Original Graph Research Articles

GMMDA: Gaussian mixture modeling of graph in latent space for graph data augmentation

Graph data augmentation (GDA), which manipulates graph structure and/or attributes, has been demonstrated as an effective method for improving the generalization of graph neural networks on semi-supervised node classification. As a data augmentation technique, label preservation is critical, that is, node labels should not change after data manipulation. However, most existing methods overlook the label preservation requirements. Determining the label-preserving nature of a GDA method is highly challenging, owing to the non-Euclidean nature of the graph structure. In this study, for the first time, we formulate a label-preserving problem (LPP) in the context of GDA. The LPP is formulated as an optimization problem in which, given a fixed augmentation budget, the objective is to find an augmented graph with minimal difference in data distribution compared to the original graph. To solve the LPP problem, we propose GMMDA, a generative data augmentation (DA) method based on Gaussian mixture modeling (GMM) of a graph in a latent space. We designed a novel learning objective that jointly learns a low-dimensional graph representation and estimates the GMM. The learning is followed by sampling from the GMM, and the samples are converted back to the graph as additional nodes. To uphold label preservation, we designed a minimum description length (MDL)-based method to select a set of samples that produces the minimum shift in the data distribution captured by the GMM. Through experiments, we demonstrate that GMMDA can improve the performance of graph convolutional network on Cora, Citeseer and Pubmed by as much as 7.75%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.75\\%$$\\end{document}, 8.75%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$8.75\\%$$\\end{document} and 5.87%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5.87\\%$$\\end{document}, respectively, significantly outperforming the state-of-the-art methods.

Dynamic graph topology generating mechanism: Framework for feature-level multimodal information fusion applied to lower-limb activity recognition

Lower-limb activity recognition (LLAR), which is driven by wearable sensors, has recently become a popular research topic in human assistive devices. Although multimodal information fusion is crucial for improving the accuracy of LLAR, traditional feature-level fusion strategies cannot directly model the relationship between multimodal features according to the lower-limb activity patterns and they realize fusion based on the relationship. To address these limitations, a dynamic graph topology generation (DGTG) mechanism that uses a graph topology to model the relationship between multimodal features mined by a convolutional neural network (CNN) is proposed in this study. A weighted graph isomorphism network (WGIN) that can realize multimodal feature fusion based on the relationship (i.e., graph topology) is also proposed, resulting in a novel feature-level multimodal information fusion framework called CNN-DGTG-WGIN. This proposed method achieved the best average accuracies of 96.3 and 99.7% for two publicly available datasets. This method integrates the determination of the graph topology into an end-to-end learning process without requiring any prior knowledge or original graph structures. Further, CNN-DGTG-WGIN effectively incorporates both linear and nonlinear correlations between features during the DGTG process. Analysis results revealed that the graph topology (multimodal feature relationship) learned by CNN-DGTG-WGIN was closely related to lower-limb activity patterns, encoding relevant information about these patterns, which is the essence of its superior performance.

MvGraphDTA: multi-view-based graph deep model for drug-target affinity prediction by introducing the graphs and line graphs

BackgroundAccurately identifying drug-target affinity (DTA) plays a pivotal role in drug screening, design, and repurposing in pharmaceutical industry. It not only reduces the time, labor, and economic costs associated with biological experiments but also expedites drug development process. However, achieving the desired level of computational accuracy for DTA identification methods remains a significant challenge.ResultsWe proposed a novel multi-view-based graph deep model known as MvGraphDTA for DTA prediction. MvGraphDTA employed a graph convolutional network (GCN) to extract the structural features from original graphs of drugs and targets, respectively. It went a step further by constructing line graphs with edges as vertices based on original graphs of drugs and targets. GCN was also used to extract the relationship features within their line graphs. To enhance the complementarity between the extracted features from original graphs and line graphs, MvGraphDTA fused the extracted multi-view features of drugs and targets, respectively. Finally, these fused features were concatenated and passed through a fully connected (FC) network to predict DTA.ConclusionsDuring the experiments, we performed data augmentation on all the training sets used. Experimental results showed that MvGraphDTA outperformed the competitive state-of-the-art methods on benchmark datasets for DTA prediction. Additionally, we evaluated the universality and generalization performance of MvGraphDTA on additional datasets. Experimental outcomes revealed that MvGraphDTA exhibited good universality and generalization capability, making it a reliable tool for drug-target interaction prediction.

