Relevant bibliographies by topics / Simple graph

Academic literature on the topic 'Simple graph'

Author: Grafiati
Published: 18 May 2024
Last updated: 8 June 2024

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Journal articles on the topic "Simple graph"

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Voorhees, Burton, and Alex Murray. "Fixation probabilities for simple digraphs." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2154 (June 8, 2013): 20120676. http://dx.doi.org/10.1098/rspa.2012.0676.

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The problem of finding birth–death fixation probabilities for configurations of normal and mutants on an N -vertex graph is formulated in terms of a Markov process on the 2 N -dimensional state space of possible configurations. Upper and lower bounds on the fixation probability after any given number of iterations of the birth–death process are derived in terms of the transition matrix of this process. Consideration is then specialized to a family of graphs called circular flows, and we present a summation formula for the complete bipartite graph, giving the fixation probability for an arbitrary configuration of mutants in terms of a weighted sum of the single-vertex fixation probabilities. This also yields a closed-form solution for the fixation probability of bipartite graphs. Three entropy measures are introduced, providing information about graph structure. Finally, a number of examples are presented, illustrating cases of graphs that enhance or suppress fixation probability for fitness r >1 as well as graphs that enhance fixation probability for only a limited range of fitness. Results are compared with recent results reported in the literature, where a positive correlation is observed between vertex degree variance and fixation probability for undirected graphs. We show a similar correlation for directed graphs, with correlation not directly to fixation probability but to the difference between fixation probability for a given graph and a complete graph.
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TROTTA, BELINDA. "RESIDUAL PROPERTIES OF SIMPLE GRAPHS." Bulletin of the Australian Mathematical Society 82, no. 3 (August 18, 2010): 488–504. http://dx.doi.org/10.1017/s0004972710000420.

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AbstractClark et al. [‘The axiomatizability of topological prevarieties’, Adv. Math.218 (2008), 1604–1653] have shown that, for k≥2, there exists a Boolean topological graph that is k-colourable but not topologically k-colourable; that is, for every ϵ>0, it cannot be coloured by a paintbrush of width ϵ. We generalize this result to show that, for k≥2, there is a Boolean topological graph that is 2-colourable but not topologically k-colourable. This graph is an inverse limit of finite graphs which are shown to exist by an Erdős-style probabilistic argument of Hell and Nešetřil [‘The core of a graph’, Discrete Math.109 (1992), 117–126]. We use the fact that there exists a Boolean topological graph that is 2-colourable but not k-colourable, and some other results (some new and some previously known), to answer the question of which finitely generated topological residual classes of graphs are axiomatizable by universal Horn sentences. A more general version of this question was raised in the above-mentioned paper by Clark et al., and has been investigated by various authors for other structures.
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Ali, Akbar. "Tetracyclic graphs with maximum second Zagreb index: A simple approach." Asian-European Journal of Mathematics 11, no. 05 (October 2018): 1850064. http://dx.doi.org/10.1142/s179355711850064x.

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In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum [Formula: see text] value among all members of the collection [Formula: see text]. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.
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Abughazalah, Nabilah, Naveed Yaqoob, and Asif Bashir. "Cayley Graphs over LA-Groups and LA-Polygroups." Mathematical Problems in Engineering 2021 (May 10, 2021): 1–9. http://dx.doi.org/10.1155/2021/4226232.

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The purpose of this paper is the study of simple graphs that are generalized Cayley graphs over LA-polygroups GCLAP − graphs . In this regard, we construct two new extensions for building LA-polygroups. Then, we define Cayley graph over LA-group and GCLAP-graph. Further, we investigate a few properties of them to show that each simple graph of order three, four, and five (except cycle graph of order five which may or may not be a GCLAP-graph) is a GCLAP-graph and then we prove this result.
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Amanto, Amanto, Notiragayu Notiragayu, La Zakaria, and Wamiliana Wamiliana. "The relationship of the formulas for the number of connected vertices labeled graphs with order five and order six without loops." Desimal: Jurnal Matematika 4, no. 3 (November 30, 2021): 357–64. http://dx.doi.org/10.24042/djm.v4i3.10006.

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Given a graph with n points and m lines. If each vertex is labeled, then it can be constructed many graphs, connected, or disconnected graphs. A graph G is called a connected graph if there is at least one path that connects a pair of vertices in G. In addition, the graph formed may be simple or not simple. A simple graph is a graph that does not contain loops or parallel lines. A loop is a line that connects a point to itself, and a parallel line is two or more lines that connect the same pair of points. This paper will discuss the relationship between the formula patterns for calculating the number of connected graphs labeled with vertices of order five and six without loops.
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BAHR, PATRICK. "Convergence in infinitary term graph rewriting systems is simple." Mathematical Structures in Computer Science 28, no. 8 (August 9, 2018): 1363–414. http://dx.doi.org/10.1017/s0960129518000166.

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Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by emulating duplication via sharing. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to model non-strict evaluation. In this paper, we unify term graph rewriting and infinitary term rewriting thereby addressing both components of lazy evaluation: non-strictness and sharing. In contrast to previous attempts to formalise infinitary term graph rewriting, our approach is based on a simple and natural generalisation of the modes of convergence of infinitary term rewriting. We show that this new approach is better suited for infinitary term graph rewriting as it is simpler and more general. The latter is demonstrated by the fact that our notions of convergence give rise to two independent canonical and exhaustive constructions of infinite term graphs from finite term graphs via metric and ideal completion. In addition, we show that our notions of convergence on term graphs are sound w.r.t. the ones employed in infinitary term rewriting in the sense that convergence is preserved by unravelling term graphs to terms. Moreover, the resulting infinitary term graph calculi provide a unified framework for both infinitary term rewriting and term graph rewriting, which makes it possible to study the correspondences between these two worlds more closely.
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KHEIRABADI, M., and A. R. MOGHADDAMFAR. "RECOGNIZING SOME FINITE SIMPLE GROUPS BY NONCOMMUTING GRAPH." Journal of Algebra and Its Applications 11, no. 04 (July 31, 2012): 1250077. http://dx.doi.org/10.1142/s0219498812500776.

