Journal articles on the topic 'Relation Graphs'
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1
Gholap, P. S., and V. E. Nikumbh. "TOPOLOGICAL SPACES GENERATED BY GRAPH." Jnanabha 52, no. 01 (2022): 01–07. http://dx.doi.org/10.58250/jnanabha.2022.52101.
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n this paper we discuss topological spaces generated by simple graphs using adjacency relation and non adjacency relation on vertices. We establish important results showing relations between complete graph and discrete topological space. We also discuss the topological spaces related to complete graphs, isomorphic graphs and study their properties. Further we discuss the interior and closure operators and their properties. Our motivation is to give an fundamental step toward linkage between topology and graph so as to study different aspects of graphs in terms of topological properties
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Ke, Xiangyu, Arijit Khan, and Francesco Bonchi. "Multi-relation Graph Summarization." ACM Transactions on Knowledge Discovery from Data 16, no. 5 (October 31, 2022): 1–30. http://dx.doi.org/10.1145/3494561.
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Graph summarization is beneficial in a wide range of applications, such as visualization, interactive and exploratory analysis, approximate query processing, reducing the on-disk storage footprint, and graph processing in modern hardware. However, the bulk of the literature on graph summarization surprisingly overlooks the possibility of having edges of different types. In this article, we study the novel problem of producing summaries of multi-relation networks, i.e., graphs where multiple edges of different types may exist between any pair of nodes. Multi-relation graphs are an expressive model of real-world activities, in which a relation can be a topic in social networks, an interaction type in genetic networks, or a snapshot in temporal graphs. The first approach that we consider for multi-relation graph summarization is a two-step method based on summarizing each relation in isolation, and then aggregating the resulting summaries in some clever way to produce a final unique summary. In doing this, as a side contribution, we provide the first polynomial-time approximation algorithm based on the k -Median clustering for the classic problem of lossless single-relation graph summarization. Then, we demonstrate the shortcomings of these two-step methods, and propose holistic approaches, both approximate and heuristic algorithms, to compute a summary directly for multi-relation graphs. In particular, we prove that the approximation bound of k -Median clustering for the single relation solution can be maintained in a multi-relation graph with proper aggregation operation over adjacency matrices corresponding to its multiple relations. Experimental results and case studies (on co-authorship networks and brain networks) validate the effectiveness and efficiency of the proposed algorithms.
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Ratheesh, K. P. "On Soft Graphs and Chained Soft Graphs." International Journal of Fuzzy System Applications 7, no. 2 (April 2018): 85–102. http://dx.doi.org/10.4018/ijfsa.2018040105.
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Soft set theory has a rich potential for application in many scientific areas such as medical science, engineering and computer science. This theory can deal uncertainties in nature by parametrization process. In this article, the authors explore the concepts of soft relation on a soft set, soft equivalence relation on a soft set, soft graphs using soft relation, vertex chained soft graphs and edge chained soft graphs and investigate various types of operations on soft graphs such as union, join and complement. Also, it is established that every fuzzy graph is an edge chained soft graph.
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Guo, Yunfei, Fei Yin, Wei Feng, Xudong Yan, Tao Xue, Shuqi Mei, and Cheng-Lin Liu. "Social Relation Reasoning Based on Triangular Constraints." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 1 (June 26, 2023): 737–45. http://dx.doi.org/10.1609/aaai.v37i1.25151.
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Social networks are essentially in a graph structure where persons act as nodes and the edges connecting nodes denote social relations. The prediction of social relations, therefore, relies on the context in graphs to model the higher-order constraints among relations, which has not been exploited sufficiently by previous works, however. In this paper, we formulate the paradigm of the higher-order constraints in social relations into triangular relational closed-loop structures, i.e., triangular constraints, and further introduce the triangular reasoning graph attention network (TRGAT). Our TRGAT employs the attention mechanism to aggregate features with triangular constraints in the graph, thereby exploiting the higher-order context to reason social relations iteratively. Besides, to acquire better feature representations of persons, we introduce node contrastive learning into relation reasoning. Experimental results show that our method outperforms existing approaches significantly, with higher accuracy and better consistency in generating social relation graphs.
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Koch, Sebastian. "Unification of Graphs and Relations in Mizar." Formalized Mathematics 28, no. 2 (July 1, 2020): 173–86. http://dx.doi.org/10.2478/forma-2020-0015.
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Summary A (di)graph without parallel edges can simply be represented by a binary relation of the vertices and on the other hand, any binary relation can be expressed as such a graph. In this article, this correspondence is formalized in the Mizar system [2], based on the formalization of graphs in [6] and relations in [11], [12]. Notably, a new definition of createGraph will be given, taking only a non empty set V and a binary relation E ⊆ V × V to create a (di)graph without parallel edges, which will provide to be very useful in future articles.
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Yang, Wenjie, Jianlin Zhang, Jingju Cai, and Zhiyong Xu. "Relation Selective Graph Convolutional Network for Skeleton-Based Action Recognition." Symmetry 13, no. 12 (November 30, 2021): 2275. http://dx.doi.org/10.3390/sym13122275.
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Graph convolutional networks (GCNs) have made significant progress in the skeletal action recognition task. However, the graphs constructed by these methods are too densely connected, and the same graphs are used repeatedly among channels. Redundant connections will blur the useful interdependencies of joints, and the overly repetitive graphs among channels cannot handle changes in joint relations between different actions. In this work, we propose a novel relation selective graph convolutional network (RS-GCN). We also design a trainable relation selection mechanism. It encourages the model to choose solid edges to work and build a stable and sparse topology of joints. The channel-wise graph convolution and multiscale temporal convolution are proposed to strengthening the model’s representative power. Furthermore, we introduce an asymmetrical module named the spatial-temporal attention module for more stable context modeling. Combining those changes, our model achieves state-of-the-art performance on three public benchmarks, namely NTU-RGB+D, NTU-RGB+D 120, and Northwestern-UCLA.