Distribution-aware hybrid noise augmentation in graph contrastive learning for recommendation

The recommender systems are one of the most effective big data tools for solving the information overload problem, but data sparsity greatly affects its performance. However, most of the existing graph-based contrastive learning methods perturb the original graph structure for data augmentation, which may lead to semantic loss and subsequently degrade the recommendation performance. Meanwhile, studies have shown that improving the uniformity of data distribution is more effective than data augmentation using graph perturbation. In this paper, to enhance the uniformity of data distribution, we propose Distribution-Aware Hybrid Noise augmentation in graph contrastive learning for Recommendation (DAHNRec). Specifically, we design distribution-aware hybrid noise augmentation (DAHN) method to generate noise suitable for the users and items, instead of simply utilizing random noise following uniform distributions. By applying DAHN, the model can learn the appropriate noise distribution during the training process to enhance the uniformity of the embedding space. Additionally, we propose Balanced Bayesian Personalized Ranking (BBPR) as the loss function for recommendation tasks to improve difference characterizing between positive and negative samples. This improves the ranking tasks’ performance. Furthermore, we conduct extensive experiments based on public benchmark datasets. The results indicate that DAHNRec outperforms several existing methods. Furthermore, DAHNRec is a general recommendation model based on user–item interactions, which can be used to improve the recommendation performance in various real-world scenarios, such as e-commerce platforms and social media.

Semantic community query in a large‐scale attributed graph based on an attribute cohesiveness optimization strategy

AbstractThe task of a semantic community query is to obtain a subgraph based on a given query vertex (or vertex set) and other query parameters in an attributed graph such that belongs to , contains and satisfies a predefined community cohesiveness model. In most cases, existing community query models based on the network structure for traditional attributed networks usually lack community semantics. However, the features of vertex attributes, especially the attributes of the query vertices, which are closely related to the community semantics, are rarely considered in an attributed graph. Existing community query algorithms based on both structure cohesiveness and attribute cohesiveness usually do not take the attributes of the query vertex as an important factor of the community cohesiveness model, which leads to weak semantics of the communities. This paper proposes a semantic community query method named in a large‐scale attributed graph. First, the k‐core structure model is adopted as the structure cohesiveness of our community query model to obtain a subgraph of the original graph. Second, we define attribute cohesiveness based on the average distance between the query vertices and other vertices in terms of attributes in the community to prune the subgraph and obtain the semantic community. In order to improve the community query efficiency in large‐scale attributed graphs, applies two heuristic pruning strategies. The experimental results show that our method outperforms the existing community query methods in multiple evaluation metrics and is ideal for querying semantic communities in large‐scale attributed graphs.

Constructing neural networks with pre-specified dynamics

A main goal in neuroscience is to understand the computations carried out by neural populations that give animals their cognitive skills. Neural network models allow to formulate explicit hypotheses regarding the algorithms instantiated in the dynamics of a neural population, its firing statistics, and the underlying connectivity. Neural networks can be defined by a small set of parameters, carefully chosen to procure specific capabilities, or by a large set of free parameters, fitted with optimization algorithms that minimize a given loss function. In this work we alternatively propose a method to make a detailed adjustment of the network dynamics and firing statistic to better answer questions that link dynamics, structure, and function. Our algorithm—termed generalised Firing-to-Parameter (gFTP)—provides a way to construct binary recurrent neural networks whose dynamics strictly follows a user pre-specified transition graph that details the transitions between population firing states triggered by stimulus presentations. Our main contribution is a procedure that detects when a transition graph is not realisable in terms of a neural network, and makes the necessary modifications in order to obtain a new transition graph that is realisable and preserves all the information encoded in the transitions of the original graph. With a realisable transition graph, gFTP assigns values to the network firing states associated with each node in the graph, and finds the synaptic weight matrices by solving a set of linear separation problems. We test gFTP performance by constructing networks with random dynamics, continuous attractor-like dynamics that encode position in 2-dimensional space, and discrete attractor dynamics. We then show how gFTP can be employed as a tool to explore the link between structure, function, and the algorithms instantiated in the network dynamics.

Global-local aware Heterogeneous Graph Contrastive Learning for multifaceted association prediction in miRNA-gene-disease networks.

