Showing papers on "Line graph published in 2021"

Self-Supervised Hypergraph Convolutional Networks for Session-based Recommendation

Abstract: Session-based recommendation (SBR) focuses on next-item prediction at a certain time point. As user profiles are generally not available in this scenario, capturing the user intent lying in the item transitions plays a pivotal role. Recent graph neural networks (GNNs) based SBR methods regard the item transitions as pairwise relations, which neglect the complex high-order information among items. Hypergraph provides a natural way to capture beyond-pairwise relations, while its potential for SBR has remained unexplored. In this paper, we fill this gap by modeling session-based data as a hypergraph and then propose a hypergraph convolutional network to improve SBR. Moreover, to enhance hypergraph modeling, we devise another graph convolutional network which is based on the line graph of the hypergraph and then integrate self-supervised learning into the training of the networks by maximizing mutual information between the session representations learned via the two networks, serving as an auxiliary task to improve the recommendation task. Since the two types of networks both are based on hypergraph, which can be seen as two channels for hypergraph modeling, we name our model DHCN (Dual Channel Hypergraph Convolutional Networks). Extensive experiments on three benchmark datasets demonstrate the superiority of our model over the SOTA methods, and the results validate the effectiveness of hypergraph modeling and self-supervised task. The implementation of our model is available via https://github.com/xiaxin1998/DHCN.

Atomistic Line Graph Neural Network for improved materials property predictions

Abstract: Graph neural networks (GNN) have been shown to provide substantial performance improvements for atomistic material representation and modeling compared with descriptor-based machine learning models. While most existing GNN models for atomistic predictions are based on atomic distance information, they do not explicitly incorporate bond angles, which are critical for distinguishing many atomic structures. Furthermore, many material properties are known to be sensitive to slight changes in bond angles. We present an Atomistic Line Graph Neural Network (ALIGNN), a GNN architecture that performs message passing on both the interatomic bond graph and its line graph corresponding to bond angles. We demonstrate that angle information can be explicitly and efficiently included, leading to improved performance on multiple atomistic prediction tasks. We ALIGNN models for predicting 52 solid-state and molecular properties available in the JARVIS-DFT, Materials project, and QM9 databases. ALIGNN can outperform some previously reported GNN models on atomistic prediction tasks by up to 85% in accuracy with better or comparable model training speed.

Line Graph Neural Networks for Link Prediction.

Abstract: We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered at two neighboring nodes and use the features to predict the label of the link between these two nodes. In this formalism, a link prediction problem is converted to a graph classification task. In order to extract fixed-size features for classification, graph pooling layers are necessary in the deep learning model, thereby incurring information loss. To overcome this key limitation, we propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task. Experimental results on fourteen datasets from different applications demonstrate that our proposed method consistently outperforms the state-of-the-art methods, while it has fewer parameters and high training efficiency.

Multilevel Graph Matching Networks for Deep Graph Similarity Learning.

Abstract: While the celebrated graph neural networks (GNNs) yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity learning has considered either global-level graph-graph interactions or low-level node-node interactions, however, ignoring the rich cross-level interactions (e.g., between each node of one graph and the other whole graph). In this article, we propose a multilevel graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects in an end-to-end fashion. In particular, the proposed MGMN consists of a node-graph matching network (NGMN) for effectively learning cross-level interactions between each node of one graph and the other whole graph, and a siamese GNN to learn global-level interactions between two input graphs. Furthermore, to compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks with different sizes in order to evaluate the effectiveness and robustness of our models. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks. Compared with previous work, multilevel graph matching network (MGMN) also exhibits stronger robustness as the sizes of the two input graphs increase.

The general position problem on Kneser graphs and on some graph operations

Abstract: A vertex subset $S$ of a graph $G$ is a general position set of $G$ if no vertex of $S$ lies on a geodesic between two other vertices of $S$. The cardinality of a largest general position set of $G$ is the general position number (gp-number) ${\rm gp}(G)$ of $G$. The gp-number is determined for some families of Kneser graphs, in particular for $K(n,2)$ and $K(n,3)$. A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.

