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line graph neural networks for link weight prediction

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2025年 661卷

作者： Liang, Jinbi Pu, Cunlai Shu, Xiangbo Xia, Yongxiang Xia, Chengyi Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Jiangsu Peoples R China Hangzhou Dianzi Univ Sch Commun Engn Hangzhou 310018 Zhejiang Peoples R China Tiangong Univ Sch Artificial Intelligence Tianjin 300387 Peoples R China

In real-world networks, predicting the weight (strength) of links is as crucial as predicting the existence of the links themselves. Previous studies have primarily used shallow graph features for link weight prediction, limiting the prediction performance. In this paper, we propose a new link weight prediction method, namely line graph Neural Networks for Link Weight Prediction (LGLWP), which learns intrinsic graph features through deep learning. In our method, we first extract the enclosing subgraph around a target link and then employ a weighted graph labeling algorithm to label the subgraph nodes. Next, we transform the subgraph into the line graph and apply graph convolutional neural networks to learn the node embeddings in the line graph, which can represent the links in the original subgraph. Finally, the node embeddings are fed into a fully-connected neural network to predict the weight of the target link, treated as a regression problem. Our method directly learns link features, surpassing previous methods that splice node features for link weight prediction. Experimental results on six network datasets of various sizes and types demonstrate that our method outperforms state-of-the-art methods.

关键词： Complex network Link weight prediction line graph graph neural network

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line graph contrastive learning for link prediction

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PATTERN RECOGNITION 2023年 140卷

作者： Zhang, Zehua Sun, Shilin Ma, Guixiang Zhong, Caiming Taiyuan Univ Technol Coll Informat & Comp Jinzhong 030600 Shanxi Peoples R China Intel Labs Hillsboro OR 97229 USA Ning bo Univ Coll Sci & Technol Cixi Ningbo 315300 Zhejiang Peoples R China

Link prediction tasks focus on predicting possible future connections. Most existing researches measure the likelihood of links by different similarity scores on node pairs and predict links between nodes. How-ever, the similarity-based approaches have some challenges in information loss on nodes and general-ization ability on similarity indexes. To address the above issues, we propose a line graph Contrastive Learning (LGCL) method to obtain rich information with multiple perspectives. LGCL obtains a subgraph view by h-hop subgraph sampling with target node pairs. After transforming the sampled subgraph into a line graph, the link prediction task is converted into a node classification task, which graph convolution progress can learn edge embeddings from graphs more effectively. Then we design a novel cross-scale contrastive learning framework on the line graph and the subgraph to maximize the mutual information of them, so that fuses the structure and feature information. The experimental results demonstrate that the proposed LGCL outperforms the state-of-the-art methods and has better performance on generaliza-tion and robustness.& COPY;2023 Elsevier Ltd. All rights reserved.

关键词： line graph Contrastive learning Link prediction Node classification Mutual information

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Extremal Values on the Kirchhoff Index of the line graph of Unicyclic Networks

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年第3期44卷 1523-1544页

作者： Sardar, Muhammad Shoaib Xu, Shou-Jun Harbin Engn Univ Coll Math Sci Harbin Peoples R China Lanzhou Univ Gansu Ctr Appl Math Sch Math & Stat Lanzhou 730000 Gansu Peoples R China

Let G be a simple connected graph with vertex set V(G) and edge set E(G). Suppose N represents a network derived from G by substituting a 1-ohm resistor for each edge of G. In that case, the resistance between u,v is an element of V(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u, v \in V(G)$$\end{document} is analogous to the resistance between two equivalent nodes in network N. The Kirchhoff index of G is the summation of the resistance distances between all pairs of vertices in G. The line graph LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_G$$\end{document} of G is a graph whose vertices correspond to the edges of G, and any two vertices of LG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_G$$\end{document} are adjacent if and only if the corresponding edges of G are incident with the same vertex of G. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we will identify the extremal values and unicyclic graphs for the Kirchhoff index of the line graph of unicyclic graphs by utilizing techniques derived from electrical networks.