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Let G be a nonabelian group. We define the noncommuting graph ∇(G) of G as follows: its vertex set is G\Z(G), the noncentral elements of G, and two distinct vertices x and y of ∇(G) are joined by an edge if and only if x and y do not commute as elements of G, i.e. [x, y] ≠ 1. The finite group L is said to be recognizable by noncommuting graph if, for every finite group G, ∇(G) ≅ ∇ (L) implies G ≅ L. In the present article, it is shown that the noncommuting graph of a group with trivial center can determine its prime graph. From this, the following theorem is derived. If two finite groups with trivial centers have isomorphic noncommuting graphs, then their prime graphs coincide. It is also proved that the projective special unitary groups U4(4), U4(8), U4(9), U4(11), U4(13), U4(16), U4(17) and the projective special linear groups L9(2), L16(2) are recognizable by noncommuting graph.
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Malik, M. Aslam, and M. Khalid Mahmood. "On Simple Graphs Arising from Exponential Congruences." Journal of Applied Mathematics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/292895.

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We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integersaandb, letG(n)denote the graph for whichV={0,1,…,n−1}is the set of vertices and there is an edge betweenaandbif the congruenceax≡b (mod n)is solvable. Letn=p1k1p2k2⋯prkrbe the prime power factorization of an integern, wherep1<p2<⋯<prare distinct primes. The number of nontrivial self-loops of the graphG(n)has been determined and shown to be equal to∏i=1r(ϕ(piki)+1). It is shown that the graphG(n)has2rcomponents. Further, it is proved that the componentΓpof the simple graphG(p2)is a tree with root at zero, and ifnis a Fermat's prime, then the componentΓϕ(n)of the simple graphG(n)is complete.
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Yang, Xiaocheng, Mingyu Yan, Shirui Pan, Xiaochun Ye, and Dongrui Fan. "Simple and Efficient Heterogeneous Graph Neural Network." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (June 26, 2023): 10816–24. http://dx.doi.org/10.1609/aaai.v37i9.26283.

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Heterogeneous graph neural networks (HGNNs) have the powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) designed for homogeneous graphs, especially the attention mechanism and the multi-layer structure. These mechanisms bring excessive complexity, but seldom work studies whether they are really effective on heterogeneous graphs. In this paper, we conduct an in-depth and detailed study of these mechanisms and propose the Simple and Efficient Heterogeneous Graph Neural Network (SeHGNN). To easily capture structural information, SeHGNN pre-computes the neighbor aggregation using a light-weight mean aggregator, which reduces complexity by removing overused neighbor attention and avoiding repeated neighbor aggregation in every training epoch. To better utilize semantic information, SeHGNN adopts the single-layer structure with long metapaths to extend the receptive field, as well as a transformer-based semantic fusion module to fuse features from different metapaths. As a result, SeHGNN exhibits the characteristics of a simple network structure, high prediction accuracy, and fast training speed. Extensive experiments on five real-world heterogeneous graphs demonstrate the superiority of SeHGNN over the state-of-the-arts on both accuracy and training speed.
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BURNESS, TIMOTHY C., and ELISA COVATO. "ON THE PRIME GRAPH OF SIMPLE GROUPS." Bulletin of the Australian Mathematical Society 91, no. 2 (October 8, 2014): 227–40. http://dx.doi.org/10.1017/s0004972714000707.

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AbstractLet $G$ be a finite group, let ${\it\pi}(G)$ be the set of prime divisors of $|G|$ and let ${\rm\Gamma}(G)$ be the prime graph of $G$. This graph has vertex set ${\it\pi}(G)$, and two vertices $r$ and $s$ are adjacent if and only if $G$ contains an element of order $rs$. Many properties of these graphs have been studied in recent years, with a particular focus on the prime graphs of finite simple groups. In this note, we determine the pairs $(G,H)$, where $G$ is simple and $H$ is a proper subgroup of $G$ such that ${\rm\Gamma}(G)={\rm\Gamma}(H)$.
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Dissertations / Theses on the topic "Simple graph"

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CRUCIANI, EMILIO. "Simple Randomized Distributed Algorithms for Graph Clustering." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9951.

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Label Propagation Algorithms are a class of heuristics for the problem of graph clustering, i.e., the problem of detecting groups of nodes whose connections are dense within each group and sparse between the groups. At the onset, a label is assigned to each node of the graph; then, each node iteratively updates its label according to a function of the labels of its neighbors. Empirical studies show that, after only a few rounds, nodes in the same cluster share the same label while nodes in different clusters have different labels. Although they are widely used in practice given their simplicity, efficiency, and effectiveness, there is no theoretical foundation to explain why such simple algorithms are able to perform such a hard task. The absence of theoretical progress in the analysis of Label Propagation Algorithms is due to the lack of mathematical techniques for handling the interplay between the non-linearity of their update rule and the topology of the underlying graph. In this thesis we contextualize Label Propagation Algorithms in the framework of computational dynamics, simple dynamical processes on networks whose behavior has been formally characterized on some classes of graphs. The analyses of computational dynamics were mainly focused on graphs with good connectivity properties, such as cliques or expanders, and on the problem of consensus, showing that they naturally converge to a configuration in which all the nodes agree on some value. We move a step forward in this direction by rigorously analyzing two simple dynamics, the 2-Choices dynamics and the Averaging dynamics, reaching a more fine-grained comprehension of their consensus behavior in classes of graphs that exhibit a clustered structure. In particular we formally prove that, with non-negligible probability, the two dynamics quickly bring the graph in a configuration where each cluster reaches an internal consensus on a value that is different among the clusters, and then enters a long metastable phase in which the internal consensus are maintained. We show how to exploit such metastable behavior to design simple randomized distributed algorithms for graph clustering.
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Matos, Jody Maick Araujo de. "Graph based algorithms to efficiently map VLSI circuits with simple cells." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/174523.