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Flippen, Christopher, Allison H. Moore, and Essak Seddiq. "Quotients of the Gordian and H(2)-Gordian graphs." Journal of Knot Theory and Its Ramifications 30, no. 05 (April 2021): 2150037. http://dx.doi.org/10.1142/s0218216521500371.
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The Gordian graph and H(2)-Gordian graphs of knots are abstract graphs whose vertex sets represent isotopy classes of unoriented knots, and whose edge sets record whether pairs of knots are related by crossing changes or H(2)-moves, respectively. We investigate quotients of these graphs under equivalence relations defined by several knot invariants including the determinant, the span of the Jones polynomial, and an invariant related to tricolorability. We show, in all cases considered, that the quotient graphs are Gromov hyperbolic. We then prove a collection of results about the graph isomorphism type of the quotient graphs. In particular, we find that the H(2)-Gordian graph of links modulo the relation induced by the span of the Jones polynomial is isomorphic with the complete graph on infinitely many vertices.
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Sun, Ke, Shuo Yu, Ciyuan Peng, Yueru Wang, Osama Alfarraj, Amr Tolba, and Feng Xia. "Relational Structure-Aware Knowledge Graph Representation in Complex Space." Mathematics 10, no. 11 (June 4, 2022): 1930. http://dx.doi.org/10.3390/math10111930.
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Relations in knowledge graphs have rich relational structures and various binary relational patterns. Various relation modelling strategies are proposed for embedding knowledge graphs, but they fail to fully capture both features of relations, rich relational structures and various binary relational patterns. To address the problem of insufficient embedding due to the complexity of the relations, we propose a novel knowledge graph representation model in complex space, namely MARS, to exploit complex relations to embed knowledge graphs. MARS takes the mechanisms of complex numbers and message-passing and then embeds triplets into relation-specific complex hyperplanes. Thus, MARS can well preserve various relation patterns, as well as structural information in knowledge graphs. In addition, we find that the scores generated from the score function approximate a Gaussian distribution. The scores in the tail cannot effectively represent triplets. To address this particular issue and improve the precision of embeddings, we use the standard deviation to limit the dispersion of the score distribution, resulting in more accurate embeddings of triplets. Comprehensive experiments on multiple benchmarks demonstrate that our model significantly outperforms existing state-of-the-art models for link prediction and triple classification.
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Yurttas Gunes, Aysun, Sadik Delen, Musa Demirci, Ahmet Sinan Cevik, and Ismail Naci Cangul. "Fibonacci Graphs." Symmetry 12, no. 9 (August 19, 2020): 1383. http://dx.doi.org/10.3390/sym12091383.
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Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant Ω to obtain some more information on these graphs. We give the necessary and sufficient conditions for the realizability of a set D of n successive Fibonacci numbers for every n and also list all possible realizations called Fibonacci graphs for 1≤n≤4.
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An, Dezhi, Xuejie Ma, Cao Jiang, Lei Liu, and Yanxu Wang. "Research and Application of Relation Extraction based on Triple Relation Graph Convolutional Networks." Journal of Physics: Conference Series 2166, no. 1 (January 1, 2022): 012060. http://dx.doi.org/10.1088/1742-6596/2166/1/012060.
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Abstract In recent years, data in non-Euclidean spaces is becoming more and more. Traditional methods cannot perform feature extraction on these data. Most of existing methods just extract contextual semantic features from relational instances. Their structural features in corpora are ignored. To solve this problem, the paper proposed a relation extraction method based on triple relation graph convolutional networks (TRGCN). Based on the extraction of semantic features of sentences using convolutional neural networks, this method used the concept of triple relation graphs to represent structural features. In other words, triple relation graphs were formed by considering triples formed by the relation between two entities in one sentence as nodes and triples with common entities and same relations as edges. Finally, multiple-layer graph convolutional networks were used for training. As shown by experimental results, the method proposed in this paper achieved an F1 value of 86.8% on the SemEval 2010 Tesk 8 data set, indicating that it is better than mainstream convolutional neural networks and recurrent neural networks.
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Shukor, Noorsufia Abd, Tahir Ahmad, Amidora Idris, Siti Rahmah Awang, and Amirul Aizad Ahmad Fuad. "Graph of Fuzzy Topographic Topological Mapping in relation to k-Fibonacci Sequence." Journal of Mathematics 2021 (August 24, 2021): 1–10. http://dx.doi.org/10.1155/2021/7519643.
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A generated n-sequence of fuzzy topographic topological mapping, FTTM n , is a combination of n number of FTTM’s graphs. An assembly graph is a graph whereby its vertices have valency of one or four. A Hamiltonian path is a path that visits every vertex of the graph exactly once. In this paper, we prove that assembly graphs exist in FTTM n and establish their relations to the Hamiltonian polygonal paths. Finally, the relation between the Hamiltonian polygonal paths induced from FTTM n to the k-Fibonacci sequence is established and their upper and lower bounds’ number of paths is determined.
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Qiao, Ziyue, Zhiyuan Ning, Yi Du, and Yuanchun Zhou. "Context-Enhanced Entity and Relation Embedding for Knowledge Graph Completion (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (May 18, 2021): 15871–72. http://dx.doi.org/10.1609/aaai.v35i18.17932.
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Most researches for knowledge graph completion learn representations of entities and relations to predict missing links in incomplete knowledge graphs. However, these methods fail to take full advantage of both the contextual information of entity and relation. Here, we extract contexts of entities and relations from the triplets which they compose. We propose a model named AggrE, which conducts efficient aggregations respectively on entity context and relation context in multi-hops, and learns context-enhanced entity and relation embeddings for knowledge graph completion. The experiment results show that AggrE is competitive to existing models.
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Chen, Xuelu, Muhao Chen, Weijia Shi, Yizhou Sun, and Carlo Zaniolo. "Embedding Uncertain Knowledge Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3363–70. http://dx.doi.org/10.1609/aaai.v33i01.33013363.
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Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge they contain into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different confidence score modeling strategies. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results, and it consistently outperforms baselines on these tasks.
