Danai Koutra

Jing Zhu, Xiang Song, Vassilis N. Ioannidis et al.

How can we enhance the node features acquired from Pretrained Models (PMs) to better suit downstream graph learning tasks? Graph Neural Networks (GNNs) have become the state-of-the-art approach for many high-impact, real-world graph applications. For feature-rich graphs, a prevalent practice involves utilizing a PM directly to generate features, without incorporating any domain adaptation techniques. Nevertheless, this practice is suboptimal because the node features extracted from PM are graph-agnostic and prevent GNNs from fully utilizing the potential correlations between the graph structure and node features, leading to a decline in GNNs performance. In this work, we seek to improve the node features obtained from a PM for downstream graph tasks and introduce TOUCHUP-G, which has several advantages. It is (a) General: applicable to any downstream graph task, including link prediction which is often employed in recommender systems; (b) Multi-modal: able to improve raw features of any modality (e.g. images, texts, audio); (c) Principled: it is closely related to a novel metric, feature homophily, which we propose to quantify the potential correlations between the graph structure and node features and we show that TOUCHUP-G can effectively shrink the discrepancy between the graph structure and node features; (d) Effective: achieving state-of-the-art results on four real-world datasets spanning different tasks and modalities.

Gaotang Li, Marlena Duda, Xiang Zhang et al.

Brain graphs, which model the structural and functional relationships between brain regions, are crucial in neuroscientific and clinical applications involving graph classification. However, dense brain graphs pose computational challenges including high runtime and memory usage and limited interpretability. In this paper, we investigate effective designs in Graph Neural Networks (GNNs) to sparsify brain graphs by eliminating noisy edges. While prior works remove noisy edges based on explainability or task-irrelevant properties, their effectiveness in enhancing performance with sparsified graphs is not guaranteed. Moreover, existing approaches often overlook collective edge removal across multiple graphs. To address these issues, we introduce an iterative framework to analyze different sparsification models. Our findings are as follows: (i) methods prioritizing interpretability may not be suitable for graph sparsification as they can degrade GNNs' performance in graph classification tasks; (ii) simultaneously learning edge selection with GNN training is more beneficial than post-training; (iii) a shared edge selection across graphs outperforms separate selection for each graph; and (iv) task-relevant gradient information aids in edge selection. Based on these insights, we propose a new model, Interpretable Graph Sparsification (IGS), which enhances graph classification performance by up to 5.1% with 55.0% fewer edges. The retained edges identified by IGS provide neuroscientific interpretations and are supported by well-established literature.

Puja Trivedi, Danai Koutra, Jayaraman J. Thiagarajan

Advances in the expressivity of pretrained models have increased interest in the design of adaptation protocols which enable safe and effective transfer learning. Going beyond conventional linear probing (LP) and fine tuning (FT) strategies, protocols that can effectively control feature distortion, i.e., the failure to update features orthogonal to the in-distribution, have been found to achieve improved out-of-distribution generalization (OOD). In order to limit this distortion, the LP+FT protocol, which first learns a linear probe and then uses this initialization for subsequent FT, was proposed. However, in this paper, we find when adaptation protocols (LP, FT, LP+FT) are also evaluated on a variety of safety objectives (e.g., calibration, robustness, etc.), a complementary perspective to feature distortion is helpful to explain protocol behavior. To this end, we study the susceptibility of protocols to simplicity bias (SB), i.e. the well-known propensity of deep neural networks to rely upon simple features, as SB has recently been shown to underlie several problems in robust generalization. Using a synthetic dataset, we demonstrate the susceptibility of existing protocols to SB. Given the strong effectiveness of LP+FT, we then propose modified linear probes that help mitigate SB, and lead to better initializations for subsequent FT. We verify the effectiveness of the proposed LP+FT variants for decreasing SB in a controlled setting, and their ability to improve OOD generalization and safety on three adaptation datasets.