Unraveling the intricate network of associations among microRNAs (miRNAs), genes, and diseases is pivotal for deciphering molecular mechanisms, refining disease diagnosis, and crafting targeted therapies. Computational strategies, leveraging link prediction within biological graphs, present a cost-efficient alternative to high-cost empirical assays. However, while plenty of methods excel at predicting specific associations, such as miRNA-disease associations (MDAs), miRNA-target interactions (MTIs), and disease-gene associations (DGAs), a holistic approach harnessing diverse data sources for multifaceted association prediction remains largely unexplored. The limited availability of high-quality data, as vitro experiments to comprehensively confirm associations are often expensive and time-consuming, results in a sparse and noisy heterogeneous graph, hindering an accurate prediction of these complex associations. To address this challenge, we propose a novel framework called Global-local aware Heterogeneous Graph Contrastive Learning (GlaHGCL). GlaHGCL combines global and local contrastive learning to improve node embeddings in the heterogeneous graph. In particular, global contrastive learning enhances the robustness of node embeddings against noise by aligning global representations of the original graph and its augmented counterpart. Local contrastive learning enforces representation consistency between functionally similar or connected nodes across diverse data sources, effectively leveraging data heterogeneity and mitigating the issue of data scarcity. The refined node representations are applied to downstream tasks, such as MDA, MTI, and DGA prediction. Experiments show GlaHGCL outperforming state-of-the-art methods, and case studies further demonstrate its ability to accurately uncover new associations among miRNAs, genes, and diseases. We have made the datasets and source code publicly available at https://github.com/Sue-syx/GlaHGCL.

Attributed graph clustering under the contrastive mechanism with cluster-preserving augmentation

Attributed graph clustering is a fundamental task in complex network analysis. Many existing graph clustering methods utilize graph representation learning techniques to learn node representations, subsequently applying K-means for clustering. Despite the significant attention and promising outcomes of graph contrastive learning in graph representation learning, we find two essential problems that need to be solved. (1) How to achieve augmentation for contrast that preserves the cluster structure of a given graph? (2) How to design an effective contrastive learning mechanism that collaborates with clustering? Therefore, we propose an attributed graph clustering method under the contrastive mechanism with cluster-preserving augmentation, integrating node representation learning and clustering into a unified framework. Specifically, we construct a contrasting view based on a generated kNN graph and edge betweenness centrality to preserve the cluster structure in the original graph. Meanwhile, a multilevel contrast mechanism based on pseudo-label-guided negative sampling is proposed to maximize the agreement between node representations in multiple latent spaces. We jointly optimize a specific clustering objective during the contrastive process, leading to refined cluster distribution directly in training. Extensive experiments on several datasets demonstrate that our proposed model consistently outperforms existing state-of-the-art methods on clustering.

Learning from Feature and Global Topologies: Adaptive Multi-View Parallel Graph Contrastive Learning

To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation learning method designed to generate task-agnostic node embeddings. AMPGCL constructs and encodes feature and topological views to mine feature and global topological information. To encode global topological information, we introduce an H-Transformer to decouple multi-hop neighbor aggregations, capturing global topology from node subgraphs. AMPGCL learns embedding consistency among feature, topology, and original graph encodings through a multi-view contrastive loss, generating semantically rich embeddings while avoiding information redundancy. Experiments on nine real datasets demonstrate that AMPGCL consistently outperforms thirteen state-of-the-art graph representation learning models in classification accuracy, whether in homophilous or non-homophilous graphs.

A Local Search Algorithm with Vertex Weighting Strategy and Two-Level Configuration Checking for the Minimum Connected Dominating Set Problem.

The minimum connected dominating set problem is a combinatorial optimization problem with a wide range of applications in many fields. We propose an efficient local search algorithm to solve this problem. In this work, first, we adopt a new initial solution construction method based on three simplification rules. This method can reduce the size of the original graph and thus obtain a high-quality initial solution. Second, we propose an approach based on a two-level configuration checking strategy and a tabu strategy to reduce the cycling problem. Third, we introduce a perturbation strategy and a vertex weighting strategy to help the algorithm be able to jump out of the local optimum effectively. Fourth, we combine the scoring functions Cscore and Mscore with the aforementioned strategies to propose effective methods for selecting vertices. These methods assist the algorithm in selecting vertices that are suitable for addition to or removal from the current candidate solution. Finally, we verify the performance advantages of the local search algorithm by comparing it with existing optimal heuristic algorithms on two sets of instances. The experimental results show that the algorithm exhibits better performance on two sets of classical instances.