LGESQL: Line Graph Enhanced Text-to-SQL Model with Mixed Local and Non-Local Relations

Abstract: This work aims to tackle the challenging heterogeneous graph encoding problem in the text-to-SQL task. Previous methods are typically node-centric and merely utilize different weight matrices to parameterize edge types, which 1) ignore the rich semantics embedded in the topological structure of edges, and 2) fail to distinguish local and non-local relations for each node. To this end, we propose a Line Graph Enhanced Text-to-SQL (LGESQL) model to mine the underlying relational features without constructing meta-paths. By virtue of the line graph, messages propagate more efficiently through not only connections between nodes, but also the topology of directed edges. Furthermore, both local and non-local relations are integrated distinctively during the graph iteration. We also design an auxiliary task called graph pruning to improve the discriminative capability of the encoder. Our framework achieves state-of-the-art results (62.8% with Glove, 72.0% with Electra) on the cross-domain text-to-SQL benchmark Spider at the time of writing.

The enumeration of spanning tree of weighted graphs

Abstract: A polynomial associated with G is defined as $$t(G,w)=\sum _{T\in {\mathbb {T}}(G)}\prod _{e\in E(T)}w_e(G)$$ ( $${\mathbb {T}}(G)$$ is the set of spanning trees of G), which is a weighted enumeration of spanning trees of graphs It is known that any graph G is an intersection graph of a linear hypergraph, which corresponds to a clique partition of G In this paper, we introduce the Schur complement formula and local transformation formula of t(G, w) By using these formulas, we obtain some expressions of t(G, w) for weighted intersection graphs and express the number of spanning trees of graph G in terms of clique partitions of G As applications, expressions for enumerating spanning trees in bipartite graphs, line graphs, generalized line graphs, middle graphs, total graphs, generalized join graphs and vertex-weighted graphs are derived from our work

Compact Graph Architecture for Speech Emotion Recognition

Abstract: We propose a deep graph approach to address the task of speech emotion recognition. A compact, efficient and scalable way to represent data is in the form of graphs. Following the theory of graph signal processing, we propose to model speech signal as a cycle graph or a line graph. Such graph structure enables us to construct a Graph Convolution Network (GCN)-based architecture that can perform an accurate graph convolution in contrast to the approximate convolution used in standard GCNs. We evaluated the performance of our model for speech emotion recognition on the popular IEMOCAP and MSP-IMPROV databases. Our model outperforms standard GCN and other relevant deep graph architectures indicating the effectiveness of our approach. When compared with existing speech emotion recognition methods, our model achieves comparable performance to the state-of-the-art with significantly fewer learnable parameters (~30K) indicating its applicability in resource-constrained devices. Our code is available at /github.com/AmirSh15/Compact_SER.

M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

Abstract: Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

Polypharmacy Side effect Prediction with Enhanced Interpretability Based on Graph Feature Attention Network.

Abstract: Motivation Polypharmacy side effects should be carefully considered for new drug development. However, considering all the complex drug-drug interactions that cause polypharma-cy side effects is challenging. Recently, graph neural network (GNN) models have handled these complex interactions successfully and shown great predictive perfor-mance. Nevertheless, the GNN models have difficulty providing intelligible factors of the prediction for biomedical and pharmaceutical domain experts. Method A novel approach, graph feature attention network (GFAN), is presented for inter-pretable prediction of polypharmacy side effects by emphasizing target genes differ-ently. To artificially simulate polypharmacy situations, where two different drugs are taken together, we formulated a node classification problem by using the concept of line graph in graph theory. Results Experiments with benchmark datasets validated interpretability of the GFAN and demonstrated competitive performance with the graph attention network in a previous work. And the specific cases in the polypharmacy side effect prediction experiments showed that the GFAN model is capable of very sensitively extracting the target genes for each side effect prediction. Availability and implementation https://github.com/SunjooBang/Polypharmacy-side-effect-prediction.

Cayley properties of the line graphs induced by consecutive layers of the hypercube

Abstract: Let $$n >3$$ and $$ 0< k < \frac{n}{2} $$ be integers. In this paper, we investigate some algebraic properties of the line graph of the graph $$ {Q_n}(k,k+1) $$ where $$ {Q_n}(k,k+1) $$ is the subgraph of the hypercube $$Q_n$$ which is induced by the set of vertices of weights k and $$k+1$$ . The graph $$ {Q_n}(k,k+1) $$ has a close relation to Johnson graph $$J(n+1,k+1)$$ . In fact, it is the square root of the graph $$J(n+1,k+1)$$ . We will see that when $$ n e 2k+1$$ , then the graph $$ {Q_n}(k,k+1) $$ is a non-regular edge-transitive graph; hence, its line graph is a vertex-transitive graph. In the first step, we determine the automorphism groups of these graphs for all values of n, k. In the second step, we study Cayley properties of the line graphs of these graphs. In particular, we show that if $$k\ge 3$$ and $$ n e 2k+1$$ , then except for the cases $$(k,n) e (3,9)$$ and $$(k,n) e (3,33)$$ , the line graph of the graph $$ {Q_n}(k,k+1) $$ is a vertex-transitive non-Cayley graph. Also, we show that the line graph of the graph $$ {Q_n}(1,2) $$ is a Cayley graph if and only if n is a power of a prime p. Moreover, we show that for ‘almost all’ even values of k, the line graph of the graph $$ {Q_{2k+1}}(k,k+1) $$ is a vertex-transitive non-Cayley graph.

