge betweenness centrality index

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Authors: Zahra Ramezanpanah, Joachim Carvallo, Aurelien Rodriguez

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This paper aims to detect anomalies in streaming data using machine learning algorithms. In this regard, we designed two separate pipelines and evaluated the effectiveness of each separately. The first pipeline, based on supervised machine learning methods, consists of two phases. In the first phase, we trained several supervised models using the UNSW-NB15 data-set. We measured the efficiency of each using different performance metrics and selected the best model for the second phase. At the beginning of the second phase, we first, using Argus Server, sniffed a local area network. Several types of attacks were simulated and then sent the sniffed data to a running algorithm at short intervals. This algorithm can display the results of each packet of received data in real-time using the trained model. The second pipeline presented in this paper is based on unsupervised algorithms, in which a Temporal Graph Network (TGN) is used to monitor a local network. The TGN is trained to predict the probability of future states of the network based on its past behavior. Our contribution in this section is introducing an indicator to identify anomalies from these predicted probabilities.

Keywords: temporal graph network, anomaly detection, cyber security, IDS

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Authors: Po-Jen Chen, Jian-Jiun Ding, Hung-Wei Hsu, Chien-Yao Wang, Jia-Ching Wang

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A more accurate scene classification algorithm using label relations and the hierarchy neural network was developed in this work. In many classification algorithms, it is assumed that the labels are mutually exclusive. This assumption is true in some specific problems, however, for scene classification, the assumption is not reasonable. Because there are a variety of objects with a photo image, it is more practical to assign multiple labels for an image. In this paper, two label relations, which are exclusive relation and hierarchical relation, were adopted in the classification process to achieve more accurate multiple label classification results. Moreover, the hierarchy neural network (hierarchy NN) is applied to classify the image and the directed acyclic graph structure is used for predicting a more reasonable result which obey exclusive and hierarchical relations. Simulations show that, with these techniques, a much more accurate scene classification result can be achieved.

Keywords: convolutional neural network, label relation, hierarchy neural network, scene classification

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Authors: Yan Li

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Purpose: There is a lack of suitable recommendation systems to assist engineering teaching. The existing traditional engineering pedagogies lack learning interests for postgraduate students. The knowledge graph-based recommender system aims to enhance postgraduate students’ programming skills, with a focus on programming courses. Design/methodology/approach: The case study will be used as a major research method, and the two case studies will be taken in both two teaching styles of the universities (Zhejiang University and the University of Nottingham Ningbo China), followed by the interviews. Quantitative and qualitative research methods will be combined in this study. Research limitations/implications: The case studies were only focused on two teaching styles universities, which is not comprehensive enough. The subject was limited to postgraduate students. Originality/value: The study collected and analyzed the data from two teaching styles of universities’ perspectives. It explored the challenges of Engineering education and tried to seek potential enhancement.

Keywords: knowledge graph and recommender system, engineering pedagogy, programming skills, postgraduate students

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Authors: Mostafa Gamal, Hoda K. Mohamed, Islam El-Maddah, Ali Hamdi

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In recent years, many digital documents on the web have been created due to the rapid growth of ’social applications’ communities or ’Data-intensive applications’. The evolution of online-based multimedia data poses new challenges in storing and querying large amounts of data for online recommender systems. Graph data models have been shown to be more efficient than relational data models for processing complex data. This paper will explain the key differences between graph and relational databases, their strengths and weaknesses, and why using graph databases is the best technology for building a realtime recommendation system. Also, The paper will discuss several similarity metrics algorithms that can be used to compute a similarity score of pairs of nodes based on their neighbourhoods or their properties. Finally, the paper will discover how NLP strategies offer the premise to improve the accuracy and coverage of realtime recommendations by extracting the information from the stored unstructured knowledge, which makes up the bulk of the world’s data to enrich the graph database with this information. As the size and number of data items are increasing rapidly, the proposed system should meet current and future needs.

Keywords: graph databases, NLP, recommendation systems, similarity metrics

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Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.

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One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.

Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial

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Authors: A. Kulandai Therese

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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: Tet H. Yeap

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An analog restricted Hopfield Network is presented in this paper. It consists of two layers of nodes, visible and hidden nodes, connected by directional weighted paths forming a bipartite graph with no intralayer connection. An energy or Lyapunov function was derived to show that the proposed network will converge to stable states. By introducing hidden nodes, the proposed network can be trained to store patterns and has increased memory capacity. Training to be an associative memory, simulation results show that the associative memory performs better than a classical Hopfield network by being able to perform better memory recall when the input is noisy.