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Smart, J. F., and M. Roux. "A Model for Medical Knowledge Representation Application to the Analysis of Descriptive Pathology Reports." Methods of Information in Medicine 34, no. 04 (July 1995): 352–60. http://dx.doi.org/10.1055/s-0038-1634608.
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Abstract:A new knowledge-representation system is presented, designed for medical knowledge-based applications and in particular for the analysis of descriptive medical reports. Knowledge is represented at two levels. A definitional level uses a concept-type hierarchy, a relation-type hierarchy, and a set of schematic graphs to define the concepts used and the relations between them, as well as different types of cardinality restrictions on these relations. A set of compositional hierarchies using the classic “has-part” relation as well as a new set-inclusion relation allows concept composition to be precisely defined. An assertional level allows the creation and manipulation of empirical data, in the form of graphs using the concepts, relations, and constraints defined at the definition level. The use of cardinality constraints in graph unification is considered in the context of descriptive medical discourse analysis.
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Chen, Fukun, Guisheng Yin, Yuxin Dong, Gesu Li, and Weiqi Zhang. "KHGCN: Knowledge-Enhanced Recommendation with Hierarchical Graph Capsule Network." Entropy 25, no. 4 (April 20, 2023): 697. http://dx.doi.org/10.3390/e25040697.
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Knowledge graphs as external information has become one of the mainstream directions of current recommendation systems. Various knowledge-graph-representation methods have been proposed to promote the development of knowledge graphs in related fields. Knowledge-graph-embedding methods can learn entity information and complex relationships between the entities in knowledge graphs. Furthermore, recently proposed graph neural networks can learn higher-order representations of entities and relationships in knowledge graphs. Therefore, the complete presentation in the knowledge graph enriches the item information and alleviates the cold start of the recommendation process and too-sparse data. However, the knowledge graph’s entire entity and relation representation in personalized recommendation tasks will introduce unnecessary noise information for different users. To learn the entity-relationship presentation in the knowledge graph while effectively removing noise information, we innovatively propose a model named knowledge—enhanced hierarchical graph capsule network (KHGCN), which can extract node embeddings in graphs while learning the hierarchical structure of graphs. Our model eliminates noisy entities and relationship representations in the knowledge graph by the entity disentangling for the recommendation and introduces the attentive mechanism to strengthen the knowledge-graph aggregation. Our model learns the presentation of entity relationships by an original graph capsule network. The capsule neural networks represent the structured information between the entities more completely. We validate the proposed model on real-world datasets, and the validation results demonstrate the model’s effectiveness.
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FRIESEN, TYLER, and VASSILY OLEGOVICH MANTUROV. "EMBEDDINGS OF *-GRAPHS INTO 2-SURFACES." Journal of Knot Theory and Its Ramifications 22, no. 12 (October 2013): 1341005. http://dx.doi.org/10.1142/s0218216513410058.
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This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency structure on the half-edges around each vertex, and an embedding of a *-graph is an embedding under which the formal adjacency relation on half-edges corresponds to the adjacency relation induced by the embedding. *-graphs are a natural generalization of four-valent framed graphs, which are four-valent graphs with an opposite half-edge structure. In [Embeddings of four-valent framed graphs into 2-surfaces, Dokl. Akad. Nauk424(3) (2009) 308–310], the question of whether a four-valent framed graph admits a ℤ2-homologically trivial embedding into a given surface was shown to be equivalent to a problem on matrices. We show that a similar result holds for *-graphs in which all vertices have degree 4 or 6. This gives an algorithm in quadratic time to determine whether a *-graph admits an embedding into the plane.
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Hu, Ganglin, and Jun Pang. "Relation-Aware Weighted Embedding for Heterogeneous Graphs." Information Technology and Control 52, no. 1 (March 28, 2023): 199–214. http://dx.doi.org/10.5755/j01.itc.52.1.32390.
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Heterogeneous graph embedding, aiming to learn the low-dimensional representations of nodes, is effective in many tasks, such as link prediction, node classification, and community detection. Most existing graph embedding methods conducted on heterogeneous graphs treat the heterogeneous neighbours equally. Although it is possible to get node weights through attention mechanisms mainly developed using expensive recursive message-passing, they are difficult to deal with large-scale networks. In this paper, we propose R-WHGE, a relation-aware weighted embedding model for heterogeneous graphs, to resolve this issue. R-WHGE comprehensively considers structural information, semantic information, meta-paths of nodes and meta-path-based node weights to learn effective node embeddings. More specifically, we first extract the feature importance of each node and then take the nodes’ importance as node weights. A weighted random walks-based embedding learning model is proposed to generate the initial weighted node embeddings according to each meta-path. Finally, we feed these embeddings to a relation-aware heterogeneous graph neural network to generate compact embeddings of nodes, which captures relation-aware characteristics. Extensive experiments on real-world datasets demonstrate that our model is competitive against various state-of-the-art methods.
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Hanif, Muhammad Zeeshan, Naveed Yaqoob, Muhammad Riaz, and Muhammad Aslam. "Linear Diophantine fuzzy graphs with new decision-making approach." AIMS Mathematics 7, no. 8 (2022): 14532–56. http://dx.doi.org/10.3934/math.2022801.
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<abstract><p>The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these operations with various illustrations. We analyze some interesting results that the composition of two LDF-graphs is a LDF-graph, cartesian product of two LDF-graphs is a LDF-graph, and the join of two LDF-graphs is a LDF-graph. We describe the idea of homomorphisms for LDF-graphs. We observe the equivalence relation via an isomorphism between LDF-graphs. Some significant results related to complement of LDF-graph are also investigated. Lastly, an algorithm based on LDFSs and LDF-relations is proposed for decision-making problems. A numerical example of medical diagnosis application is presented based on proposed approach.</p></abstract>
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An, Byung Hee, and Tomasz Maciazek. "Geometric Presentations of Braid Groups for Particles on a Graph." Communications in Mathematical Physics 384, no. 2 (April 28, 2021): 1109–40. http://dx.doi.org/10.1007/s00220-021-04095-x.