关键词： Distance Resistance distance line graph Unicyclic graphs Kirchhoff index 05C12 05C35 05C81

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Equivariant line graph Neural Network for Protein-Ligand Binding Affinity Prediction

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS 2024年第7期28卷 4336-4347页

作者： Yi, Yiqiang Wan, Xu Zhao, Kangfei Le, Ou-Yang Zhao, Peilin Shenzhen Univ State Key Lab Radio Frequency Heterogeneous Integr Shenzhen 518060 Peoples R China Shenzhen Univ Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Peoples R China Shenzhen Univ Shenzhen Key Lab Media Secur Shenzhen 518060 Peoples R China Shenzhen Univ Coll Elect & Informat Engn Shenzhen 518060 Peoples R China Shenzhen Inst Artificial Intelligence & Robot Soc Shenzhen 64289 Peoples R China Beijing Inst Technol Sch Comp Sci Beijing 100081 Peoples R China Tencent AI Lab Shenzhen 518057 Peoples R China

Binding affinity prediction of three-dimensional (3D) protein-ligand complexes is critical for drug repositioning and virtual drug screening. Existing approaches usually transform a 3D protein-ligand complex to a two-dimensional (2D) graph, and then use graph neural networks (GNNs) to predict its binding affinity. However, the node and edge features of the 2D graph are extracted based on invariant local coordinate systems of the 3D complex. As a result, these approaches can not fully learn the global information of the complex, such as the physical symmetry and the topological information of bonds. To address these issues, we propose a novel Equivariant line graph Network (ELGN) for binding affinity prediction of 3D protein-ligand complexes. The proposed ELGN firstly adds a super node to the 3D complex, and then builds a line graph based on the 3D complex. After that, ELGN uses a new E(3)-equivariant network layer to pass the messages between nodes and edges based on the global coordinate system of the 3D complex. Experimental results on two real datasets demonstrate the effectiveness of ELGN over several state-of-the-art baselines.

关键词： Proteins Protein engineering Three-dimensional displays Drugs graph neural networks Topology Solid modeling Drug discovery graph neural network equivariant line graph

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Extremal values on the Kirchhoff index of the line graph of trees

KUWAIT JOURNAL OF SCIENCE

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KUWAIT JOURNAL OF SCIENCE 2025年第1期52卷

作者： Sardar, Muhammad Shoaib Xu, Shou-Jun Pan, Xiang-Feng Lanzhou Univ Gansu Ctr Appl Math Sch Math & Stat Lanzhou 730000 Peoples R China Harbin Engn Univ Coll Math Sci Harbin Peoples R China Anhui Univ Sch Math Sci Hefei 230601 Anhui Peoples R China

The computation of resistance distance and the Kirchhoff index is a classical problem that has been extensively investigated by numerous mathematicians, physicists, and scientists. Consider a simple connected graph G with vertex set V(G) and edge set E(G). If we replace each edge of G with a resistor of 1 ohm resistance, we create an electrical network N;in that case, the distance between any two nodes between network N is called resistance distance. The Kirchhoff index is a mathematical term that quantifies the complexity of a graph;it is defined as the total resistance distance among each pair of vertices in G. The line graph L-G is constructed from G by swapping out the edges for vertices;in L-G, if two vertices share endpoints in G, then they are connected in L-G. In this study, extremal values for the Kirchhoff index of the line graph of trees are calculated. Further, we will also calculate the Kirchhoff index for the line graph of some special trees and establish the relationship between them.

关键词： Distance Resistance distance Kirchhoff index line graph Tree Series-reduced tree

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The decycling number of a line graph

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DISCRETE MATHEMATICS 2025年第2期348卷

作者： Ma, Mingyuan Ren, Han East China Normal Univ Sch Math Sci Shanghai 200241 Peoples R China

关键词： line graph Decycling number Cycle rank

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Multiplicity of Powers of Path Ideals of A line graph

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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2025年第1期48卷 1-16页

作者： Shan, Jiawen Wang, Zexin Lu, Dancheng Soochow Univ Sch Math Sci Suzhou 215006 Peoples R China