Keywords: restricted Hopfield network, Lyapunov function, simultaneous perturbation stochastic approximation

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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

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Authors: Raed Hanandeh

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This empirical study examines how knowledge sharing behaviors mediate the effect Technology-driven strategy on virtual organization success in Jordanian tourism sector firms. The results reveal that Social network ties are positively related to web knowledge seeking, web knowledge contributing and interactive system, but negatively related to accidental knowledge leakage. Furthermore, all types of knowledge sharing behavior are positively related to virtual organization success. Data collected from 23 firms. The total number of questionnaires mailed, 250 questionnaires were delivered. 214 were considered valid out of 241 Responses were received. The findings provide evidence that knowledge sharing behavior play a mediating role between Social network ties and virtual organization success and show that, web knowledge seeking, web knowledge contributing and interactive system playing an important impact on virtual organization success through knowledge sharing behaviors.

Keywords: social network ties, virtual organization success, knowledge sharing behaviors, web knowledge

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Authors: Mo-Se Lee, Cheol-Hwi Ahn, Kee-Young Kwahk, Hyunchul Ahn

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Over the past decade, deep learning has been in spotlight among various machine learning algorithms. In particular, CNN (Convolutional Neural Network), which is known as effective solution for recognizing and classifying images, has been popularly applied to classification and prediction problems in various fields. In this study, we try to apply CNN to stock market prediction, one of the most challenging tasks in the machine learning research. In specific, we propose to apply CNN as the binary classifier that predicts stock market direction (up or down) by using a graph as its input. That is, our proposal is to build a machine learning algorithm that mimics a person who looks at the graph and predicts whether the trend will go up or down. Our proposed model consists of four steps. In the first step, it divides the dataset into 5 days, 10 days, 15 days, and 20 days. And then, it creates graphs for each interval in step 2. In the next step, CNN classifiers are trained using the graphs generated in the previous step. In step 4, it optimizes the hyper parameters of the trained model by using the validation dataset. To validate our model, we will apply it to the prediction of KOSPI200 for 1,986 days in eight years (from 2009 to 2016). The experimental dataset will include 14 technical indicators such as CCI, Momentum, ROC and daily closing price of KOSPI200 of Korean stock market.

Keywords: convolutional neural network, deep learning, Korean stock market, stock market prediction

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Authors: Ezgi Kaya, A. Dilek Maden

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A topological index is a number related to graph which is invariant under graph isomorphism. In theoretical chemistry, molecular structure descriptors (also called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds. Let G be a graph with n vertices and m edges. For a given edge uv, the quantity nu(e) denotes the number of vertices closer to u than v, the quantity nv(e) is defined analogously. The vertex PI index defined as the sum of the nu(e) and nv(e). Here the sum is taken over all edges of G. The energy of a graph is defined as the sum of the eigenvalues of adjacency matrix of G and the Laplacian energy of a graph is defined as the sum of the absolute value of difference of laplacian eigenvalues and average degree of G. In theoretical chemistry, the π-electron energy of a conjugated carbon molecule, computed using the Hückel theory, coincides with the energy. Hence results on graph energy assume special significance. The Laplacian matrix of a graph G weighted by the vertex PI weighting is the Laplacian vertex PI matrix and the Laplacian vertex PI eigenvalues of a connected graph G are the eigenvalues of its Laplacian vertex PI matrix. In this study, Laplacian vertex PI energy of a graph is defined of G. We also give some bounds for the Laplacian vertex PI energy of graphs in terms of vertex PI index, the sum of the squares of entries in the Laplacian vertex PI matrix and the absolute value of the determinant of the Laplacian vertex PI matrix.

Keywords: energy, Laplacian energy, laplacian vertex PI eigenvalues, Laplacian vertex PI energy, vertex PI index

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Authors: Stefan Wagenpfeil, Felix Engel, Paul McKevitt, Matthias Hemmje

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Multimedia Indexing and Retrieval is generally designed and implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results but also leads to more complex graph structures. However, graph-traversal-based algorithms for similarity are quite inefficient and computation intensive, especially for large data structures. To deliver fast and effective retrieval, an efficient similarity algorithm, particularly for large graphs, is mandatory. Hence, in this paper, we define a graph-projection into a 2D space (Graph Code) as well as the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph-traversals due to a simpler processing model and a high level of parallelization. In consequence, we prove that the effectiveness of retrieval also increases substantially, as Graph Codes facilitate more levels of detail in feature fusion. Thus, Graph Codes provide a significant increase in efficiency and effectiveness (especially for Multimedia indexing and retrieval) and can be applied to images, videos, audio, and text information.

Keywords: indexing, retrieval, multimedia, graph algorithm, graph code

Procedia PDF Downloads 161