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AbstractWe study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of the graph and of certain circular moves where one particle travels around a simple cycle of the graph. We point out that so defined generators often do not satisfy the braiding relation known from 2D physics. We accomplish a full description of relations between the generators for star graphs where we derive certain quasi-braiding relations. We also describe how graph braid groups depend on the (graph-theoretic) connectivity of the graph. This is done in terms of quotients of graph braid groups where one-particle moves are put to identity. In particular, we show that for 3-connected planar graphs such a quotient reconstructs the well-known planar braid group. For 2-connected graphs this approach leads to generalisations of the Yang–Baxter equation. Our results are of particular relevance for the study of non-abelian anyons on networks showing new possibilities for non-abelian quantum statistics on graphs.
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Ma, Xintao, Liyan Dong, Yuequn Wang, Yongli Li, and Minghui Sun. "AIRC: Attentive Implicit Relation Recommendation Incorporating Content Information for Bipartite Graphs." Mathematics 8, no. 12 (November 30, 2020): 2132. http://dx.doi.org/10.3390/math8122132.
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With users being exposed to the growing volume of online information, the recommendation system aiming at mining the important or interesting information is becoming a modern research topic. One approach of recommendation is to integrate the graph neural network with deep learning algorithms. However, some of them are not tailored for bipartite graphs, which is a unique type of heterogeneous graph having two entity types. Others, though customized, neglect the importance of implicit relation and content information. In this paper, we propose the attentive implicit relation recommendation incorporating content information (AIRC) framework that is designed for bipartite graphs based on the GC–MC algorithm. First, through reconstructing the bipartite graphs, we obtain the implicit relation graphs. Then we analyze the content information of users and items with a CNN process, so that each user and item has its feature-tailored embeddings. Besides, we expand the GC–MC algorithms by adding a graph attention mechanism layer, which handles the implicit relation graph by highlighting important features and neighbors. Therefore, our framework takes into consideration both the implicit relation and content information. Finally, we test our framework on Movielens dataset and the results show that our framework performs better than other state-of-art recommendation algorithms.
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Yan, Jiahuan, Jintai Chen, Yixuan Wu, Danny Z. Chen, and Jian Wu. "T2G-FORMER: Organizing Tabular Features into Relation Graphs Promotes Heterogeneous Feature Interaction." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (June 26, 2023): 10720–28. http://dx.doi.org/10.1609/aaai.v37i9.26272.
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Recent development of deep neural networks (DNNs) for tabular learning has largely benefited from the capability of DNNs for automatic feature interaction. However, the heterogeneity nature of tabular features makes such features relatively independent, and developing effective methods to promote tabular feature interaction still remains an open problem. In this paper, we propose a novel Graph Estimator, which automatically estimates the relations among tabular features and builds graphs by assigning edges between related features. Such relation graphs organize independent tabular features into a kind of graph data such that interaction of nodes (tabular features) can be conducted in an orderly fashion. Based on our proposed Graph Estimator, we present a bespoke Transformer network tailored for tabular learning, called T2G-Former, which processes tabular data by performing tabular feature interaction guided by the relation graphs. A specific Cross-level Readout collects salient features predicted by the layers in T2G-Former across different levels, and attains global semantics for final prediction. Comprehensive experiments show that our T2G-Former achieves superior performance among DNNs and is competitive with non-deep Gradient Boosted Decision Tree models. The code and detailed results are available at https://github.com/jyansir/t2g-former.
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Long, Yangjing, and Peter F. Stadler. "Exact-2-relation graphs." Discrete Applied Mathematics 285 (October 2020): 212–26. http://dx.doi.org/10.1016/j.dam.2020.05.015.
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El-Kholy, E. M., and H. Ahmed. "Folding List of Graphs Obtained from a Given Graph." International Journal of Mathematics and Mathematical Sciences 2020 (November 23, 2020): 1–9. http://dx.doi.org/10.1155/2020/1316497.
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In this paper, we examine the relation between graph folding of a given graph and foldings of new graphs obtained from this graph by some techniques like dual, gear, subdivision, web, crown, simplex, crossed prism, and clique-sum graphs. In each case, we obtained the necessary and sufficient conditions, if exist, for these new graphs to be folded.
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Lin, Lin, Jie Liu, Feng Guo, Changsheng Tong, Lizheng Zu, and Hao Guo. "ERDERP: Entity and Relation Double Embedding on Relation Hyperplanes and Relation Projection Hyperplanes." Mathematics 10, no. 22 (November 9, 2022): 4182. http://dx.doi.org/10.3390/math10224182.
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Since data are gradually enriched over time, knowledge graphs are inherently imperfect. Thus, knowledge graph completion is proposed to perfect knowledge graph by completing triples. Currently, a family of translation models has become the most effective method for knowledge graph completion. These translation models are modeled to solve the complexity and diversity of entities, such as one-to-many, many-to-one, and many-to-many, which ignores the diversity of relations themselves, such as multiple relations between a pair of entities. As a result, with current translation models, it is difficult to effectively extract the semantic information of entities and relations. To effectively extract the semantic information of the knowledge graph, this paper fundamentally analyzes the complex relationships of the knowledge graph. Then, considering the diversity of relations themselves, the complex relationships are refined as one-to-one-to-many, many-to-one-to-one, one-to-many-to-one, many-to-one-to-many, many-to-many-to-one, one-to-many-to-many, and many-to-many-to-many. By analyzing the complex relationships, a novel knowledge graph completion model, entity and relation double embedding on relation hyperplanes and relation projection hyperplanes (ERDERP), is proposed to extract the semantic information of entities and relations. First, ERDERP establishes a relation hyperplane for each relation and projects the relation embedding into the relation hyperplane. Thus, the semantic information of the relations is extracted effectively. Second, ERDERP establishes a relation projection hyperplane for each relation projection and projects entities into relation projection hyperplane. Thus, the semantic information of the entities is extracted effectively. Moreover, it is theoretically proved that ERDERP can solve antisymmetric problems. Finally, the proposed ERDERP are compared with several typical knowledge graph completion models. The experimental results show that ERDERP is significantly effective in link prediction, especially in relation prediction. For instance, on FB15k and FB15k-237, Hits@1 of ERDERP outperforms TransH at least 30%.