Let R=K[x1,& mldr;,xn]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=\mathbb {K}[x_1,\ldots ,x_n]$$\end{document} be the polynomial ring over a field K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {K}$$\end{document}, and let I subset of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I\subseteq R$$\end{document} be the t-path ideal of the line graph Ln\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_n$$\end{document} with n-vertices. It is shown that the set of associated prime ideals of Is\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I<^>s$$\end{document} is equal to the set of minimal prime ideals of I for all s >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s\ge 1$$\end{document}, and we provide an explicit description of these prime ideals. Additionally, as the main contribution of this paper, we derive an explicit formula for the multiplicity of R/Is\documentclass[12p

关键词： Path ideals line graph Multiplicity Normally torsion-free

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LGSMOTE-IDS: line graph based Weighted-Distance SMOTE for imbalanced network traffic detection

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 281卷

作者： Zhao, Guyu Li, Linwei He, Hongdou Ren, Jiadong Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066000 Hebei Peoples R China

The application of graph Neural Networks (GNNs) to Network Intrusion Detection Systems (NIDS) has become a prominent research focus. However, NIDS often struggles to classify minority attack samples due to the severe class imbalance in NIDS datasets, where the number of samples varies significantly across classes. Additionally, prior studies have frequently overlooked the importance of edge features in GNNs. To address these challenges, we propose LGSMOTE-IDS, a novel framework that integrates a L line G graph based Weighted-Distance SMOTE for I Intrusion D Detection S Systems. First, we define the fine-grained protocol service graph (PSG) and transform it into its corresponding protocol service line graph (L(PSG)). This transformation provides a novel perspective for describing network traffic interactions and enables the conversion of the edge classification task into a node classification task. Second, we introduce Weighted-Distance SMOTE, an oversampling algorithm specifically tailored to NIDS datasets, which employs an improved interpolation strategy to generate synthetic minority class samples. Finally, we utilize a GNN-based classifier to predict labels for all samples. We conduct experiments on three widely used datasets-NF-UNSW-NB15, NF-BoT-IoT, and NF-ToN-IoT. LGSMOTE-IDS achieves average increases of 18.11%, 45.91%, and 36.41% in weighted F1-scores for five, one, and three minority classes across the three datasets, respectively, compared to baseline method. Moreover, LGSMOTE-IDS successfully detects attack types that previous models fail to recognize. To the best of our knowledge, LGSMOTE-IDS is the first framework to integrate GNNs with an oversampling algorithm to address the class imbalance issue in NIDS datasets.

关键词： Network Intrusion Detection System Weighted-Distance SMOTE graph Neural Network line graph

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On the line graph structure of the cozero-divisor graph of a commutative ring

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INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS 2024年 1-7页

作者： Afkhami, Mojgan Barati, Zahra Univ Neyshabur Dept Math POB 91136-899 Neyshabur Iran Kosar Univ Bojnord Dept Math POB *** Bojnord Iran

Assume that R is a commutative ring with non-zero identity and W*(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W<^>*(R)$$\end{document} is the set of all non-zero non-unit elements of R. Also, for x is an element of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\in R$$\end{document}, the ideal which is generated by x, is denoted by Rx. The cozero-divisor graph of R, which is denoted by Gamma '(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma '(R)$$\end{document}, is a graph with W*(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W<^>*(R)$$\end{document} as the vertex-set, and two distinct vertices x and y are adjacent in W*(R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W<^>*(R)$$\end{document} if and only if x is not an element of Ry\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\notin Ry$$\end{document} and y is not an element of Rx\documentclass[12pt]{minimal} \usepack

关键词： Cozero-divisor graph line graph Commutative ring

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3-Path Decompositions of the line graph of the Complete Bipartite graph

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JOURNAL OF INTERCONNECTION NETWORKS 2025年第1期25卷

作者： Gao, Limin Yang, Weihua Taiyuan Univ Technol Dept Math Taiyuan 030024 Shanxi Peoples R China

The line graph is a very popular research object in graph theory, in complex networks and also in social networks recently. Let L(K-m,K-n) be the line graph of the complete bipartite graph K-m,K-n and Pk+1 be a path of length k. In this paper, we give necessary and sufficient conditions for the existence of P4-decompositions of L(K-m,K-n).

关键词： Path decomposition complete bipartite graph line graph Cartesian product

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