Jing Zhu, Yuhang Zhou, Vassilis N. Ioannidis et al.

While Graph Neural Networks (GNNs) are remarkably successful in a variety of high-impact applications, we demonstrate that, in link prediction, the common practices of including the edges being predicted in the graph at training and/or test have outsized impact on the performance of low-degree nodes. We theoretically and empirically investigate how these practices impact node-level performance across different degrees. Specifically, we explore three issues that arise: (I1) overfitting; (I2) distribution shift; and (I3) implicit test leakage. The former two issues lead to poor generalizability to the test data, while the latter leads to overestimation of the model's performance and directly impacts the deployment of GNNs. To address these issues in a systematic way, we introduce an effective and efficient GNN training framework, SpotTarget, which leverages our insight on low-degree nodes: (1) at training time, it excludes a (training) edge to be predicted if it is incident to at least one low-degree node; and (2) at test time, it excludes all test edges to be predicted (thus, mimicking real scenarios of using GNNs, where the test data is not included in the graph). SpotTarget helps researchers and practitioners adhere to best practices for learning from graph data, which are frequently overlooked even by the most widely-used frameworks. Our experiments on various real-world datasets show that SpotTarget makes GNNs up to 15x more accurate in sparse graphs, and significantly improves their performance for low-degree nodes in dense graphs.

Puja Trivedi, Ekdeep Singh Lubana, Mark Heimann et al.

Recent analyses of self-supervised learning (SSL) find the following data-centric properties to be critical for learning good representations: invariance to task-irrelevant semantics, separability of classes in some latent space, and recoverability of labels from augmented samples. However, given their discrete, non-Euclidean nature, graph datasets and graph SSL methods are unlikely to satisfy these properties. This raises the question: how do graph SSL methods, such as contrastive learning (CL), work well? To systematically probe this question, we perform a generalization analysis for CL when using generic graph augmentations (GGAs), with a focus on data-centric properties. Our analysis yields formal insights into the limitations of GGAs and the necessity of task-relevant augmentations. As we empirically show, GGAs do not induce task-relevant invariances on common benchmark datasets, leading to only marginal gains over naive, untrained baselines. Our theory motivates a synthetic data generation process that enables control over task-relevant information and boasts pre-defined optimal augmentations. This flexible benchmark helps us identify yet unrecognized limitations in advanced augmentation techniques (e.g., automated methods). Overall, our work rigorously contextualizes, both empirically and theoretically, the effects of data-centric properties on augmentation strategies and learning paradigms for graph SSL.

Jiong Zhu, Gaotang Li, Yao-An Yang et al.

Heterophily, or the tendency of connected nodes in networks to have different class labels or dissimilar features, has been identified as challenging for many Graph Neural Network (GNN) models. While the challenges of applying GNNs for node classification when class labels display strong heterophily are well understood, it is unclear how heterophily affects GNN performance in other important graph learning tasks where class labels are not available. In this work, we focus on the link prediction task and systematically analyze the impact of heterophily in node features on GNN performance. Theoretically, we first introduce formal definitions of homophilic and heterophilic link prediction tasks, and present a theoretical framework that highlights the different optimizations needed for the respective tasks. We then analyze how different link prediction encoders and decoders adapt to varying levels of feature homophily and introduce designs for improved performance. Our empirical analysis on a variety of synthetic and real-world datasets confirms our theoretical insights and highlights the importance of adopting learnable decoders and GNN encoders with ego- and neighbor-embedding separation in message passing for link prediction tasks beyond homophily.

Donald Loveland, Jiong Zhu, Mark Heimann et al.

