Edges Of Graph Research Articles

Partially broken orientations of Eulerian graphs on closed surfaces

In this paper, we discuss orientations given to edges of Eulerian graphs embedded on closed surfaces, and give a characterization of such a graph having a good orientation, i.e., incoming edges and outgoing edges appear alternately around each vertex of the graph. Furthermore, we consider the partially broken orientations of Eulerian graphs embedded on closed surfaces, that is, one in which only for each of specified vertices, incoming edges and outgoing edges appear alternately around it. We discuss a little about good orientations defined for Eulerian graphs drawn on closed surfaces with crossings, and for general connected graphs, i.e., not necessarily Eulerian graphs, embedded on closed surfaces.

LocalTGEP: A Lightweight Edge Partitioner for Time-Varying Graph

Graph edge partitioning (GEP), the allocation of edges into different parts through cut vertices, is essential for the analytics of large-scale graphs. Most GEP models cannot be directly applied to a time-varying graph unless repartitioning the entire graph, which leads to a large consumption of resources. Although a few studies have focused on time-varying graph edge partitioning, they have ignored the memory consumption during the partitioning process. Therefore, a lightweight edge partitioner, referred to as LocalTGEP, broadening the application to time-varying graphs, is proposed herein. Three superiorities of LocalTGEP are highlighted as follows: 1) A satisfactory partitioning quality for a time-varying graph can be achieved without requiring global information owing to the local edge partitioning. 2) Memory consumption of the partitioner is significantly reduced using a novel storage framework of graph data in LocalTGEP. 3) The quality and efficiency of time-varying graph edge partitioning are optimized by designing the push and pop stages in LocalTGEP. Extensive experimental results obtained on 12 real-world graphs demonstrate that LocalTGEP outperforms rival algorithms in terms of memory consumption, partitioning quality, and efficiency.

Super (a,d)-P_2⨀P_m-Antimagic Total Labeling of Corona Product of Two Paths

Graph labeling involves mapping the elements of a graph (edges and vertices) to a set of positive integers. The concept of an anti-magic super outer labeling (a,d)-H pertains to assigning labels to the vertices and edges of a graph using natural numbers {1,2,3,...,p+q}. The weights of the outer labels H form an arithmetic sequence {a,a+d,a+2d,...,a+(k-1)d}, where 'a' represents the first term, 'd' is the common difference, and 'k' denotes the total number of outer labels, with the smallest label assigned to a vertex. This study investigates the super (a,d)-P_2⨀P_m-antimagic total labeling of the corona product P_n⨀P_m, where n and m are both greater than or equal to 3. We define the labeling functions for vertices and edges based on the partitioning of labels into three subsets. Using k-balanced and (k,δ)-anti balanced multisets, we demonstrate that for m being odd, P_n⨀P_m is super (9m^2 n+4mn+m-n+3,1)-P_2 ⨀▒P_(m ) -antimagic, and for m being even, P_n⨀P_m is super (9m^2 n+4mn+m-2n+5,3)-P_2 ⨀▒P_(m ) -antimagic. The labeling scheme is illustrated through examples. For the case when m is odd, an antimagic total labeling of P_3 ⨀▒P_3 forms a super (282,1)- P_2 ⨀▒P_(3 ) -antimagic labeling. In the case of even m, an antimagic total labeling of P_3 ⨀▒P_(4 ) results in a super (483,3)- P_2 ⨀▒P_(4 ) -antimagic labeling. Both of these examples provide insights into the antimagic properties of corona products.

Exploring social networks through stochastic multilayer graph modeling

Several graph models are available today to model online social networks. These graph models are used to analyze the structural properties of the online social network, such as detecting communities, finding the influential spreader and predicting the behavior of the network. However, these models are based on deterministic single-layer graphs that may not be appropriate when online users use multiple social networks at the same time and social networks provide specific services. Moreover, because of the unknown and dynamic nature related to the behaviors and activities of online users, as well as structural and behavioral parameters, which may vary over time, stochastic multi-layer models could be applied to better capture and represent this phenomenon, as well as the dynamic nature of social networks. For example, in recommender systems, users' interests are unknown parameters and vary over time. Therefore, stochastic multilayer graph modeling can be used to develop recommender systems by considering different layers for different types of interests or preferences. In this paper, we propose a stochastic multilayer graph in which the edges are associated with random variables as a potential graph model for the analysis of online social networks. Therefore, after redefine some network measures related to stochastic multilayer graphs, we propose a Cellular Goore Game (CGG) based algorithm to computes the redefine network measures. A CGG-based algorithm computes defined network measures by learning automata from the edges of stochastic multilayer graphs. The experimental results show that the new CGG-based algorithm requires fewer samples from the edges of stochastic multilayer graphs than the standard sampling method in network measures calculation. Furthermore, the obtained results demonstrate that, from an evaluation perspective, the CGG-based algorithm provides superior results in terms of Kolmogorov-Smirnov (KS-test), Pearson Correlation Coefficient (PCC), Normalized Root Mean Square Error (NRMSE) and Kullback–Leibler divergence (KL-test).