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GLEBOV, ROMAN, TIBOR SZABÓ, and GÁBOR TARDOS. "Conflict-Free Colouring of Graphs." Combinatorics, Probability and Computing 23, no. 3 (November 29, 2013): 434–48. http://dx.doi.org/10.1017/s0963548313000540.
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We study the conflict-free chromatic number χCFof graphs from extremal and probabilistic points of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number ann-vertex graph can have. Our construction is randomized. In relation to this we study the evolution of the conflict-free chromatic number of the Erdős–Rényi random graphG(n,p) and give the asymptotics forp= ω(1/n). We also show that forp≥ 1/2 the conflict-free chromatic number differs from the domination number by at most 3.
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Uras, Tansel, and Sven Koenig. "Feasibility Study: Subgoal Graphs on State Lattices." Proceedings of the International Symposium on Combinatorial Search 8, no. 1 (September 1, 2021): 100–108. http://dx.doi.org/10.1609/socs.v8i1.18434.
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Search using subgoal graphs is a recent preprocessing-based path-planning algorithm that can find shortest paths on 8-neighbor grids several orders of magnitude faster than A*, while requiring little preprocessing time and memory overhead. In this paper, we first generalize the ideas behind subgoal graphs to a framework that can be specialized to different types of environments (represented as weighted directed graphs) through the choice of a reachability relation. Intuitively, a reachability relation identifies pairs of vertices for which a shortest path can be found quickly. A subgoal graph can then be constructed as an overlay graph that is guaranteed to have edges only between vertices that satisfy the reachability relation, which allows one to find shortest paths on the original graph quickly. In the context of this general framework, subgoal graphs on grids use freespace-reachability (originally called h-reachability) as the reachability relation, which holds for pairs of vertices if and only if their distance on the grid with blocked cells is equal to their distance on the grid without blocked cells (freespace assumption). We apply this framework to state lattices by using variants of freespace-reachability as the reachability relation. We provide preliminary results on (x,y,theta)-state lattices, which shows that subgoal graphs can be used to speed up path planning on state lattices as well, although the speed-up is not as significant as it is on grids.
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Abu-Saleem, M. "Retractions and Homomorphisms on Some Operations of Graphs." Journal of Mathematics 2018 (October 1, 2018): 1–4. http://dx.doi.org/10.1155/2018/7328065.
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The aim of the present article is to introduce and study a new type of operations on graph, namely, edge graph. The relation between the homomorphisms and retractions on edge graphs is deduced. The limit retractions on the edge graphs are presented. Retractions on a finite number of edge graphs are obtained.
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Raza, Ali, Mobeen Munir, Tasawar Abbas, Sayed M. Eldin, and Ilyas Khan. "Spectrum of prism graph and relation with network related quantities." AIMS Mathematics 8, no. 2 (2022): 2634–47. http://dx.doi.org/10.3934/math.2023137.
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<abstract><p>Spectra of network related graphs have numerous applications in computer sciences, electrical networks and complex networks to explore structural characterization like stability and strength of these different real-world networks. In present article, our consideration is to compute spectrum based results of generalized prism graph which is well-known planar and polyhedral graph family belongs to the generalized Petersen graphs. Then obtained results are applied to compute some network related quantities like global mean-first passage time, average path length, number of spanning trees, graph energies and spectral radius.</p></abstract>
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Mehry, Shahram, and Saadoun Mahmoudi. "Graphs over Graded Rings and Relation with Hamming Graph." Bulletin of the Malaysian Mathematical Sciences Society 44, no. 5 (April 17, 2021): 3413–29. http://dx.doi.org/10.1007/s40840-021-01121-y.
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Darabian, E., and R. A. Borzooei. "Results on Vague Graphs with Applications in Human Trafficking." New Mathematics and Natural Computation 14, no. 01 (March 2018): 37–52. http://dx.doi.org/10.1142/s1793005718500047.
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A vague graph is a generalized structure of a fuzzy graph that gives more precision, exibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the concepts of eccentricity of nodes, radius and diameter of vague graphs are introduced. The special types of graphs such as eccentrice and antipodal vague graphs are investigated. Then, the relation between eccentrice and antipodal vague graphs are discussed. Finally, an application of eccentrice and antipodal vague graphs in human traffickingn studied.
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CARPENTIER, RUI PEDRO. "FROM PLANAR GRAPHS TO EMBEDDED GRAPHS - A NEW APPROACH TO KAUFFMAN AND VOGEL'S POLYNOMIAL." Journal of Knot Theory and Its Ramifications 09, no. 08 (December 2000): 975–86. http://dx.doi.org/10.1142/s0218216500000578.
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In [4] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying the skein relations: [Formula: see text] and is defined in terms of a state-sum and the Dubrovnik polynomial for links. Using the graphical calculus of [4] it is shown that the polynomial of a planar graph can be calculated recursively from that of planar graphs with less vertices, which also allows the polynomial of an embedded graph to be calculated without resorting to links. The same approach is used to give a direct proof of uniqueness of the (normalized) polynomial restricted to planar graphs. In the case B=A-1 and a=A, it is proved that for a planar graph G we have [G]=2c-1(-A-A-1)v, where c is the number of connected components of G and v is the number of vertices of G. As a corollary, a necessary, but not sufficient, condition is obtained for an embedded graph to be ambient isotopic to a planar graph. In an appendix it is shown that, given a polynomial for planar graphs satisfying the graphical calculus, and imposing the first skein relation above, the polynomial extends to a rigid vertex regular isotopy invariant for embedded graphs, satisfying the remaining skein relations. Thus, when existence of the planar polynomial is guaranteed, this provides a direct way, not depending on results for the Dubrovnik polynomial, to show consistency of the polynomial for embedded graphs.