Graph Neural Network (GNN) research has highlighted a relationship between high homophily (i.e., the tendency of nodes of the same class to connect) and strong predictive performance in node classification. However, recent work has found the relationship to be more nuanced, demonstrating that simple GNNs can learn in certain heterophilous settings. To resolve these conflicting findings and align closer to real-world datasets, we go beyond the assumption of a global graph homophily level and study the performance of GNNs when the local homophily level of a node deviates from the global homophily level. Through theoretical and empirical analysis, we systematically demonstrate how shifts in local homophily can introduce performance degradation, leading to performance discrepancies across local homophily levels. We ground the practical implications of this work through granular analysis on five real-world datasets with varying global homophily levels, demonstrating that (a) GNNs can fail to generalize to test nodes that deviate from the global homophily of a graph, and (b) high local homophily does not necessarily confer high performance for a node. We further show that GNNs designed for globally heterophilous graphs can alleviate performance discrepancy by improving performance across local homophily levels, offering a new perspective on how these GNNs achieve stronger global performance.

Puja Trivedi, Mark Heimann, Rushil Anirudh et al.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-$Δ$UQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-$Δ$UQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

Jing Zhu, Danai Koutra, Mark Heimann

Network alignment, or the task of finding corresponding nodes in different networks, is an important problem formulation in many application domains. We propose CAPER, a multilevel alignment framework that Coarsens the input graphs, Aligns the coarsened graphs, Projects the alignment solution to finer levels and Refines the alignment solution. We show that CAPER can improve upon many different existing network alignment algorithms by enforcing alignment consistency across multiple graph resolutions: nodes matched at finer levels should also be matched at coarser levels. CAPER also accelerates the use of slower network alignment methods, at the modest cost of linear-time coarsening and refinement steps, by allowing them to be run on smaller coarsened versions of the input graphs. Experiments show that CAPER can improve upon diverse network alignment methods by an average of 33% in accuracy and/or an order of magnitude faster in runtime.

Donald Loveland, Jiong Zhu, Mark Heimann et al.

We study the task of node classification for graph neural networks (GNNs) and establish a connection between group fairness, as measured by statistical parity and equal opportunity, and local assortativity, i.e., the tendency of linked nodes to have similar attributes. Such assortativity is often induced by homophily, the tendency for nodes of similar properties to connect. Homophily can be common in social networks where systemic factors have forced individuals into communities which share a sensitive attribute. Through synthetic graphs, we study the interplay between locally occurring homophily and fair predictions, finding that not all node neighborhoods are equal in this respect -- neighborhoods dominated by one category of a sensitive attribute often struggle to obtain fair treatment, especially in the case of diverging local class and sensitive attribute homophily. After determining that a relationship between local homophily and fairness exists, we investigate if the issue of unfairness can be associated to the design of the applied GNN model. We show that by adopting heterophilous GNN designs capable of handling disassortative group labels, group fairness in locally heterophilous neighborhoods can be improved by up to 25% over homophilous designs in real and synthetic datasets.

Houquan Zhou, Shenghua Liu, Danai Koutra et al.

Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn embeddings on a smaller summary graph, and then restore the node embeddings of the original graph. However, all existing works depend on heuristic designs and lack theoretical analysis. Different from existing works, we contribute an in-depth theoretical analysis of three specific embedding learning methods based on introduced kernel matrix, and reveal that learning embeddings via graph summarization is actually learning embeddings on a approximate graph constructed by the configuration model. We also give analysis about approximation error. To the best of our knowledge, this is the first work to give theoretical analysis of this approach. Furthermore, our analysis framework gives interpretation of some existing methods and provides great insights for future work on this problem.

Puja Trivedi, Ryan Rossi, David Arbour et al.

Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive generative capabilities that have been used to correct corruptions in images, and the similarities between "in-painting" and filling in missing nodes and edges conditioned on the observed graph, we propose a novel graph generative framework, SGDM, which is based on subgraph diffusion. Our framework not only improves the scalability and fidelity of graph diffusion models, but also leverages the reverse process to perform novel, conditional generation tasks. In particular, through extensive empirical analysis and a set of novel metrics, we demonstrate that our proposed model effectively supports the following refinement tasks for partially observable networks: T1: denoising extraneous subgraphs, T2: expanding existing subgraphs and T3: performing "style" transfer by regenerating a particular subgraph to match the characteristics of a different node or subgraph.