Generation-based Multi-view Contrast for Self-supervised Graph Representation Learning

Graph contrastive learning has made remarkable achievements in the self-supervised representation learning of graph-structured data. By employing perturbation function (i.e., perturbation on the nodes or edges of graph), most graph contrastive learning methods construct contrastive samples on the original graph. However, the perturbation-based data augmentation methods randomly change the inherent information (e.g., attributes or structures) of the graph. Therefore, after nodes embedding on the perturbed graph, we cannot guarantee the validity of the contrastive samples as well as the learned performance of graph contrastive learning. To this end, in this article, we propose a novel generation-based multi-view contrastive learning framework (GMVC) for self-supervised graph representation learning, which generates the contrastive samples based on our generator rather than perturbation function. Specifically, after nodes embedding on the original graph we first employ random walk in the neighborhood to develop multiple relevant node sequences for each anchor node. We then utilize the transformer to generate the representations of relevant contrastive samples of anchor node based on the features and structures of the sampled node sequences. Finally, by maximizing the consistency between the anchor view and the generated views, we force the model to effectively encode graph information into nodes embeddings. We perform extensive experiments of node classification and link prediction tasks on eight benchmark datasets, which verify the effectiveness of our generation-based multi-view graph contrastive learning method.

Equivalence between Graph Spectral Clustering and Column Subset Selection (Student Abstract)

The common criteria for evaluating spectral clustering are NCut and RatioCut. The seemingly unrelated column subset selection (CSS) problem aims to compute a column subset that linearly approximates the entire matrix. A common criterion is the approximation error in the Frobenius norm (ApproxErr). We show that any algorithm for CSS can be viewed as a clustering algorithm that minimizes NCut by applying it to a matrix formed from graph edges. Conversely, any clustering algorithm can be seen as identifying a column subset from that matrix. In both cases, ApproxErr and NCut have the same value. Analogous results hold for RatioCut with a slightly different matrix. Therefore, established results for CSS can be mapped to spectral clustering. We use this to obtain new clustering algorithms, including an optimal one that is similar to A*. This is the first nontrivial clustering algorithm with such an optimality guarantee. A variant of the weighted A* runs much faster and provides bounds on the accuracy. Finally, we use the results from spectral clustering to prove the NP-hardness of CSS from sparse matrices.

SGFormer: Semantic Graph Transformer for Point Cloud-Based 3D Scene Graph Generation

In this paper, we propose a novel model called SGFormer, Semantic Graph TransFormer for point cloud-based 3D scene graph generation. The task aims to parse a point cloud-based scene into a semantic structural graph, with the core challenge of modeling the complex global structure. Existing methods based on graph convolutional networks (GCNs) suffer from the over-smoothing dilemma and can only propagate information from limited neighboring nodes. In contrast, SGFormer uses Transformer layers as the base building block to allow global information passing, with two types of newly-designed layers tailored for the 3D scene graph generation task. Specifically, we introduce the graph embedding layer to best utilize the global information in graph edges while maintaining comparable computation costs. Furthermore, we propose the semantic injection layer to leverage linguistic knowledge from large-scale language model (i.e., ChatGPT), to enhance objects' visual features. We benchmark our SGFormer on the established 3DSSG dataset and achieve a 40.94% absolute improvement in relationship prediction's R@50 and an 88.36% boost on the subset with complex scenes over the state-of-the-art. Our analyses further show SGFormer's superiority in the long-tail and zero-shot scenarios. Our source code is available at https://github.com/Andy20178/SGFormer.