MDGCL: Graph Contrastive Learning Framework with Multiple Graph Diffusion Methods

In recent years, some classical graph contrastive learning(GCL) frameworks have been proposed to address the problem of sparse labeling of graph data in the real world. However, in node classification tasks, there are two obvious problems with existing GCL frameworks: first, the stochastic augmentation methods they adopt lose a lot of semantic information; second, the local–local contrasting mode selected by most frameworks ignores the global semantic information of the original graph, which limits the node classification performance of these frameworks. To address the above problems, this paper proposes a novel graph contrastive learning framework, MDGCL, which introduces two graph diffusion methods, Markov and PPR, and a deterministic–stochastic data augmentation strategy while retaining the local–local contrasting mode. Specifically, before using the two stochastic augmentation methods (FeatureDrop and EdgeDrop), MDGCL first uses two deterministic augmentation methods (Markov diffusion and PPR diffusion) to perform data augmentation on the original graph to increase the semantic information, this step ensures subsequent stochastic augmentation methods do not lose too much semantic information. Meanwhile, the diffusion matrices carried by the augmented views contain global semantic information of the original graph, allowing the framework to utilize the global semantic information while retaining the local-local contrasting mode, which further enhances the node classification performance of the framework. We conduct extensive comparative experiments on multiple benchmark datasets, and the results show that MDGCL outperforms the representative baseline frameworks on node classification tasks. Among them, compared with COSTA, MDGCL’s node classification accuracy has been improved by 1.07% and 0.41% respectively on two representative datasets, Amazon-Photo and Coauthor-CS. In addition, we also conduct ablation experiments on two datasets, Cora and CiteSeer, to verify the effectiveness of each improvement work of our framework.

A Study on Graph Optimization Method for GNSS/IMU Integrated Navigation System Based on Virtual Constraints.

In GNSS/IMU integrated navigation systems, factors like satellite occlusion and non-line-of-sight can degrade satellite positioning accuracy, thereby impacting overall navigation system results. To tackle this challenge and leverage historical pseudorange information effectively, this paper proposes a graph optimization-based GNSS/IMU model with virtual constraints. These virtual constraints in the graph model are derived from the satellite's position from the previous time step, the rate of change of pseudoranges, and ephemeris data. This virtual constraint serves as an alternative solution for individual satellites in cases of signal anomalies, thereby ensuring the integrity and continuity of the graph optimization model. Additionally, this paper conducts an analysis of the graph optimization model based on these virtual constraints, comparing it with traditional graph models of GNSS/IMU and SLAM. The marginalization of the graph model involving virtual constraints is analyzed next. The experiment was conducted on a set of real-world data, and the results of the proposed method were compared with tightly coupled Kalman filtering and the original graph optimization method. In instantaneous performance testing, the method maintains an RMSE error within 5% compared with real pseudorange measurement, while in a continuous performance testing scenario with no available GNSS signal, the method shows approximately a 30% improvement in horizontal RMSE accuracy over the traditional graph optimization method during a 10-second period. This demonstrates the method's potential for practical applications.

Topological consistency with low imperceptibility for graph adversarial attacks

Recent research shows that graph neural networks (GNNs) are easy to receive disruptions due to the lack of robustness, the phenomenon that poses a serious security threat. Currently, most efforts to attack GNNs mainly use gradient information to guide the attacks. However, the unreliability of gradient information, and the perceptibility of adversarial examples pose challenges that impede further progress in researching on graph adversarial attacks. From the unreliability of gradient information, we propose a Graph Distance Topological Consistency (GDTC). The scheme introduces graph connectivity, geodesic distance, cosine similarity, and Minkowski distance to construct the similarity matrices of the input space and embedding space of the surrogate model. The difference between the two similarities matrices is constrained during the training process of the surrogate model so that the surrogate model fully learns the topology of the original graph. From adversarial examples perceptibility, we propose attack loss with homogeneity restriction. Experiments show that GDTC can study the topological information of the original graph, enhance the reliability of gradient information, and significantly boost attack performance.