Puja Trivedi, Danai Koutra, Jayaraman J. Thiagarajan

Generalization error predictors (GEPs) aim to predict model performance on unseen distributions by deriving dataset-level error estimates from sample-level scores. However, GEPs often utilize disparate mechanisms (e.g., regressors, thresholding functions, calibration datasets, etc), to derive such error estimates, which can obfuscate the benefits of a particular scoring function. Therefore, in this work, we rigorously study the effectiveness of popular scoring functions (confidence, local manifold smoothness, model agreement), independent of mechanism choice. We find, absent complex mechanisms, that state-of-the-art confidence- and smoothness- based scores fail to outperform simple model-agreement scores when estimating error under distribution shifts and corruptions. Furthermore, on realistic settings where the training data has been compromised (e.g., label noise, measurement noise, undersampling), we find that model-agreement scores continue to perform well and that ensemble diversity is important for improving its performance. Finally, to better understand the limitations of scoring functions, we demonstrate that simplicity bias, or the propensity of deep neural networks to rely upon simple but brittle features, can adversely affect GEP performance. Overall, our work carefully studies the effectiveness of popular scoring functions in realistic settings and helps to better understand their limitations.

Zhenning Yang, Yuhan Chen, Patrick Tser Jern Kon et al.

To unleash the full potential of AI for Science, we must untether the agents from a purely digital environment. The agent's ability to control and explore in real-world labs is essential because the physical lab remains foundational to scientific discovery. While some tasks can be performed on a computer (e.g., data analysis, running simulated experiments), Eureka moments could occur at any time while operating lab instruments (e.g., when a scientist notices unexpected clues, intuition may prompt a real-time course change). Although autonomous labs are on the rise, which expose programmable APIs to control scientific instruments via software, bridging the gap between increasingly powerful AI agents and automated lab equipment requires innovation that draws insights from computer systems. We propose a new paradigm called ``Experiment-as-Code (EaC) Labs,'' where a core concept is to encode experiments as declarative configurations that can be compiled down to device-level APIs. AI agents come up with hypotheses and experiments, written as an ensemble of declarative configurations. The systems layer performs program analysis, safety checks, resource assignment, and job orchestration. Finally, programmatic experimentation occurs via actuating the device APIs. This is a general stack that is science-, lab-, and instrument-independent, representing a novel synthesis across the physical, systems, and intelligence layers to unleash the next breakthrough in AI for Science.

Ekdeep Singh Lubana, Puja Trivedi, Danai Koutra et al.

Catastrophic forgetting undermines the effectiveness of deep neural networks (DNNs) in scenarios such as continual learning and lifelong learning. While several methods have been proposed to tackle this problem, there is limited work explaining why these methods work well. This paper has the goal of better explaining a popularly used technique for avoiding catastrophic forgetting: quadratic regularization. We show that quadratic regularizers prevent forgetting of past tasks by interpolating current and previous values of model parameters at every training iteration. Over multiple training iterations, this interpolation operation reduces the learning rates of more important model parameters, thereby minimizing their movement. Our analysis also reveals two drawbacks of quadratic regularization: (a) dependence of parameter interpolation on training hyperparameters, which often leads to training instability and (b) assignment of lower importance to deeper layers, which are generally the place forgetting occurs in DNNs. Via a simple modification to the order of operations, we show these drawbacks can be easily avoided, resulting in 6.2\% higher average accuracy at 4.5\% lower average forgetting. We confirm the robustness of our results by training over 2000 models in different settings. Code available at \url{https://github.com/EkdeepSLubana/QRforgetting}

Charles Dickens, Eddie Huang, Aishwarya Reganti et al.