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Essa tese introduz um conjunto de algoritmos baseados em grafos para o mapeamento eficiente de circuitos VLSI com células simples. Os algoritmos propostos se baseiam em minimizar de maneira eficiente o número de elementos lógicos usados na implementação do circuito. Posteriormente, uma quantidade significativa de esforço é aplicada na minimização do número de inversores entre esses elementos lógicos. Por fim, essa representação lógica é mapeada para circuitos compostos somente por células NAND e NOR de duas entradas, juntamente com inversores. Células XOR e XNOR de duas entradas também podem ser consideradas. Como nós também consideramos circuitos sequenciais, flips-flops também são levados em consideração. Com o grande esforço de minimização de elementos lógicos, o circuito gerado pode conter algumas células com um fanout impraticável para os nodos tecnológicos atuais. Para corrigir essas ocorrências, nós propomos um algoritmo de limitação de fanout que considera tanto a área sendo utilizada pelas células quanto a sua profundidade lógica. Os algoritmos propostos foram aplicados sobre um conjunto de circuitos de benchmark e os resultados obtidos demonstram a utilidade dos métodos. Essa tese introduz um conjunto de algoritmos baseados em grafos para o mapeamento eficiente de circuitos VLSI com células simples. Os algoritmos propostos se baseiam em minimizar de maneira eficiente o número de elementos lógicos usados na implementação do circuito. Posteriormente, uma quantidade significativa de esforço é aplicada na minimização do número de inversores entre esses elementos lógicos. Por fim, essa representação lógica é mapeada para circuitos compostos somente por células NAND e NOR de duas entradas, juntamente com inversores. Células XOR e XNOR de duas entradas também podem ser consideradas. Como nós também consideramos circuitos sequenciais, flips-flops também são levados em consideração. Com o grande esforço de minimização de elementos lógicos, o circuito gerado pode conter algumas células com um fanout impraticável para os nodos tecnológicos atuais. Para corrigir essas ocorrências, nós propomos um algoritmo de limitação de fanout que considera tanto a área sendo utilizada pelas células quanto a sua profundidade lógica. Os algoritmos propostos foram aplicados sobre um conjunto de circuitos de benchmark e os resultados obtidos demonstram a utilidade dos métodos. Adicionalmente, algumas aplicações Morethan-Moore, tais como circuitos baseados em eletrônica impressa, também podem ser beneficiadas pela abordagem proposta.
This thesis introduces a set of graph-based algorithms for efficiently mapping VLSI circuits using simple cells. The proposed algorithms are concerned to, first, effectively minimize the number of logic elements implementing the synthesized circuit. Then, we focus a significant effort on minimizing the number of inverters in between these logic elements. Finally, this logic representation is mapped into a circuit comprised of only two-input NANDs and NORS, along with the inverters. Two-input XORs and XNORs can also be optionally considered. As we also consider sequential circuits in this work, flip-flops are taken into account as well. Additionally, with high-effort optimization on the number of logic elements, the generated circuits may contain some cells with unfeasible fanout for current technology nodes. In order to fix these occurrences, we propose an area-oriented, level-aware algorithm for fanout limitation. The proposed algorithms were applied over a set of benchmark circuits and the obtained results have shown the usefulness of the method. We show that efficient implementations in terms of inverter count, transistor count, area, power and delay can be generated from circuits with a reduced number of both simple cells and inverters, combined with XOR/XNOR-based optimizations. The proposed buffering algorithm can handle all unfeasible fanout occurrences, while (i) optimizing the number of added inverters; and (ii) assigning cells to the inverter tree based on their level criticality. When comparing with academic and commercial approaches, we are able to simultaneously reduce the average number of inverters, transistors, area, power dissipation and delay up to 48%, 5%, 5%, 5%, and 53%, respectively. As the adoption of a limited set of simple standard cells have been showing benefits for a variety of modern VLSI circuits constraints, such as layout regularity, routability constraints, and/or ultra low power constraints, the proposed methods can be of special interest for these applications. Additionally, some More-than-Moore applications, such as printed electronics designs, can also take benefit from the proposed approach.
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Bereczki, Márk. "Graph Neural Networks for Article Recommendation based on Implicit User Feedback and Content." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-300092.

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Recommender systems are widely used in websites and applications to help users find relevant content based on their interests. Graph neural networks achieved state- of-the- art results in the field of recommender systems, working on data represented in the form of a graph. However, most graph- based solutions hold challenges regarding computational complexity or the ability to generalize to new users. Therefore, we propose a novel graph- based recommender system, by modifying Simple Graph Convolution, an approach for efficient graph node classification, and add the capability of generalizing to new users. We build our proposed recommender system for recommending the articles of Peltarion Knowledge Center. By incorporating two data sources, implicit user feedback based on pageview data as well as the content of articles, we propose a hybrid recommender solution. Throughout our experiments, we compare our proposed solution with a matrix factorization approach as well as a popularity- based and a random baseline, analyse the hyperparameters of our model, and examine the capability of our solution to give recommendations to new users who were not part of the training data set. Our model results in slightly lower, but similar Mean Average Precision and Mean Reciprocal Rank scores to the matrix factorization approach, and outperforms the popularity- based and random baselines. The main advantages of our model are computational efficiency and its ability to give relevant recommendations to new users without the need for retraining the model, which are key features for real- world use cases.
Rekommendationssystem används ofta på webbplatser och applikationer för att hjälpa användare att hitta relevant innehåll baserad på deras intressen. Med utvecklingen av grafneurala nätverk nådde toppmoderna resultat inom rekommendationssystem och representerade data i form av en graf. De flesta grafbaserade lösningar har dock svårt med beräkningskomplexitet eller att generalisera till nya användare. Därför föreslår vi ett nytt grafbaserat rekommendatorsystem genom att modifiera Simple Graph Convolution. De här tillvägagångssätt är en effektiv grafnodsklassificering och lägga till möjligheten att generalisera till nya användare. Vi bygger vårt föreslagna rekommendatorsystem för att rekommendera artiklarna från Peltarion Knowledge Center. Genom att integrera två datakällor, implicit användaråterkoppling baserad på sidvisningsdata samt innehållet i artiklar, föreslår vi en hybridrekommendatörslösning. Under våra experiment jämför vi vår föreslagna lösning med en matrisfaktoriseringsmetod samt en popularitetsbaserad och en slumpmässig baslinje, analyserar hyperparametrarna i vår modell och undersöker förmågan hos vår lösning att ge rekommendationer till nya användare som inte deltog av träningsdatamängden. Vår modell resulterar i något mindre men liknande Mean Average Precision och Mean Reciprocal Rank poäng till matrisfaktoriseringsmetoden och överträffar de popularitetsbaserade och slumpmässiga baslinjerna. De viktigaste fördelarna med vår modell är beräkningseffektivitet och dess förmåga att ge relevanta rekommendationer till nya användare utan behov av omskolning av modellen, vilket är nyckelfunktioner för verkliga användningsfall.
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Kaykobad, M. Tanvir. "Transforming Plane Triangulations by Simultaneous Diagonal Flips." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40499.