Self-supervised reconstructed graph learning for link prediction in bipartite graphs

Graph Neural Network(GNN) has achieved remarkable performance in classification tasks due to its strong distinctive power of different graph topologies. However, traditional GNNs face great limitations in link prediction tasks since they learn vertex embeddings from fixed input graphs thus the learned embeddings cannot reflect unobserved graph structures. Graph-learning based GNNs have shown better performance by collaborative learning of graph structures and vertex embeddings, but most of them rely on available initial features to refine graphs and almost perform graph learning at once. Recently, some methods utilizes contrastive learning to facilitate link prediction, but their graph augmentation strategies are predefined only on original graphs, and do not introduce unobserved edges into augmented graphs. To this end, a self-supervised reconstructed graph learning (SRGL) method is proposed. The key points of SRGL lie in two folds: Firstly, it generates augmented graphs for contrasting by learning reconstructed graphs and vertex embeddings from each other, which brings unobserved edges into augmented graphs. Secondly, it maximizes the mutual information between edge-level embeddings of reconstructed graphs and the graph-level embedding of an original graph, which guarantees learned reconstructed graphs to be relevant to the original graph.

Edge Private Graph Neural Networks with Singular Value Perturbation

Graph neural networks (GNNs) play a key role in learning representations from graph-structured data and are demonstrated to be useful in many applications. However, the GNN training pipeline has been shown to be vulnerable to node feature leakage and edge extraction attacks. This paper investigates a scenario where an attacker aims to recover private edge information from a trained GNN model. Previous studies have employed differential privacy (DP) to add noise directly to the adjacency matrix or a compact graph representation. The added perturbations cause the graph structure to be substantially morphed, reducing the model utility. We propose a new privacy-preserving GNN training algorithm, Eclipse, that maintains good model utility while providing strong privacy protection on edges. Eclipse is based on two key observations. First, adjacency matrices in graph structures exhibit low-rank behavior. Thus, Eclipse trains GNNs with a low-rank format of the graph via singular values decomposition (SVD), rather than the original graph. Using the low-rank format, Eclipse preserves the primary graph topology and removes the remaining residual edges. Eclipse adds noise to the low-rank singular values instead of the entire graph, thereby preserving the graph privacy while still maintaining enough of the graph structure to maintain model utility. We theoretically show Eclipse provide formal DP guarantee on edges. Experiments on benchmark graph datasets show that Eclipse achieves significantly better privacy-utility tradeoff compared to existing privacy-preserving GNN training methods. In particular, under strong privacy constraints (𝜖 < 4), Eclipse shows significant gains in the model utility by up to 46%. We further demonstrate that Eclipse also has better resilience against common edge attacks (e.g., LPA), lowering the attack AUC by up to 5% compared to other state-of-the-art baselines.

Learnable Graph Matching: A Practical Paradigm for Data Association.

Data association is at the core of many computer vision tasks, e.g., multiple object tracking, image matching, and point cloud registration. however, current data association solutions have some defects: they mostly ignore the intra-view context information; besides, they either train deep association models in an end-to-end way and hardly utilize the advantage of optimization-based assignment methods, or only use an off-the-shelf neural network to extract features. In this paper, we propose a general learnable graph matching method to address these issues. Especially, we model the intra-view relationships as an undirected graph. Then data association turns into a general graph matching problem between graphs. Furthermore, to make optimization end-to-end differentiable, we relax the original graph matching problem into continuous quadratic programming and then incorporate training into a deep graph neural network with KKT conditions and implicit function theorem. In MOT task, our method achieves state-of-the-art performance on several MOT datasets. For image matching, our method outperforms state-of-the-art methods on a popular indoor dataset, ScanNet. For point cloud registration, we also achieve competitive results.

Probability graph complementation contrastive learning

Graph Neural Network (GNN) has achieved remarkable progress in the field of graph representation learning. The most prominent characteristic, propagating features along the edges, degrades its performance in most heterophilic graphs. Certain researches make attempts to construct KNN graph to improve the graph homophily. However, there is no prior knowledge to choose proper K and they may suffer from the problem of Inconsistent Similarity Distribution (ISD). To accommodate this issue, we propose Probability Graph Complementation Contrastive Learning (PGCCL) which adaptively constructs the complementation graph. We employ Beta Mixture Model (BMM) to distinguish intra-class similarity and inter-class similarity. Based on the posterior probability, we construct Probability Complementation Graphs to form contrastive views. The contrastive learning prompts the model to preserve complementary information for each node from different views. By combining original graph embedding and complementary graph embedding, the final embedding is able to capture rich semantics in the finetuning stage. At last, comprehensive experimental results on 20 datasets including homophilic and heterophilic graphs firmly verify the effectiveness of our algorithm as well as the quality of probability complementation graph compared with other state-of-the-art methods.