Graph summarization as a preprocessing step is an effective and complementary technique for scalable graph neural network (GNN) training. In this work, we propose the Coarsening Via Convolution Matching (CONVMATCH) algorithm and a highly scalable variant, A-CONVMATCH, for creating summarized graphs that preserve the output of graph convolution. We evaluate CONVMATCH on six real-world link prediction and node classification graph datasets, and show it is efficient and preserves prediction performance while significantly reducing the graph size. Notably, CONVMATCH achieves up to 95% of the prediction performance of GNNs on node classification while trained on graphs summarized down to 1% the size of the original graph. Furthermore, on link prediction tasks, CONVMATCH consistently outperforms all baselines, achieving up to a 2x improvement.

Puja Trivedi, Mark Heimann, Rushil Anirudh et al.

While graph neural networks (GNNs) are widely used for node and graph representation learning tasks, the reliability of GNN uncertainty estimates under distribution shifts remains relatively under-explored. Indeed, while post-hoc calibration strategies can be used to improve in-distribution calibration, they need not also improve calibration under distribution shift. However, techniques which produce GNNs with better intrinsic uncertainty estimates are particularly valuable, as they can always be combined with post-hoc strategies later. Therefore, in this work, we propose G-$Δ$UQ, a novel training framework designed to improve intrinsic GNN uncertainty estimates. Our framework adapts the principle of stochastic data centering to graph data through novel graph anchoring strategies, and is able to support partially stochastic GNNs. While, the prevalent wisdom is that fully stochastic networks are necessary to obtain reliable estimates, we find that the functional diversity induced by our anchoring strategies when sampling hypotheses renders this unnecessary and allows us to support G-$Δ$UQ on pretrained models. Indeed, through extensive evaluation under covariate, concept and graph size shifts, we show that G-$Δ$UQ leads to better calibrated GNNs for node and graph classification. Further, it also improves performance on the uncertainty-based tasks of out-of-distribution detection and generalization gap estimation. Overall, our work provides insights into uncertainty estimation for GNNs, and demonstrates the utility of G-$Δ$UQ in obtaining reliable estimates.

Michael Ito, Jiong Zhu, Dexiong Chen et al.

In this work, we theoretically demonstrate that current graph positional encodings (PEs) are not beneficial and could potentially hurt performance in tasks involving heterophilous graphs, where nodes that are close tend to have different labels. This limitation is critical as many real-world networks exhibit heterophily, and even highly homophilous graphs can contain local regions of strong heterophily. To address this limitation, we propose Learnable Laplacian Positional Encodings (LLPE), a new PE that leverages the full spectrum of the graph Laplacian, enabling them to capture graph structure on both homophilous and heterophilous graphs. Theoretically, we prove LLPE's ability to approximate a general class of graph distances and demonstrate its generalization properties. Empirically, our evaluation on 12 benchmarks demonstrates that LLPE improves accuracy across a variety of GNNs, including graph transformers, by up to 35% and 14% on synthetic and real-world graphs, respectively. Going forward, our work represents a significant step towards developing PEs that effectively capture complex structures in heterophilous graphs.

Donald Loveland, Xinyi Wu, Tong Zhao et al.

Collaborative Filtering (CF) methods dominate real-world recommender systems given their ability to learn high-quality, sparse ID-embedding tables that effectively capture user preferences. These tables scale linearly with the number of users and items, and are trained to ensure high similarity between embeddings of interacted user-item pairs, while maintaining low similarity for non-interacted pairs. Despite their high performance, encouraging dispersion for non-interacted pairs necessitates expensive regularization (e.g., negative sampling), hurting runtime and scalability. Existing research tends to address these challenges by simplifying the learning process, either by reducing model complexity or sampling data, trading performance for runtime. In this work, we move beyond model-level modifications and study the properties of the embedding tables under different learning strategies. Through theoretical analysis, we find that the singular values of the embedding tables are intrinsically linked to different CF loss functions. These findings are empirically validated on real-world datasets, demonstrating the practical benefits of higher stable rank, a continuous version of matrix rank which encodes the distribution of singular values. Based on these insights, we propose an efficient warm-start strategy that regularizes the stable rank of the user and item embeddings. We show that stable rank regularization during early training phases can promote higher-quality embeddings, resulting in training speed improvements of up to 66%. Additionally, stable rank regularization can act as a proxy for negative sampling, allowing for performance gains of up to 21% over loss functions with small negative sampling ratios. Overall, our analysis unifies current CF methods under a new perspective, their optimization of stable rank, motivating a flexible regularization method.