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Cui, Zijun, Pavan Kapanipathi, Kartik Talamadupula, Tian Gao, and Qiang Ji. "Type-augmented Relation Prediction in Knowledge Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (May 18, 2021): 7151–59. http://dx.doi.org/10.1609/aaai.v35i8.16879.
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Knowledge graphs (KGs) are of great importance to many real world applications, but they generally suffer from incomplete information in the form of missing relations between entities. Knowledge graph completion (also known as relation prediction) is the task of inferring missing facts given existing ones. Most of the existing work is proposed by maximizing the likelihood of observed instance-level triples. Not much attention, however, is paid to the ontological information, such as type information of entities and relations. In this work, we propose a type-augmented relation prediction (TaRP) method, where we apply both the type information and instance-level information for the relation prediction. In particular, type information and instance-level information are encoded as prior probabilities and likelihoods of relations respectively, and are combined by following the Bayes' rule. Our proposed TaRP method achieves significantly better performance than state-of-the-art methods on four benchmark datasets: FB15K, FB15K-237, YAGO26K-906, and DB111K-174. In addition, we show that the TaRP achieves the significantly improved data efficiency. More importantly, the type information extracted from a specific dataset can generalize well to different datasets through the proposed TaRP model.
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Weaver, Nik. "Quantum Graphs as Quantum Relations." Journal of Geometric Analysis 31, no. 9 (January 13, 2021): 9090–112. http://dx.doi.org/10.1007/s12220-020-00578-w.
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AbstractThe “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We use this perspective to interpret the Knill–Laflamme error-correction conditions (Knill and Laflamme in Theory of quantum error-correcting codes. Phys Rev A 55:900-911, 1997) in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke’s noncommutative graph homomorphisms (Stahlke in Quantum zero-error source-channel coding and non-commutative graph theory. IEEE Trans Inf Theory 62:554–577, 2016) and Duan, Severini, and Winter’s noncommutative bipartite graphs (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013), and to realize the noncommutative confusability graph associated to a quantum channel (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013) as the pullback of a diagonal relation. Our framework includes as special cases not only purely classical and purely quantum information theory, but also the “mixed” setting which arises in quantum systems obeying superselection rules. Thus we are able to define noncommutative confusability graphs, give error correction conditions, and so on, for such systems. This could have practical value, as superselection constraints on information encoding can be physically realistic.
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Kechris, Alexander. "Global aspects of measure preserving equivalence relations and graphs." New Zealand Journal of Mathematics 52 (November 10, 2021): 691–726. http://dx.doi.org/10.53733/96.
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This paper is an introduction and survey of a “global” theory of measure preserving equivalence relations and graphs. In this theory one views a measure preserving equivalence relation or graph as a point in an appropriate topological space and then studies the properties of this space from a topological, descriptive set theoretic and dynamical point of view.
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Lu, Xinyu, Lifang Wang, Zejun Jiang, Shizhong Liu, and Jiashi Lin. "MRE: A translational knowledge graph completion model based on multiple relation embedding." Mathematical Biosciences and Engineering 20, no. 3 (2023): 5881–900. http://dx.doi.org/10.3934/mbe.2023253.
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<abstract><p>Knowledge graph completion (KGC) has attracted significant research interest in applying knowledge graphs (KGs). Previously, many works have been proposed to solve the KGC problem, such as a series of translational and semantic matching models. However, most previous methods suffer from two limitations. First, current models only consider the single form of relations, thus failing to simultaneously capture the semantics of multiple relations (direct, multi-hop and rule-based). Second, the data-sparse problem of knowledge graphs would make part of relations challenging to embed. This paper proposes a novel translational knowledge graph completion model named multiple relation embedding (MRE) to address the above limitations. We attempt to embed multiple relations to provide more semantic information for representing KGs. To be more specific, we first leverage PTransE and AMIE+ to extract multi-hop and rule-based relations. Then, we propose two specific encoders to encode extracted relations and capture semantic information of multiple relations. We note that our proposed encoders can achieve interactions between relations and connected entities in relation encoding, which is rarely considered in existing methods. Next, we define three energy functions to model KGs based on the translational assumption. At last, a joint training method is adopted to perform KGC. Experimental results illustrate that MRE outperforms other baselines on KGC, demonstrating the effectiveness of embedding multiple relations for advancing knowledge graph completion.</p></abstract>
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Krzywkowski, Marcin, and Doost Ali Mojdeh. "Bicritical domination and double coalescence of graphs." Georgian Mathematical Journal 23, no. 3 (September 1, 2016): 399–404. http://dx.doi.org/10.1515/gmj-2016-0019.
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AbstractA graph is bicritical if the removal of any pair of vertices decreases the domination number. We study the properties of bicritical graphs and their relation with critical graphs, and we obtain results for bicritical graphs with edge connectivity two or three. We also generalize the notion of the coalescence of two graphs and investigate the bicriticality of such graphs.
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Janz, Arkadiusz, Paweł Kędzia, and Maciej Piasecki. "Graph-Based Complex Representation in Inter-Sentence Relation Recognition in Polish Texts." Cybernetics and Information Technologies 18, no. 1 (March 1, 2018): 152–70. http://dx.doi.org/10.2478/cait-2018-0013.
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Abstract This paper presents a supervised approach to the recognition of Cross-document Structure Theory (CST) relations in Polish texts. Its core is a graph-based representation constructed for sentences. Graphs are built on the basis of lexicalised syntactic-semantic relations extracted from text. Similarity between sentences is calculated as similarity between their graphs, and the values are used as features to train the classifiers. Several different configurations of graphs, as well as graph similarity methods were analysed for this task. The approach was evaluated on a large open corpus annotated manually with 17 types of selected CST relations. The configuration of experiments was similar to those known from SEMEVAL and we obtained very promising results.