Linear-Time Algorithms for Front-Door Adjustment in Causal Graphs

Causal effect estimation from observational data is a fundamental task in empirical sciences. It becomes particularly challenging when unobserved confounders are involved in a system. This paper focuses on front-door adjustment – a classic technique which, using observed mediators allows to identify causal effects even in the presence of unobserved confounding. While the statistical properties of the front-door estimation are quite well understood, its algorithmic aspects remained unexplored for a long time. In 2022, Jeong, Tian, and Bareinboim presented the first polynomial-time algorithm for finding sets satisfying the front-door criterion in a given directed acyclic graph (DAG), with an O(n³(n+m)) run time, where n denotes the number of variables and m the number of edges of the causal graph. In our work, we give the first linear-time, i.e., O(n+m), algorithm for this task, which thus reaches the asymptotically optimal time complexity. This result implies an O(n(n+m)) delay enumeration algorithm of all front-door adjustment sets, again improving previous work by a factor of n³. Moreover, we provide the first linear-time algorithm for finding a minimal front-door adjustment set. We offer implementations of our algorithms in multiple programming languages to facilitate practical usage and empirically validate their feasibility, even for large graphs.

Advancing storm surge forecasting from scarce observation data: A causal-inference based Spatio-Temporal Graph Neural Network approach

Rapid and precise forecasting of storm surge in coastal regions is crucial for ensuring safety of coastal communities’ life and property. Yet, learning a data-driven forecasting model from observation data such as gauges and post-event reconnaissance remains challenging, due to the observation data scarcity and the real-world complexity. Recently, deep learning has received increasing attention, but existing deep learning approaches solely focus on individual site scenarios, ignoring the value of information contained in neighboring sites’ observations. In this study, we propose to integrate graph neural networks (GNN) and gated recurrent unit (GRU) to capture the spatial and temporal storm surge dependencies across multiple observation stations. GNN provides the unique capability to model non-Euclidean complex spatial relationship across observation stations, while GRU enhances the data efficiency of temporal dependency modeling. To account for the effect of complex coastline topography, the Liang–Kleeman information flow theory is employed to establish a causal-inference based graph edge scheme connecting multiple observation stations. The Causal-inference based Spatio-Temporal Graph Neural Network (CSTGNN) were trained and evaluated on 13-year observation data from 4 observation stations along Florida coastline. Experiments affirm the competence of CSTGNN, which outperformed six commonly used competitive baselines across different metrics and observation stations, under lead times up to six hours. Furthermore, benefits of capturing the spatial dependency and leveraging causal inference are also comprehensively examined. To conclude, we believe that this novel spatio-temporal forecasting framework can result in enhanced coastal resilience by its improved storm surge forecasting capability.

On the girth of forbidden subgraphs of coloring graphs

The k-coloring graph of G, denoted Ck(G), is the graph whose vertex set is the proper k-colorings of the vertices of G, and where two k-colorings are adjacent if and only if they differ at exactly one vertex. A graph H is called permissible if there exists a graph G and a natural number k such that H is an induced subgraph of Ck(G), otherwise H is called forbidden. We show that every graph is either permissible or some subdivision of it is permissible. Furthermore, we prove if every edge in a triangle-free permissible graph is subdivided, the resulting graph is permissible, and all further subdivisions are also permissible. Although subdivisions tend to increase the girth of a graph, we conjecture that there exist forbidden subgraphs of arbitrarily large girth. Finally, we define forbidden subgraphs of girth seven and nine, the largest girths found so far.

A Novel Money Laundering Prediction Model Based on a Dynamic Graph Convolutional Neural Network and Long Short-Term Memory

Money laundering is an illicit activity that seeks to conceal the nature and origins of criminal proceeds, posing a substantial threat to the national economy, the political order, and social stability. To scientifically and reasonably predict money laundering risks, this paper focuses on the “layering” stage of the money laundering process in the field of supervised learning for money laundering fraud prediction. A money laundering and fraud prediction model based on deep learning, referred to as MDGC-LSTM, is proposed. The model combines the use of a dynamic graph convolutional network (MDGC) and a long short-term memory (LSTM) network to efficiently identify illegal money laundering activities within financial transactions. MDGC-LSTM constructs dynamic graph snapshots with symmetrical spatiotemporal structures based on transaction information, representing transaction nodes and currency flows as graph nodes and edges, respectively, and effectively captures the relationships between temporal and spatial structures, thus achieving the dynamic prediction of fraudulent transactions. The experimental results demonstrate that compared with traditional algorithms and other deep learning models, MDGC-LSTM achieves significant advantages in comprehensive spatiotemporal feature modeling. Specifically, based on the Elliptic dataset, MDGC-LSTM improves the Macro-F1 score by 0.25 compared to that of the anti-money laundering fraud prediction model currently considered optimal.