Multi-view Heterogeneous Graph Neural Networks for Node Classification

Recently, with graph neural networks (GNNs) becoming a powerful technique for graph representation, many excellent GNN-based models have been proposed for processing heterogeneous graphs, which are termed Heterogeneous graph neural networks (HGNNs). However, existing HGNNs tend to aggregate information from either direct neighbors or those connected by short metapaths, thereby neglecting the higher-order information and global feature similarity information in heterogeneous graphs. In this paper, we propose a Multi-View Heterogeneous graph neural network (MV-HGNN) to aggregate these information. Firstly, two auxiliary views, specifically a global feature similarity view and a graph diffusion view, are generated from the original heterogeneous graph. Secondly, MV-HGNN performs two message-passing strategies to get the representation of different views. Subsequently, a transformer-based aggregator is used to get the semantic information. Subsequently, the representations of the three views are fused into a final composite representation. We evaluate our method on the node classification task over three commonly used heterogeneous graph datasets, and the results demonstrate that our proposed MV-HGNN significantly outperforms state-of-the-art baselines.

Graph structure estimation neural network-based service classification

PurposeWith the introduction of graph structure learning into service classification, more accurate graph structures can significantly improve the precision of service classification. However, existing graph structure learning methods tend to rely on a single information source when attempting to eliminate noise in the original graph structure and lack consideration for the graph generation mechanism. To address this problem, this paper aims to propose a graph structure estimation neural network-based service classification (GSESC) model.Design/methodology/approachFirst, this method uses the local smoothing properties of graph convolutional networks (GCN) and combines them with the stochastic block model to serve as the graph generation mechanism. Next, it constructs a series of observation sets reflecting the intrinsic structure of the service from different perspectives to minimize biases introduced by a single information source. Subsequently, it integrates the observation model with the structural model to calculate the posterior distribution of the graph structure. Finally, it jointly optimizes GCN and the graph estimation process to obtain the optimal graph.FindingsThe authors conducted a series of experiments on the API data set and compared it with six baseline methods. The experimental results demonstrate the effectiveness of the GSESC model in service classification.Originality/valueThis paper argues that the data set used for service classification exhibits a strong community structure. In response to this, the paper innovatively applies a graph-based learning model that considers the underlying generation mechanism of the graph to the field of service classification and achieves good results.

A Branch-and-Price algorithm for the electric autonomous Dial-A-Ride Problem

The Electric Autonomous Dial-A-Ride Problem (E-ADARP) consists in scheduling a fleet of electric autonomous vehicles to provide ride-sharing services for customers that specify their origins and destinations. The E-ADARP considers the following perspectives: (i) a weighted-sum objective that minimizes both total travel time and total excess user ride time; (ii) the employment of electric autonomous vehicles and a partial recharging policy. This paper presents the first labeling algorithm for a path-based formulation of the DARP/E-ADARP, where the main ingredient includes: (1) fragment-based representation of paths, (2) a novel approach that abstracts fragments to arcs while ensuring excess-user-ride-time optimality, (3) construction of a sparser new graph with the abstracted arcs, which is proven to preserve all feasible routes of the original graph, and (4) strong dominance rules and constant-time feasibility checks to compute the shortest paths efficiently. This labeling algorithm is then integrated into Branch-and-Price (B&P) algorithms to solve the E-ADARP. In the computational experiments, the B&P algorithm achieves optimality in 71 out of 84 instances. Remarkably, among these instances, 50 were solved optimally at the root node without branching. We identify 26 new best solutions, improve 30 previously reported lower bounds, and provide 17 new lower bounds for large-scale instances with up to 8 vehicles and 96 requests. In total 42 new best solutions are generated on previously solved and unsolved instances. In addition, we analyze the impact of incorporating the total excess user ride time within the objectives and allowing unlimited visits to recharging stations. The following managerial insights are provided: (1) solving a weighted-sum objective function can significantly enhance the service quality, while still maintaining operational costs at nearly optimal levels, (2) the relaxation on charging visits allows us to solve all instances feasibly and further reduces the average solution cost.