Michael Ito, Danai Koutra, Jenna Wiens

Homophily, as a measure, has been critical to increasing our understanding of graph neural networks (GNNs). However, to date this measure has only been analyzed in the context of static graphs. In our work, we explore homophily in dynamic settings. Focusing on graph convolutional networks (GCNs), we demonstrate theoretically that in dynamic settings, current GCN discriminative performance is characterized by the probability that a node's future label is the same as its neighbors' current labels. Based on this insight, we propose dynamic homophily, a new measure of homophily that applies in the dynamic setting. This new measure correlates with GNN discriminative performance and sheds light on how to potentially design more powerful GNNs for dynamic graphs. Leveraging a variety of dynamic node classification datasets, we demonstrate that popular GNNs are not robust to low dynamic homophily. Going forward, our work represents an important step towards understanding homophily and GNN performance in dynamic node classification.

Jing Zhu, Mingxuan Ju, Yozen Liu et al.

Generative recommendation (GR) has become a powerful paradigm in recommendation systems that implicitly links modality and semantics to item representation, in contrast to previous methods that relied on non-semantic item identifiers in autoregressive models. However, previous research has predominantly treated modalities in isolation, typically assuming item content is unimodal (usually text). We argue that this is a significant limitation given the rich, multimodal nature of real-world data and the potential sensitivity of GR models to modality choices and usage. Our work aims to explore the critical problem of Multimodal Generative Recommendation (MGR), highlighting the importance of modality choices in GR nframeworks. We reveal that GR models are particularly sensitive to different modalities and examine the challenges in achieving effective GR when multiple modalities are available. By evaluating design strategies for effectively leveraging multiple modalities, we identify key challenges and introduce MGR-LF++, an enhanced late fusion framework that employs contrastive modality alignment and special tokens to denote different modalities, achieving a performance improvement of over 20% compared to single-modality alternatives.

Jiacheng Lin, Kun Qian, Haoyu Han et al.

Graph-structured information offers rich contextual information that can enhance language models by providing structured relationships and hierarchies, leading to more expressive embeddings for various applications such as retrieval, question answering, and classification. However, existing methods for integrating graph and text embeddings, often based on Multi-layer Perceptrons (MLPs) or shallow transformers, are limited in their ability to fully exploit the heterogeneous nature of these modalities. To overcome this, we propose GT2Vec, a simple yet effective framework that leverages Large Language Models (LLMs) to jointly encode text and graph data. Specifically, GT2Vec employs an MLP adapter to project graph embeddings into the same space as text embeddings, allowing the LLM to process both modalities jointly. Unlike prior work, we also introduce contrastive learning to align the graph and text spaces more effectively, thereby improving the quality of learned joint embeddings. Empirical results across six datasets spanning three tasks, knowledge graph-contextualized question answering, graph-text pair classification, and retrieval, demonstrate that GT2Vec consistently outperforms existing baselines, achieving significant improvements across multiple datasets. These results highlight GT2Vec's effectiveness in integrating graph and text data. Ablation studies further validate the effectiveness of our method.