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We explore the problem of transforming plane triangulations using simultaneous diagonal flips. Wagner showed that any n-vertex plane triangulation can be transformed to any other plane triangulation on equal number of vertices using a finite sequence of diagonal flips. Later on it has been established that O(n) individual flips suffice to complete this transformation. Bose et al. showed that the transformation can also be done in 4 × ( 2 / log 54/53 + 2 / log 6/5 ) logn + 2 ≈ 327.1 log n simultaneous flips. This bound is asymptotically tight. We present two algorithms to improve the leading coefficient of this bound for transforming any plane triangulation into any other. The first of the two algorithms lowers this bound down to 4 × ( 2 / log 12/11 + 2 / log 9/7 ) logn + 2 ≈ 85.8 log n. By processing and preprocessing the interior and exterior of the triangulation’s Hamiltonian cycle parallelly in an interlaced fashion, we make further improvement of the algorithm from ≈ 327.1 log n down to 12 / log 6/5 logn + 2 ≈ 45.6 log n.
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Islam, Md Kamrul. "Explainable link prediction in large complex graphs - application to drug repurposing." Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0203.

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De nombreux systèmes complexes du monde réel peuvent être représentés par des graphes, où les nœuds représentent des entités et les liens des relations entre les paires de nœuds. La prédiction de liens (LP) est l'un des problèmes les plus intéressants et les plus anciens dans le domaine de l'exploration de graphes ; elle prédit la probabilité d'un lien entre deux nœuds non connectés. Cette thèse étudie le problème LP dans les graphes simples et les graphes de connaissances (KGs). La première partie de cette thèse se concentre sur le problème LP dans les graphes simples. Dans la première étude, des approches basées sur la similarité et sur l'encastrement sont évaluées et comparées sur des graphes simples de différents domaines. L'étude a également identifié la difficulté de fixer le seuil du score de similarité pour calculer la métrique de précision des approches basées sur la similarité et a proposé une nouvelle méthode pour calculer la métrique. Les résultats ont montré la supériorité attendue des approches basées sur l'intégration. Cependant, chaque approche basée sur la similarité s'est avérée compétitive sur des graphes aux propriétés spécifiques. Nous avons pu vérifier expérimentalement que les approches basées sur la similarité sont explicables mais manquent de généralisation, tandis que les approches basées sur l'encastrement sont générales mais non explicables. La deuxième étude tente de surmonter la limitation de l'inexplicabilité des approches basées sur l'encastrement en découvrant des connexions intéressantes entre elles et les approches basées sur la similarité. La troisième étude démontre comment les approches basées sur la similarité peuvent être assemblées pour concevoir une approche LP supervisée explicable. Il est intéressant de noter que l'étude montre des performances LP élevées pour l'approche supervisée sur différents graphes, ce qui est très satisfaisant. La deuxième partie de la thèse se concentre sur les LP dans les KGs. Un KG est représenté comme une collection de triplets RDF, (head,relation,tail) où les entités head et tail sont reliées par une relation spécifique. Le problème de LP dans un KG est formulé comme la prédiction de la tête ou de la queue manquante dans un triplet. La LP basée sur l'incorporation de KG est devenue très populaire ces dernières années, et la génération de triplets négatifs est une tâche importante dans les méthodes d'incorporation. La quatrième étude traite d'une nouvelle méthode appelée SNS pour générer des triplets négatifs de haute qualité. Nos résultats montrent une meilleure performance LP lorsque SNS est utilisé que lorsque d'autres méthodes d'échantillonnage négatif sont utilisées. La deuxième étude traite d'une nouvelle méthode d'extraction de règles neuro-symboliques et d'une stratégie d'abduction pour expliquer les LP par une approche basée sur l'intégration en utilisant les règles apprises. La troisième étude applique notre LP explicable pour développer une nouvelle approche de repositionnement des médicaments pour COVID-19. L'approche apprend un ensemble d'enchâssements d'entités et de relations dans un KG centré sur COVID-19 pour obtenir un meilleur enchâssement des éléments du graphe. Pour la première fois à notre connaissance, des méthodes de criblage virtuel sont ensuite utilisées pour évaluer les prédictions obtenues à l'aide des embeddings. L'évaluation moléculaire et les chemins explicatifs apportent de la fiabilité aux résultats de prédiction et sont de nouvelles méthodes complémentaires et réutilisables pour mieux évaluer les molécules proposées pour le repositionnement. La dernière étude propose une architecture distribuée pour l'apprentissage des KG embeddings dans des environnements distribués et parallèles. Les résultats révèlent que l'apprentissage dans l'environnement distribué proposé, par rapport à un apprentissage centralisé, réduit considérablement le temps de calcul des méthodes d'incorporation KG sans affecter les performances des LP
Many real-world complex systems can be well-represented with graphs, where nodes represent objects or entities and links/relations represent interactions between pairs of nodes. Link prediction (LP) is one of the most interesting and long-standing problems in the field of graph mining; it predicts the probability of a link between two unconnected nodes based on available information in the current graph. This thesis studies the LP problem in graphs. It consists of two parts: LP in simple graphs and LP knowledge graphs (KGs). In the first part, the LP problem is defined as predicting the probability of a link between a pair of nodes in a simple graph. In the first study, a few similarity-based and embedding-based LP approaches are evaluated and compared on simple graphs from various domains. he study also criticizes the traditional way of computing the precision metric of similarity-based approaches as the computation faces the difficulty of tuning the threshold for deciding the link existence based on the similarity score. We proposed a new way of computing the precision metric. The results showed the expected superiority of embedding-based approaches. Still, each of the similarity-based approaches is competitive on graphs with specific properties. We could check experimentally that similarity-based approaches are fully explainable but lack generalization due to their heuristic nature, whereas embedding-based approaches are general but not explainable. The second study tries to alleviate the unexplainability limitation of embedding-based approaches by uncovering interesting connections between them and similarity-based approaches to get an idea of what is learned in embedding-based approaches. The third study demonstrates how the similarity-based approaches can be ensembled to design an explainable supervised LP approach. Interestingly, the study shows high LP performance for the supervised approach across various graphs, which is competitive with embedding-based approaches.The second part of the thesis focuses on LP in KGs. A KG is represented as a collection of RDF triples, (head,relation,tail) where the head and the tail are two entities which are connected by a specific relation. The LP problem in a KG is formulated as predicting missing head or tail entities in a triple. LP approaches based on the embeddings of entities and relations of a KG have become very popular in recent years, and generating negative triples is an important task in KG embedding methods. The first study in this part discusses a new method called SNS to generate high-quality negative triples during the training of embedding methods for learning embeddings of KGs. The results we produced show better LP performance when SNS is injected into an embedding approach than when injecting state-of-the-art negative triple sampling methods. The second study in the second part discusses a new neuro-symbolic method of mining rules and an abduction strategy to explain LP by an embedding-based approach utilizing the learned rules. The third study applies the explainable LP to a COVID-19 KG to develop a new drug repurposing approach for COVID-19. The approach learns ”ensemble embeddings” of entities and relations in a COVID-19 centric KG, in order to get a better latent representation of the graph elements. For the first time to our knowledge, molecular docking is then used to evaluate the predictions obtained from drug repurposing using KG embedding. Molecular evaluation and explanatory paths bring reliability to prediction results and constitute new complementary and reusable methods for assessing KG-based drug repurposing. The last study proposes a distributed architecture for learning KG embeddings in distributed and parallel settings. The results of the study that the computational time of embedding methods improves remarkably without affecting LP performance when they are trained in the proposed distributed settings than the traditional centralized settings
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Lehbab, Imène. "Problèmes métriques dans les espaces de Grassmann." Electronic Thesis or Diss., Mulhouse, 2023. http://www.theses.fr/2023MULH6508.