Fastlomap: faster lead optimization mapper algorithm for large-scale relative free energy perturbation

In recent years, free energy perturbation calculations have garnered increasing attention as tools to support drug discovery. The lead optimization mapper (Lomap) was proposed as an algorithm to calculate the relative free energy between ligands efficiently. However, Lomap requires checking whether each edge in the FEP graph is removable, which necessitates checking the constraints for all edges. Consequently, conventional Lomap requires significant computation time, at least several hours for cases involving hundreds of compounds, and is impractical for cases with more than tens of thousands of edges. In this study, we aimed to reduce the computational cost of Lomap to enable the construction of FEP graphs for hundreds of compounds. We can reduce the overall number of constraint checks required from an amount dependent on the number of edges to one dependent on the number of nodes by using the chunk check process to check the constraints for as many edges as possible simultaneously. Based on the analysis of the execution profiles, we also improved the speed of cycle constraint and diameter constraint checks. Moreover, the output graph is the same as that obtained using the conventional Lomap, enabling direct replacement of the original one with our method. With our improvement, the execution was hundreds of times faster than that of the original Lomap.

Extremal Peisert-type graphs without the strict-EKR property

It is known that Paley graphs of square order have the strict-EKR property, that is, all maximum cliques are canonical cliques. Peisert-type graphs are natural generalizations of Paley graphs and some of them also have the strict-EKR property. Given a prime power q≥3, we study Peisert-type graphs of order q2 without the strict-EKR property and with the minimum number of edges and we call such graphs extremal. We determine number of edges in extremal graphs for each value of q. If q is a square or a cube, we show the uniqueness of the extremal graph and classify all maximum cliques explicitly. Moreover, when q is a square, we prove that there is no Hilton-Milner type result for the extremal graph, and show the tightness of the weight-distribution bound for both non-principal eigenvalues of this graph.

SELECTOR: Heterogeneous graph network with convolutional masked autoencoder for multimodal robust prediction of cancer survival

Accurately predicting the survival rate of cancer patients is crucial for aiding clinicians in planning appropriate treatment, reducing cancer-related medical expenses, and significantly enhancing patients’ quality of life. Multimodal prediction of cancer patient survival offers a more comprehensive and precise approach. However, existing methods still grapple with challenges related to missing multimodal data and information interaction within modalities. This paper introduces SELECTOR, a heterogeneous graph-aware network based on convolutional mask encoders for robust multimodal prediction of cancer patient survival. SELECTOR comprises feature edge reconstruction, convolutional mask encoder, feature cross-fusion, and multimodal survival prediction modules. Initially, we construct a multimodal heterogeneous graph and employ the meta-path method for feature edge reconstruction, ensuring comprehensive incorporation of feature information from graph edges and effective embedding of nodes. To mitigate the impact of missing features within the modality on prediction accuracy, we devised a convolutional masked autoencoder (CMAE) to process the heterogeneous graph post-feature reconstruction. Subsequently, the feature cross-fusion module facilitates communication between modalities, ensuring that output features encompass all features of the modality and relevant information from other modalities. Extensive experiments and analysis on six cancer datasets from TCGA demonstrate that our method significantly outperforms state-of-the-art methods in both modality-missing and intra-modality information-confirmed cases. Our codes are made available at https://github.com/panliangrui/Selector.

MWP: Multi-Window Parallel Evaluation of Regular Path Queries on Streaming Graphs

A persistent Regular Path Query (RPQ) on a streaming graph is to continuously find every pair of vertices that are connected by a path in the graph within a sliding window, such that the edge label sequence of this path matches a given regular expression. The existing RPQ evaluation algorithm in the literature incrementally maintains a set of spanning-tree-like data structures to quickly form query results and to avoid reprocessing edges that are shared by multiple sliding windows. This approach allows parallel processing of the graph edges within a sliding window but requires a blocking expiration phase between sliding windows to remove the old edges. This blocking phase can significantly degrade the query performance, especially when the edges arrive quickly and the sliding windows overlap significantly. This paper presents a new RPQ evaluation strategy called Multi-Window Parallel (MWP) method leveraging a new data structure called Timestamped Rooted Digraph (TRD). The novel idea is to incrementally maintain TRDs for the quick formulation of query results, like the aforementioned spanning trees, but simultaneously contain needed information for multiple sliding windows. MWP eliminates the forced blocking expiration phase. Only when memory runs low, a quick "dirty garbage collection" (DGC) process is done to remove some unneeded edges and nodes on TRDs, without incurring large costs. Extensive experiments on real graph datasets show that MWP significantly outperforms the existing algorithm in terms of throughput, tail latency, and scalability, and that DGC provides an effective solution for releasing memory with minimum impact.