JONNEE: Joint Network Nodes and Edges Embedding

Abstract: Recently, graph embedding models significantly improved the quality of graph machine learning tasks, such as node classification and link prediction. In this work, we propose a model called JONNEE (JOint Network Nodes and Edges Embedding), which learns node and edge embeddings under self-supervision via joint constraints in a given graph and its edge-to-vertex dual representation as a Line graph. The model uses two graph autoencoders with additional structural feature engineering and several regularization techniques to train for an adjacency matrix reconstruction task in an unsupervised setting. Experimental results show that our model performs on par with state-of-the-art undirected attribute graph embedding models and requires less number of epochs to achieve the same quality due to Line graph self-supervision under a unified embedding framework.

Centrality measures for node-weighted networks via line graphs and the matrix exponential

Abstract: This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented.

On the topological indices of the line graphs of polyhenylene dendrimer

Abstract: Chemical graph theory are usually use in topological indices for studied their bioactivitty and physical-chemical characteristic. These topological indices mostly use in the fields of chemistry, gene therapy and other areas of applied sciences. In our article, we study the line graph of one of the families of Polyphenylene dendrimer, namely D3[n]. We also compute their topological indices of the line graph of Polyphenylene dendrimer. In additional, to makes more interesting, we analyzed and showed the behavior of above computed topological indices towards Polyphenylene dendrimer.

Extending Perfect Matchings to Hamiltonian Cycles in Line Graphs

Abstract: A graph admitting a perfect matching has the Perfect-Matching-Hamiltonian property (for short the PMH-property) if each of its perfect matchings can be extended to a Hamiltonian cycle. In this paper we establish some sufficient conditions for a graph $G$ in order to guarantee that its line graph $L(G)$ has the PMH-property. In particular, we prove that this happens when $G$ is (i) a Hamiltonian graph with maximum degree at most $3$, (ii) a complete graph, or (iii) an arbitrarily traceable graph. Further related questions and open problems are proposed along the paper.

Preservation of the Classical Meanness Property of Some Graphs Based on Line Graph Operation

Abstract: In the present paper, we introduce the classical mean labeling of graphs and investigate their related properties. Moreover, it is obtained that the line graph operation preserves the classical meanness property for some standard graphs.

Enriched line graph: A new structure for searching language collocations

Abstract: The specific terminology of a specialty language comes, essentially, from specific uses of already existing words and/or from specific combinations of words so called “collocations”. In this work we introduce a new mathematical structure (enriched line graph) and a new methodology to extract properties and characteristics of a type of multilayer linguistic networks associated with these types of languages. Specifically, this work is focused on the description of a methodology based on a variant of the PageRank algorithm to locate the linguistic collocations and on defining a new structure (enriched line graph) that can be interpreted as a certain type of “interpolation” between the original graph and its associated line graph, showing new results, properties and applications of this concept, and, in particular, certain characteristics of the specialty language produced by the scientific community of complex networks.

Omega Index of Line and Total Graphs

Abstract: A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph. Calculating some properties of a derived graph helps to calculate the same properties of the original graph. For this reason, the relations between a graph and its derived graphs are always welcomed. A recently introduced graph index which also acts as a graph invariant called omega is used to obtain such relations for line and total graphs. As an illustrative exercise, omega values and the number of faces of the line and total graphs of some frequently used graph classes are calculated.

Line graphs of complex unit gain graphs with least eigenvalue -2

Abstract: Let $\mathbb T$ be the multiplicative group of complex units, and let $\mathcal L (\Phi)$ denote a line graph of a $\mathbb{T}$-gain graph $\Phi$ Similarly to what happens in the context of signed graphs, the real number $\min Spec(A(\mathcal L (\Phi))$, that is, the smallest eigenvalue of the adjacency matrix of $\mathcal L(\Phi)$, is not less than $-2$ The structural conditions on $\Phi$ ensuring that $\min Spec(A(\mathcal L (\Phi))=-2$ are identified When such conditions are fulfilled, bases of the $-2$-eigenspace are constructed with the aid of the star complement technique

Spectral Independence via Stability and Applications to Holant-Type Problems.