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Il s'agit d'une contribution dans le domaine de la géométrie métrique du plan projectif complexe CP2 et de la variété de Grassmann réelle des plans dans R6. On s'intéresse à l'étude de tous les p-uplets, p ≥ 3, de droites équiangulaires dans C3 et des p-uplets de plans équi-isoclins dans R6. Sachant que 9 est le nombre maximum de droites équiangulaires que l'on peut construire dans C3, on décrit une méthode qui permet de construire tous les p-uplets de droites équiangulaires pour tout pϵ[3,9]. En particulier, on construit dans C3 cinq classes de congruence de quadruplets de droites équiangulaires dont une dépend d'un paramètre réel ɣ que l'on étend à une famille infinie de sextuplets de droites équiangulaires dépendant du même paramètre réel ɣ. En outre, on donne les angles pour lesquels nos sextuplets s'étendent au-delà et jusqu'aux 9-uplets. On sait qu'il existe un p-uplet, p≥3, de plans équi-isoclins engendrant Rr, r≥4, de paramètre c, 0
This work contributes to the field of metric geometry of the complex projective plane CP2 and the real Grassmannian manifold of the planes in R6. More specifically, we study all p-tuples, p ≥ 3, of equiangular lines in C3 or equidistant points in CP2, and p-tuples of equi-isoclinic planes in R6. Knowing that 9 is the maximum number of equiangular lines that can be constructed in C3, we develop a method to obtain all p-tuples of equiangular lines for all p ϵ [3,9]. In particular, we construct in C3 five congruence classes of quadruples of equiangular lines, one of which depends on a real parameter ɣ, which we extend to an infinite family of sextuples of equiangular lines depending on the same real parameter ɣ. In addition, we give the angles for which our sextuples extend beyond and up to 9-tuples. We know that there exists a p-tuple, p ≥ 3, of equi-isoclinic planes generating Rr, r ≥ 4, with parameter c, 0< c <1, if and only if there exists a square symmetric matrix, called Seidel matrix, of p × p square blocks of order 2, whose diagonal blocks are all zero and the others are orthogonal matrices in O(2) and whose smallest eigenvalue is equal to - 1/c and has multiplicity 2p-r. In this thesis, we investigate the case r=6 and we also show that we can explicitly determine the spectrum of all Seidel matrices of order 2p, p ≥ 3 whose off-diagonal blocks are in {R0, S0} where R0 and S0 are respectively the zero-angle rotation and the zero-angle symmetry. We thus show an unexpected link between some p-tuples of equi-isoclinic planes in Rr and simple graphs of order p
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Montanaro, William M. Jr. "Character Degree Graphs of Almost Simple Groups." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1398345504.

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Soames, Kieron, and Jonas Lind. "Detecting Cycles in GraphQL Schemas." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-156174.

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GraphQL is a database handling API created by Facebook, that provides an effective al-ternative to REST-style architectures. GraphQL provides the ability for a client to spec-ify exactly what data it wishes to receive. A problem with GraphQL is that the freedomof creating customized requests allows data to be included several times in the response,growing the response’s size exponentially. The thesis contributes to the field of GraphQLanalysis by studying the prevalence of simple cycles in GraphQL schemas. We have im-plemented a locally-run tool and webtool using Tarjan’s and Johnson’s algorithms, thatparses the schemas, creates a directed graph and enumerates all simple cycles in the graph.A collection of schemas was analysed with the tool to collect empirical data. It was foundthat 39.73 % of the total 2094 schemas contained at least one simple cycle, with the averagenumber of cycles per schema being 4. The runtime was found to be on average 11 mil-liseconds, most of which consisted of the time for parsing the schemas. It was found that44 out of the considered schemas could not be enumerated due to containing a staggeringamount of simple cycles. It can be concluded that it is possible to test schemas for cyclicityand enumerate all simple cycles in a given schema efficiently.
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Yan, Chenyu. "APPROXIMATING DISTANCES IN COMPLICATED GRAPHS BY DISTANCES IN SIMPLE GRAPHS WITH APPLICATIONS." Kent State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1184639623.

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Okeke, Nnamdi, and University of Lethbridge Faculty of Arts and Science. "Character generators and graphs for simple lie algebras." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2006, 2006. http://hdl.handle.net/10133/532.