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Ramane, Harishchandra S., B. Parvathalu, and K. Ashoka. "Energy of extended bipartite double graphs." MATCH Communications in Mathematical and in Computer Chemistry 87, no. 3 (December 2021): 653–60. http://dx.doi.org/10.46793/match.87-3.653r.
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The energy of a graph is the sum of the absolute values of its eigenvalues. In this article, an exact relation between the energy of extended bipartite double graph and the energy of a graph together with some other graph parameters is given. As a consequence, equienergetic, borderenergetic, orderenergetic and non-hyperenergetic extended bipartite double graphs are presented. The obtained results generalize the existing results on equienergetic bipartite graphs.
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MOCONJA, SLAVKO M., and ZORAN Z. PETROVIĆ. "ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY." Bulletin of the Australian Mathematical Society 83, no. 1 (November 26, 2010): 11–21. http://dx.doi.org/10.1017/s0004972710001875.
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AbstractIn this paper we investigate the center, radius and girth of comaximal graphs of commutative rings. We also provide some counterexamples to the results concerning the relation between isomorphisms of comaximal graphs and the rings in question. In addition, we investigate the relation between the comaximal graph of a ring and its subrings of a certain type.
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Bagheri Gh., Behrooz, and Behnaz Omoomi. "On the simultaneous edge coloring of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (October 10, 2014): 1450049. http://dx.doi.org/10.1142/s1793830914500499.
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A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et al. (2000) conjectured that every bridgeless bipartite graph is 2-simultaneous edge colorable. Luo et al. (2004) showed that every bipartite graphic sequence S with all its elements greater than one, has a realization that admits a 2-simultaneous edge coloring. In this paper, the μ-simultaneous edge coloring of graphs is studied. Moreover, the properties of the extremal counterexample to the above conjecture are investigated. Also, a relation between 2-simultaneous edge coloring of a graph and a cycle double cover with certain properties is shown and using this relation, some results about 2-simultaneous edge colorable graphs are obtained.
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GLAVAŠ, GORAN, and JAN ŠNAJDER. "Construction and evaluation of event graphs." Natural Language Engineering 21, no. 4 (May 1, 2014): 607–52. http://dx.doi.org/10.1017/s1351324914000060.
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AbstractEvents play an important role in natural language processing and information retrieval due to numerous event-oriented texts and information needs. Many natural language processing and information retrieval applications could benefit from a structured event-oriented document representation. In this paper, we proposeevent graphsas a novel way of structuring event-based information from text. Nodes in event graphs represent the individual mentions of events, whereas edges represent the temporal and coreference relations between mentions. Contrary to previous natural language processing research, which has mainly focused on individual event extraction tasks, we describe a complete end-to-end system for event graph extraction from text. Our system is a three-stage pipeline that performs anchor extraction, argument extraction, and relation extraction (temporal relation extraction and event coreference resolution), each at a performance level comparable with the state of the art. We presentEvExtra, a large newspaper corpus annotated with event mentions and event graphs, on which we train and evaluate our models. To measure the overall quality of the constructed event graphs, we propose two metrics based on the tensor product between automatically and manually constructed graphs. Finally, we evaluate the overall quality of event graphs with the proposed evaluation metrics and perform a headroom analysis of the system.
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CAO, TRU H. "A FORMALISM FOR REPRESENTING AND REASONING WITH LINGUISTIC INFORMATION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 03 (June 2002): 281–307. http://dx.doi.org/10.1142/s021848850200148x.
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Conceptual graphs and fuzzy logic are two logical formalisms that emphasize the target of natural language, where conceptual graphs provide a structure of formulas close to that of natural language sentences while fuzzy logic provides a methodology for computing with words. This paper proposes fuzzy conceptual graphs as a knowledge representation language that combines the advantages of both the two formalisms for artificial intelligence approaching human expression and reasoning. Firstly, the conceptual graph language is extended with functional relation types for representing functional dependency, and conjunctive types for joining concepts and relations. Then fuzzy conceptual graphs are formulated as a generalization of conceptual graphs where fuzzy types and fuzzy attribute-values are used in place of crisp types and crisp attribute-values. Projection and join as basic operations for reasoning on fuzzy conceptual graphs are defined, taking into account the semantics of fuzzy set-based values.
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Gyürki, Štefan. "Small Directed Strongly Regular Graphs." Algebra Colloquium 27, no. 01 (February 25, 2020): 11–30. http://dx.doi.org/10.1142/s1005386720000036.
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The goal of the present paper is to provide a gallery of small directed strongly regular graphs. For each graph of order n ≤ 12 and valency k < n/2, a diagram is depicted, its relation to other small directed strongly regular graphs is revealed, the full group of automorphisms is described, and some other nice properties are given. To each graph a list of interesting subgraphs is provided as well.
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Liu, Hongjuan, and Honghai Li. "Normalized algebraic connectivity of graphs." Discrete Mathematics, Algorithms and Applications 11, no. 03 (June 2019): 1950031. http://dx.doi.org/10.1142/s1793830919500319.
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Let [Formula: see text] be the second smallest normalized Laplacian eigenvalue of a graph [Formula: see text], called the normalized algebraic connectivity of [Formula: see text]. In this paper, we study the relation between the normalized algebraic connectivity of the coalescence of two graphs and that of these two graphs. Furthermore, we investigate how the normalized algebraic connectivity behaves when the graph is perturbed by relocating pendent edges.
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Haris, Erum, Keng Hoon Gan, and Tien-Ping Tan. "Spatial information extraction from travel narratives: Analysing the notion of co-occurrence indicating closeness of tourist places." Journal of Information Science 46, no. 5 (June 10, 2019): 581–99. http://dx.doi.org/10.1177/0165551519837188.