Roman detour domination number of generalized hypercube networks

Generalized hypercube network is an interconnection network topology. The topology of interconnection network usually takes graph as a mathematical model, in which the vertex of graph represents the server and the edge of graph represents the connection between servers. As vertex count increases, the vertex degree of hypercube network increases as well. This has advantages, such as increased performance and reliability. The domination parameters are an important basis for analyzing and measuring the reliability of interconnection networks. In this paper, few properties of generalized hypercube network and Roman detour domination number for minimum dimensional generalized hypercube networks and hypercube networks are discussed. And also we determine the bounds for [Formula: see text] and [Formula: see text].

Imperative Formal Knowledge Representation for Control Engineering: Examples from Lyapunov Theory

In this paper, we introduce a novel method to formally represent elements of control engineering knowledge in a suitable data structure. To this end, we first briefly review existing representation methods (RDF, OWL, Wikidata, ORKG). Based on this, we introduce our own approach: The Python-based imperative representation of knowledge (PyIRK) and its application to formulate the Ontology of Control Systems Engineering (OCSE). One of its main features is the possibility to represent the actual content of definitions and theorems as nodes and edges of a knowledge graph, which is demonstrated by selected theorems from Lyapunov’s theory. While the approach is still experimental, the current result already allows the application of methods of automated quality assurance and a SPARQL-based semantic search mechanism. The feature set of the framework is demonstrated by various examples. The paper concludes with a discussion of the limitations and directions for further development.

EHR-HGCN: An Enhanced Hybrid Approach for Text Classification Using Heterogeneous Graph Convolutional Networks in Electronic Health Records.

Text classification is a central part of natural language processing, with important applications in understanding the knowledge behind biomedical texts including electronic health records (EHR). In this article, we propose a novel heterogeneous graph convolutional network method for classifying EHR texts. Our method, called EHR-HGCN, is able to combine context-sensitive word and sentence embeddings with structural sentence-level and word-level relation information to perform text classification. EHR-HGCN reframes EHR text classification as a graph classification task to better capture structural information about the document using a heterogeneous graph. To mine contextual information from a document, EHR-HGCN first applies a bidirectional recurrent neural network (BiRNN) on word embeddings obtained via Global Vectors for word representation (GloVe) to obtain context-sensitive word-level and sentence-level embeddings. To mine structural relationships from the document, EHR-HGCN then constructs a heterogeneous graph over the word and sentence embeddings, where sentence-word and word-word relationships are represented by graph edges. Finally, a heterogeneous graph convolutional neural network is used to classify documents by their graph representation. We evaluate EHR-HGCN on a variety of standard text classification benchmarks and find that EHR-HGCN has higher accuracy and F1-score than other representative machine learning and deep learning methods. We also apply EHR-HGCN to the MedLit benchmark and find it performs with high accuracy and F1-score on the task of section classification in EHR texts. Our ablation experiments show that the heterogeneous graph construction and heterogeneous graph convolutional network are critical to the performance of EHR-HGCN.

Graph states of atomic ensembles engineered by photon-mediated entanglement

Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.

An impossible combinatorial counting method in distance geometry

The Distance Geometry Problem asks for a geometric representation of a given weighted graph in RK so that vertices are points and edges are segments with lengths equal to the corresponding weights. Two problem variants are defined by a vertex order given as part of the input, which allows the use of a branching algorithm based on K-lateration: find two possible positions for the next vertex j using the positions of K predecessors and their distances to j, then explore each position recursively, pruning positions at need. Whereas the first variant only requires the K predecessors to exist, the second variant also requires them to be contiguous and immediately preceding j. For this variant, fixed-parameter tractability of the algorithm can be established by means of a solution counting method that only depends on the graph edges (rather than their weights). Only in the first variant, however, it is possible to efficiently construct a suitable vertex order directly from the graph. Since both fixed-parameter tractability and efficient vertex order construction are desirable properties, one would need an analogous solution counting method for the first variant. In this paper we prove that such a counting method cannot be devised for the first variant.