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We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is ¯rst re- viewed. A new general formula is then found. It makes clear the distinct roles of \outside" and \inside" elements of the integrity basis, and helps determine their quadratic incompati- bilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We ¯nd that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simpli¯ed for the purposes of constructing the character generator. The generating functions can be written easily using the simpli¯ed versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.
vii, 92 leaves ; 29 cm.
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Books on the topic "Simple graph"

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Haviar, Miroslav. Vertex labellings of simple graphs. Lemgo, Germany: Heldermann Verlag, 2015.

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Booth, Bob. Simple use of Cricket Graph for PC Windows. Sheffield: University of Sheffield, Academic Computing Services, 1992.

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Jerrum, Mark. A very simple algorithm for estimating the numberof k-colourings of a low-degree graph. Edinburgh: LFCS, Dept. of Computer Science, University of Edinburgh, 1994.

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Praeger, Cheryl E. Low rank representations and graphs for sporadic groups. Cambridge [England]: Cambridge University Press, 1997.

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Praeger, Cheryl E. Low rank representations and graphs for sporadic groups. New York: Cambridge University Press, 1996.

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Dearing, P. M. Boolean and graph theoretic formulation of the simple plant location problem. Monterey, Calif: Naval Postgraduate School, 1987.

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FREEBERG, ERLING, and DOLORES FREEBERG. Simple Graph Art. Teacher Created Resources, 2004.

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Pancer, Richard Norman. GED - a graph EDitor for labelled simple directed acyclic graphs. 1985.

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BOOK, Modo. Notebook Isometric Graph: Simple Isometric Graph Paper Notebook - 110 Pages. Independently Published, 2021.

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press, isometric. Isometric Graph Paper: Simple Isometric Graph Paper Notebook - 110 Pages. Independently Published, 2021.

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Book chapters on the topic "Simple graph"

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Hougardy, Stefan, and Jens Vygen. "Simple Graph Algorithms." In Algorithmic Mathematics, 85–90. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-39558-6_7.

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Brandes, Ulrik, and Boris Köpf. "Fast and Simple Horizontal Coordinate Assignment." In Graph Drawing, 31–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45848-4_3.

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Barth, Wilhelm, Michael Jünger, and Petra Mutzel. "Simple and Efficient Bilayer Cross Counting." In Graph Drawing, 130–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36151-0_13.

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Fairbairn, Jon. "A simple abstract machine to execute supercombinators." In Graph Reduction, 49–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-18420-1_49.

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Mamakani, Khalegh, and Frank Ruskey. "The First Simple Symmetric 11-Venn Diagram." In Graph Drawing, 563–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36763-2_54.

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Daescu, Ovidiu, and Jun Luo. "Computing Simple Paths on Points in Simple Polygons." In Computational Geometry and Graph Theory, 41–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-89550-3_5.

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Bekos, Michael A., and Chrysanthi N. Raftopoulou. "Circle-Representations of Simple 4-Regular Planar Graphs." In Graph Drawing, 138–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36763-2_13.

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Kaugars, Karlis, Juris Reinfelds, and Alvis Brazma. "A simple algorithm for drawing large graphs on small screens." In Graph Drawing, 278–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-58950-3_382.

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Forster, Michael. "A Fast and Simple Heuristic for Constrained Two-Level Crossing Reduction." In Graph Drawing, 206–16. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31843-9_22.

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Kynčl, Jan, and Pavel Valtr. "On Edges Crossing Few Other Edges in Simple Topological Complete Graphs." In Graph Drawing, 274–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11618058_25.

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Conference papers on the topic "Simple graph"

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Wu, Junran, Shangzhe Li, Jianhao Li, Yicheng Pan, and Ke Xu. "A Simple yet Effective Method for Graph Classification." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/497.

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In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models. Intuitively, given a problem, a simpler data structure comes with a simpler algorithm. Here, we investigate the feasibility of improving graph classification performance while simplifying the learning process. Inspired by structural entropy on graphs, we transform the data sample from graphs to coding trees, which is a simpler but essential structure for graph data. Furthermore, we propose a novel message passing scheme, termed hierarchical reporting, in which features are transferred from leaf nodes to root nodes by following the hierarchical structure of coding trees. We then present a tree kernel and a convolutional network to implement our scheme for graph classification. With the designed message passing scheme, the tree kernel and convolutional network have a lower runtime complexity of O(n) than Weisfeiler-Lehman subtree kernel and other graph neural networks of at least O(hm). We empirically validate our methods with several graph classification benchmarks and demonstrate that they achieve better performance and lower computational consumption than competing approaches.
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Pho, Patrick, and Alexander V. Mantzaris. "Link prediction with Simple Graph Convolution and regularized Simple Graph Convolution." In ICISDM 2022: 2022 the 6th International Conference on Information System and Data Mining. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3546157.3546163.

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Abdelmoneum, Farida, John Shi, and José M. F. Moura. "Graph Classification via Simple Graph Based Features." In 2023 57th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2023. http://dx.doi.org/10.1109/ieeeconf59524.2023.10477007.

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Schramm, Simon. "Constructing the Simple Timeseries Event Model." In 2023 IEEE International Conference on Knowledge Graph (ICKG). IEEE, 2023. http://dx.doi.org/10.1109/ickg59574.2023.00022.

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Li, Pengyong, Jun Wang, Ziliang Li, Yixuan Qiao, Xianggen Liu, Fei Ma, Peng Gao, Sen Song, and Guotong Xie. "Pairwise Half-graph Discrimination: A Simple Graph-level Self-supervised Strategy for Pre-training Graph Neural Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/371.

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Self-supervised learning has gradually emerged as a powerful technique for graph representation learning. However, transferable, generalizable, and robust representation learning on graph data still remains a challenge for pre-training graph neural networks. In this paper, we propose a simple and effective self-supervised pre-training strategy, named Pairwise Half-graph Discrimination (PHD), that explicitly pre-trains a graph neural network at graph-level. PHD is designed as a simple binary classification task to discriminate whether two half-graphs come from the same source. Experiments demonstrate that the PHD is an effective pre-training strategy that offers comparable or superior performance on 13 graph classification tasks compared with state-of-the-art strategies, and achieves notable improvements when combined with node-level strategies. Moreover, the visualization of learned representation revealed that PHD strategy indeed empowers the model to learn graph-level knowledge like the molecular scaffold. These results have established PHD as a powerful and effective self-supervised learning strategy in graph-level representation learning.
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Dhurandhar, Amit, and Tejaswini Pedapati. "Multihop: Leveraging Complex Models to Learn Accurate Simple Models." In 2022 IEEE International Conference on Knowledge Graph (ICKG). IEEE, 2022. http://dx.doi.org/10.1109/ickg55886.2022.00014.