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Recent advancements in social media have generated a myriad of unstructured geospatial data. Travel narratives are among the richest sources of such spatial clues. They are also a reflection of writers’ interaction with places. One of the prevalent ways to model this interaction is a points of interest (POIs) graph depicting popular POIs and routes. A relevant notion is that frequent pairwise occurrences of POIs indicate their geographic proximity. This work presents an empirical interpretation of this theory and constructs spatially enriched POI graphs, a clear augmentation to popularity-based POI graphs. A triplet pattern, rule-based spatial relation extraction technique SpatRE is proposed and compared with standard relation extraction systems Ollie and Stanford OpenIE. A travel blogs data set is also contributed containing labelled spatial relations. The performance is further evaluated on SemEval 2013 benchmark data sets. Finally, spatially enriched POI graphs are qualitatively compared with TripAdvisor and Google Maps to visualise information accuracy.
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Zhang, Xiaoming, Wencheng Zhang, and Huiyong Wang. "Cross-Language Entity Alignment Based on Dual-Relation Graph and Neighbor Entity Screening." Electronics 12, no. 5 (March 3, 2023): 1211. http://dx.doi.org/10.3390/electronics12051211.
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Graph convolutional network-based methods have become mainstream for cross-language entity alignment. The graph convolutional network has multi-order characteristics that not only process data more conveniently but also reduce the interference of noise effectively. Although the existing methods have achieved good results for the task of cross-language entity alignment, they have often overlooked the same entity names in the real corpus, resulting in an entity-matching result that was not ideal. Therefore, this study proposed a neighboring-entity-screening rule by combining the entity name and the attribute (NENA) to reduce the influence of these issues. We used the NENA-screening rule to filter and delete redundant equivalent entities and to construct a dual-relation graph as auxiliary evidence for scenarios when the attribute information may be insufficient.This study adopted a graph convolutional network in order to embed knowledge graphs and entity names into a unified vector space, and then a down-sampling method was used to extract the neighboring entities of each entity, thus forming sub-graphs of the two knowledge graphs. We embedded the sub-graphs into the GCN, as the new input, and then we used a cross-graph-matching module to finally achieve alignment. Our results on the DBP15K dataset showed that our approach significantly improved the overall entity alignment.On the sub-dataset ZH-EN of DBP15K, the value of Hits@1 improved by 1.38%, as compared to the best approach mentioned in this paper, and it was useful for the construction and completion of the open knowledge graph.
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JOIŢA, CEZAR, and DANIELA JOIŢA. "MINORS IN WEIGHTED GRAPHS." Bulletin of the Australian Mathematical Society 77, no. 3 (June 2008): 455–64. http://dx.doi.org/10.1017/s0004972708000397.
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AbstractWe define the notion of minor for weighted graphs. We prove that with this minor relation, the set of weighted graphs is directed. We also prove that, given any two weights on a connected graph with the same total weight, we can transform one into the other using a sequence of edge subdivisions and edge contractions.
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Yuan, Changsen, Heyan Huang, and Chong Feng. "Multi-Graph Cooperative Learning Towards Distant Supervised Relation Extraction." ACM Transactions on Intelligent Systems and Technology 12, no. 5 (October 31, 2021): 1–21. http://dx.doi.org/10.1145/3466560.
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The Graph Convolutional Network (GCN) is a universal relation extraction method that can predict relations of entity pairs by capturing sentences’ syntactic features. However, existing GCN methods often use dependency parsing to generate graph matrices and learn syntactic features. The quality of the dependency parsing will directly affect the accuracy of the graph matrix and change the whole GCN’s performance. Because of the influence of noisy words and sentence length in the distant supervised dataset, using dependency parsing on sentences causes errors and leads to unreliable information. Therefore, it is difficult to obtain credible graph matrices and relational features for some special sentences. In this article, we present a Multi-Graph Cooperative Learning model (MGCL), which focuses on extracting the reliable syntactic features of relations by different graphs and harnessing them to improve the representations of sentences. We conduct experiments on a widely used real-world dataset, and the experimental results show that our model achieves the state-of-the-art performance of relation extraction.
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Zhao, Jianan, Xiao Wang, Chuan Shi, Binbin Hu, Guojie Song, and Yanfang Ye. "Heterogeneous Graph Structure Learning for Graph Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (May 18, 2021): 4697–705. http://dx.doi.org/10.1609/aaai.v35i5.16600.
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Heterogeneous Graph Neural Networks (HGNNs) have drawn increasing attention in recent years and achieved outstanding performance in many tasks. The success of the existing HGNNs relies on one fundamental assumption, i.e., the original heterogeneous graph structure is reliable. However, this assumption is usually unrealistic, since the heterogeneous graph in reality is inevitably noisy or incomplete. Therefore, it is vital to learn the heterogeneous graph structure for HGNNs rather than rely only on the raw graph structure. In light of this, we make the first attempt towards learning an optimal heterogeneous graph structure for HGNNs and propose a novel framework HGSL, which jointly performs Heterogeneous Graph Structure Learning and GNN parameters learning for classification task. Different from traditional GSL on homogeneous graph, considering the heterogeneity of different relations in heterogeneous graph, HGSL generates each relation subgraph independently. Specifically, in each generated relation subgraph, HGSL not only considers the feature similarity by generating feature similarity graph, but also considers the complex heterogeneous interactions in features and semantics by generating feature propagation graph and semantic graph. Then, these graphs are fused to a learned heterogeneous graph and optimized together with a GNN towards classification objective. Extensive experiments on real-world graphs demonstrate that the proposed framework significantly outperforms the state-of-the-art methods.
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ISHII, ATSUSHI. "ON NORMALIZATIONS OF A REGULAR ISOTOPY INVARIANT FOR SPATIAL GRAPHS." International Journal of Mathematics 22, no. 11 (November 2011): 1545–59. http://dx.doi.org/10.1142/s0129167x1100729x.
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We give a framework to normalize a regular isotopy invariant of a spatial graph, and introduce many normalizations satisfying the same relation under a local move. We normalize the Yamada polynomial for spatial embeddings of almost all trivalent graphs without a bridge, and see the benefit to utilize our normalizations from the viewpoint of skein relations, the finite type invariants, and evaluations of the Yamada polynomial. We show that the collection of the differences between two of our normalizations is a complete spatial-graph-homology invariant.