Abstract: This paper formalizes connections between stability of polynomials and convergence rates of Markov Chain Monte Carlo (MCMC) algorithms. We prove that if a (multivariate) partition function is nonzero in a region around a real point $\lambda$ then spectral independence holds at $\lambda$. As a consequence, for Holant-type problems (e.g., spin systems) on bounded-degree graphs, we obtain optimal $O(n\log n)$ mixing time bounds for the single-site update Markov chain known as the Glauber dynamics. Our result significantly improves the running time guarantees obtained via the polynomial interpolation method of Barvinok (2017), refined by Patel and Regts (2017). There are a variety of applications of our results. In this paper, we focus on Holant-type (i.e., edge-coloring) problems, including weighted edge covers and weighted even subgraphs. For the weighted edge cover problem (and several natural generalizations) we obtain an $O(n\log{n})$ sampling algorithm on bounded-degree graphs. The even subgraphs problem corresponds to the high-temperature expansion of the ferromagnetic Ising model. We obtain an $O(n\log{n})$ sampling algorithm for the ferromagnetic Ising model with a nonzero external field on bounded-degree graphs, which improves upon the classical result of Jerrum and Sinclair (1993) for this class of graphs. We obtain further applications to antiferromagnetic two-spin models on line graphs, weighted graph homomorphisms, tensor networks, and more.

Gap sets for the spectra of cubic graphs

Abstract: We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals $(2 \sqrt{2},3)$ and $[-3,-2)$ achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [-3,3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in $[-3,3)$ can be gapped by cubic graphs, even by planar ones. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.

Standards of Graph Construction in Special Education Research: A Review of their Use and Relevance

Abstract: Much of the special education literature features single-case experimental designs, which traditionally require researchers to determine functional relations among variables through the visual analyses of line graphs. Evidence suggests factors aside from the data influence visual analysis, including line graph construction. Fields including engineering, behavior analysis, and psychology have historically propagated standards related to the visual data displays to mitigate the effect of arbitrary graph construction on the interpretation of results. Although evidence suggests graphs featured in behavior analytic studies do not observe the standards, the extent to which researchers in special education adhere to longstanding graphing guidelines remains uncertain. The following article provides an overview of graphing standards and examines the adherence of line graphs from 532 issues of 28 distinct special education journals to traditional standards of visual display. Results indicated the majority of special education line graphs deviate from established line graph construction standards in important respects. The discussion centers on the need for updating and disseminating guidelines regarding line graph construction.

Characterization of regular bipolar fuzzy graphs

Abstract: In this paper, adjacency sequence of a vertex, first and second fundamental sequences are defined in a bipolar fuzzy graph with example. Some examples are constructed to show that if G is a regular bipolar fuzzy graph (BFG), the underlying crisp graph need not be regular and all the vertices need not have the same adjacency sequence. Also it is shown that if G and its underlying crisp graph are regular, all the vertices need not have the same adjacency sequence. A necessary and sufficient condition is established for a BFG with at most four vertices to be regular using the concept of adjacency sequences. Moreover, some characterizations have been made for a line graph of a regular BFG to be regular, the complement of a regular BFG to be regular, etc.

Atomistic Line Graph Neural Network for Improved Materials Property Predictions

Abstract: Graph neural networks (GNN) have been shown to provide much improved performance for representing and modeling atomistic materials compared with descriptor-based machine-learning models. While most existing GNN models for atomistic predictions are based on atomic distance information, they do not explicitly incorporate bond angles, which are critical for distinguishing many atomic structures. Furthermore, many material properties are known to be sensitive to slight changes in bond angles. We develop Atomistic Line Graph Neural Network (ALIGNN) using a GNN architecture that performs message passing on both the interatomic bond graph and its line graph corresponding to bond angles. We demonstrate that angle information can be explicitly and efficiently included for materials to provide much improved performance. We train 44 models for predicting several solid-state material properties available in the JARVIS-DFT and materials-project databases. ALIGNN can outperform some of the previously known GNN models by up to 43.8 %.

Exact modularity of line graphs of complete graphs

Abstract: Modularity is designed to measure the strength of a division of a network into clusters. For n∈ℕ, consider a set S of n elements. Let V be the set of all subsets of S of size r. Consider the graph G(n,r,s) with vertices V and edges that connect two vertices if and only if their intersection has size s. In this article, we find the exact modularity of G(n,2,1) for n≥5.