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Click, Cliff, and Michael Paleczny. "A simple graph-based intermediate representation." In Papers from the 1995 ACM SIGPLAN workshop. New York, New York, USA: ACM Press, 1995. http://dx.doi.org/10.1145/202529.202534.

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Zatesko, Leandro M., Renato Carmo, and André L. P. Guedes. "Novel Procedures for Graph Edge-colouring." In XXXII Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/ctd.2019.6331.

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We present a novel recolouring procedure for graph edge-colouring. We show that all graphs whose vertices have local degree sum not too large can be optimally edge-coloured in polynomial time. We also show that the set ofthe graphs satisfying this condition includes almost every graph (under the uniform distribution). We present further results on edge-colouring join graphs, chordal graphs, circular-arc graphs, and complementary prisms, whose proofs yield polynomial-time algorithms. Our results contribute towards settling the Over- full Conjecture, the main open conjecture on edge-colouring simple graphs. Fi- nally, we also present some results on total colouring.
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Wang, Huijuan, Siming Dai, Weiyue Su, Hui Zhong, Zeyang Fang, Zhengjie Huang, Shikun Feng, Zeyu Chen, Yu Sun, and Dianhai Yu. "Simple and Effective Relation-based Embedding Propagation for Knowledge Representation Learning." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/382.

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Relational graph neural networks have garnered particular attention to encode graph context in knowledge graphs (KGs). Although they achieved competitive performance on small KGs, how to efficiently and effectively utilize graph context for large KGs remains an open problem. To this end, we propose the Relation-based Embedding Propagation (REP) method. It is a post-processing technique to adapt pre-trained KG embeddings with graph context. As relations in KGs are directional, we model the incoming head context and the outgoing tail context separately. Accordingly, we design relational context functions with no external parameters. Besides, we use averaging to aggregate context information, making REP more computation-efficient. We theoretically prove that such designs can avoid information distortion during propagation. Extensive experiments also demonstrate that REP has significant scalability while improving or maintaining prediction quality. Particularly, it averagely brings about 10% relative improvement to triplet-based embedding methods on OGBL-WikiKG2 and takes 5%-83% time to achieve comparable results as the state-of-the-art GC-OTE.
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Tu, Wenxuan, Sihang Zhou, Xinwang Liu, Yue Liu, Zhiping Cai, En Zhu, Changwang Zhang, and Jieren Cheng. "Initializing Then Refining: A Simple Graph Attribute Imputation Network." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/485.

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Representation learning on the attribute-missing graphs, whose connection information is complete while the attribute information of some nodes is missing, is an important yet challenging task. To impute the missing attributes, existing methods isolate the learning processes of attribute and structure information embeddings, and force both resultant representations to align with a common in-discriminative normal distribution, leading to inaccurate imputation. To tackle these issues, we propose a novel graph-oriented imputation framework called initializing then refining (ITR), where we first employ the structure information for initial imputation, and then leverage observed attribute and structure information to adaptively refine the imputed latent variables. Specifically, we first adopt the structure embeddings of attribute-missing samples as the embedding initialization, and then refine these initial values by aggregating the reliable and informative embeddings of attribute-observed samples according to the affinity structure. Specially, in our refining process, the affinity structure is adaptively updated through iterations by calculating the sample-wise correlations upon the recomposed embeddings. Extensive experiments on four benchmark datasets verify the superiority of ITR against state-of-the-art methods.
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Reports on the topic "Simple graph"

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Green, Alastair, Paolo Guagliardo, and Leonid Libkin. Property graphs and paths in GQL: Mathematical definitions. Linked Data Benchmark Council, October 2021. http://dx.doi.org/10.54285/ldbc.tzjp7279.

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This paper provides precise mathematical definitions of a property graph as specified in the proposed GQL international standard, which is an attributed mixed multigraph with loops. It further defines a partially-oriented walk in such a property graph, which is called a path in GQL, as well as restricted classes of such walks (trails, simple/acyclic paths).
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Striuk, Andrii, Olena Rybalchenko, and Svitlana Bilashenko. Development and Using of a Virtual Laboratory to Study the Graph Algorithms for Bachelors of Software Engineering. [б. в.], November 2020. http://dx.doi.org/10.31812/123456789/4462.

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The paper presents an analysis of the importance of studying graph algorithms, the reasons for the need to implement this project and its subsequent use. The existing analogues analysis is carried out, due to which a list of advantages and disadvantages is formed and taken into account in developing the virtual laboratory. A web application is created that clearly illustrates the work of graph algorithms, such as Depth-First Search, Dijkstra’s Shortest Path, Floyd- Warshall, Kruskal Minimum Cost Spanning Tree Algorithm. A simple and user- friendly interface is developed and it is supported by all popular browsers. The software product is provided with user registration and authorization functions, chat communication, personal cabinet editing and viewing the statistics on web- application use. An additional condition is taken into account at the design stage, namely the flexibility of the architecture, which envisaged the possibility of easy expansion of an existing functionality. Virtual laboratory is used at Kryvyi Rih National University to training students of specialty 121 Software Engineering in the disciplines “Algorithms and Data Structures” and “Discrete Structures”.
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Pinzon, Mauricio, and Arturo Galindo. Revelation of Expectations in Latin America (REVELA): No. 17 : September, 2008. Inter-American Development Bank, September 2008. http://dx.doi.org/10.18235/0008250.

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REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. The September issue of REVELA reports that growth expectations for 2008 are almost unchanged with respect to last month's survey. Now the simple average expected growth rate is 5.29%. However, growth is expected to slow in 2009, to an average of 4.7%, slightly down from last month 4.8% 2009 forecast. On the other hand, the expected inflation rate for 2008 increased from 9.43% to 9.59%. Inflation expectations for 2009 decreased, reaching a simple average of 8.63%.
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Galindo, Arturo, and Mauricio Pinzon. Revelation of Expectations in Latin America (REVELA): No. 23 : March, 2009. Inter-American Development Bank, March 2009. http://dx.doi.org/10.18235/0008255.

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REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. In this March issue, REVELA reports that growth expectations for 2009 decreased with respect to last month's survey. Now the simple average expected growth rate is 1.91%. In the same way, growth is expected to slow in 2010, to an average of 3.29%, down from last month's 3.62% 2010 forecast. On the other hand, the expected inflation rate for 2009 decreased from 7.25% to 6.66%. The simple average of the expected inflation rate for 2010 is 5.99%.
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5

Salazni, Mariana, Andrew Powell, Mauricio Pinzon, and Arturo Galindo. Revelation of Expectations in Latin America (REVELA): No. 16 : August, 2008. Inter-American Development Bank, August 2008. http://dx.doi.org/10.18235/0008249.

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REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. In this August issue, REVELA reports that growth expectations for 2008 are almost unchanged with respect to last month's survey. Now the simple average expected growth rate is 5.31%. However, growth is expected to slow in 2009, to an average of 4.8%, slightly down from last month 4.9% 2009 forecast. On the other hand, inflation expectations continue to rise; the expected inflation rate for 2008 increased from 8.95% to 9.43%. Inflation expectations for 2009 have also increased, reaching a simple average of 8.4%.
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6

Pinzon, Mauricio, and Arturo Galindo. Revelation of Expectations in Latin America (REVELA): No. 21 : January, 2009. Inter-American Development Bank, January 2009. http://dx.doi.org/10.18235/0008253.

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Abstract:
REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. In this January issue, REVELA reports that growth expectations for 2009 decreased with respect to last month's survey. Now the simple average expected growth rate is 2.97%. In the same way, growth is expected to slow in 2010, to an average of 3.54%, down from last month's 3.62% 2010 forecast. On the other hand, the expected inflation rate for 2009 decreased from 8.09% to 7.56%. The simple average of the expected inflation rate for 2010 is 5.96%.
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7

Pinzon, Mauricio, and Arturo Galindo. Revelation of Expectations in Latin America (REVELA): No. 20 : December, 2008. Inter-American Development Bank, December 2008. http://dx.doi.org/10.18235/0008252.

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Abstract:
REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. In this December issue, REVELA reports that growth expectations for 2008 decreased with respect to last month's survey. Now the simple average expected growth rate is 5.22%. In the same way, growth is expected to slow in 2009, to an average of 3.12%, down from last month's 3.80% 2009 forecast. On the other hand, the expected inflation rate for 2008 decreased from 9.47% to 9.24%. Inflation expectations for 2009 decreased, reaching a simple average of 8.09%.
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8

Pinzon, Mauricio, and Arturo Galindo. Revelation of Expectations in Latin America (REVELA): No. 18 : October, 2008. Inter-American Development Bank, October 2008. http://dx.doi.org/10.18235/0008251.

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Abstract:
REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. In this October issue, REVELA reports that growth expectations for 2008 increased with respect to last month's survey. Now the simple average expected growth rate is 5.45%. However, growth is expected to slow in 2009, to an average of 4.4%, down from last month 4.7% 2009 forecast. On the other hand, the expected inflation rate for 2008 increased from 9.59% to 9.66%. Inflation expectations for 2009 decreased, reaching a simple average of 8.38%.
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9

Galindo, Arturo, and Mauricio Pinzon. Revelation of Expectations in Latin America (REVELA): No. 22 : February, 2009. Inter-American Development Bank, February 2009. http://dx.doi.org/10.18235/0008254.

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Abstract:
REVELA analyzes market expectations of growth and inflation in Latin American countries. The figures analyzed represent the results of surveys of private sector actors conducted by the central banks of each country according to their own specific methodologies. They do not represent official projections by the IDB or any other official body. RES collects the results of these surveys from participating central banks on a monthly basis to produce a report and a set of illustrative graphs and tables. In this February issue, REVELA reports that growth expectations for 2009 decreased with respect to last month's survey. Now the simple average expected growth rate is 2.66%. In the same way, growth is expected to slow in 2010, to an average of 3.34%, down from last month's 3.54% 2010 forecast. On the other hand, the expected inflation rate for 2009 decreased from 7.56% to 7.25%. The simple average of the expected inflation rate for 2010 is 5.63%.
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10

Sondheim, M., and C. Hodgson. Common hydrology features (CHyF) logical model. Natural Resources Canada/CMSS/Information Management, 2024. http://dx.doi.org/10.4095/328952.

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The Open Geospatial Consortium has defined "OGC WaterML 2: Part 3 - Surface Hydrology Features (HY_Features) - Conceptual Model", but not any particular implementation of it. The Common Hydrology Features (CHyF) model extends HY_Features and makes some minor changes to it required for implementation and the delivery of high performance services. HY_Features discusses catchment coverage and topological relations. In CHyF these are key ideas, as is the notion that hydrologically defined network components form elements of a mathematical graph, allowing for very fast network traversal. HY_Features defines catchments and catchment networks, as well as rivers, channels, flowpaths and hydrographic networks. The CHyF logical model specifies a profile and some extensions to HY_Features, as required to implement topological and graph relations. This starts with the definition of elementary catchments and elementary flowpaths, which are treated as fundamental elements. They are tightly specified terms corresponding to basic catchments and flowpaths in HY_Features and the basic components in the standard reach-catchment model (Maidment and Clark, 2016). If they are subdivided, the result is simply more elementary catchments and elementary flowpaths. Consequently, they are the building blocks used to form complementary coverages as well as a graph structure referred to as a hygraph. Building the hygraph necessitates that connections between features be manifest through their geometry. Divergences and distributaries are supported in CHyF, as the hygraph need not be hierarchical. Nevertheless, CHyF does recognize hierarchical drainage basins and the value in identifying them explicitly (Blodgett, et al, 2021). Different kinds of elementary catchments and elementary flowpaths are defined in CHyF. Of note is that polygonal waterbody features, or portions of such features, are treated as elementary catchments in their own right. In addition to these water catchments, several kinds of land-based elementary catchments are recognized. These model constructs are compatible with the higher level conceptual model in HY_Features, although they differ in detail from other popular implementation models. With the approach taken it becomes practical to handle very large lakes and rivers, as well as coastal ocean zones. CHyF also includes wetlands, glaciers and snowfields as kinds of hydro features; these features help complete the concept of a catchment coverage as put forward by HY_Features.
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