Jiaji Ma, Puja Trivedi, Danai Koutra

Text-attributed graphs (TAGs), which combine structural and textual node information, are ubiquitous across many domains. Recent work integrates Large Language Models (LLMs) with Graph Neural Networks (GNNs) to jointly model semantics and structure, resulting in more general and expressive models that achieve state-of-the-art performance on TAG benchmarks. However, this integration introduces dual vulnerabilities: GNNs are sensitive to structural perturbations, while LLM-derived features are vulnerable to prompt injection and adversarial phrasing. While existing adversarial attacks largely perturb structure or text independently, we find that uni-modal attacks cause only modest degradation in LLM-enhanced GNNs. Moreover, many existing attacks assume unrealistic capabilities, such as white-box access or direct modification of graph data. To address these gaps, we propose GRAPHTEXTACK, the first black-box, multi-modal{, poisoning} node injection attack for LLM-enhanced GNNs. GRAPHTEXTACK injects nodes with carefully crafted structure and semantics to degrade model performance, operating under a realistic threat model without relying on model internals or surrogate models. To navigate the combinatorial, non-differentiable search space of connectivity and feature assignments, GRAPHTEXTACK introduces a novel evolutionary optimization framework with a multi-objective fitness function that balances local prediction disruption and global graph influence. Extensive experiments on five datasets and two state-of-the-art LLM-enhanced GNN models show that GRAPHTEXTACK significantly outperforms 12 strong baselines.

Jing Zhu, Yuhang Zhou, Shengyi Qian et al.

Graph machine learning has made significant strides in recent years, yet the integration of visual information with graph structure and its potential for improving performance in downstream tasks remains an underexplored area. To address this critical gap, we introduce the Multimodal Graph Benchmark (MM-GRAPH), a pioneering benchmark that incorporates both visual and textual information into graph learning tasks. MM-GRAPH extends beyond existing text-attributed graph benchmarks, offering a more comprehensive evaluation framework for multimodal graph learning Our benchmark comprises seven diverse datasets of varying scales (ranging from thousands to millions of edges), designed to assess algorithms across different tasks in real-world scenarios. These datasets feature rich multimodal node attributes, including visual data, which enables a more holistic evaluation of various graph learning frameworks in complex, multimodal environments. To support advancements in this emerging field, we provide an extensive empirical study on various graph learning frameworks when presented with features from multiple modalities, particularly emphasizing the impact of visual information. This study offers valuable insights into the challenges and opportunities of integrating visual data into graph learning.

Yuhang Zhou, Jing Zhu, Paiheng Xu et al.

Large language models (LLMs) have significantly advanced various natural language processing tasks, but deploying them remains computationally expensive. Knowledge distillation (KD) is a promising solution, enabling the transfer of capabilities from larger teacher LLMs to more compact student models. Particularly, sequence-level KD, which distills rationale-based reasoning processes instead of merely final outcomes, shows great potential in enhancing students' reasoning capabilities. However, current methods struggle with sequence level KD under long-tailed data distributions, adversely affecting generalization on sparsely represented domains. We introduce the Multi-Stage Balanced Distillation (BalDistill) framework, which iteratively balances training data within a fixed computational budget. By dynamically selecting representative head domain examples and synthesizing tail domain examples, BalDistill achieves state-of-the-art performance across diverse long-tailed datasets, enhancing both the efficiency and efficacy of the distilled models.

Yu Wang, Ryan A. Rossi, Namyong Park et al.

Large Generative Models (LGMs) such as GPT, Stable Diffusion, Sora, and Suno are trained on a huge amount of language corpus, images, videos, and audio that are extremely diverse from numerous domains. This training paradigm over diverse well-curated data lies at the heart of generating creative and sensible content. However, all previous graph generative models (e.g., GraphRNN, MDVAE, MoFlow, GDSS, and DiGress) have been trained only on one dataset each time, which cannot replicate the revolutionary success achieved by LGMs in other fields. To remedy this crucial gap, we propose a new class of graph generative model called Large Graph Generative Model (LGGM) that is trained on a large corpus of graphs (over 5000 graphs) from 13 different domains. We empirically demonstrate that the pre-trained LGGM has superior zero-shot generative capability to existing graph generative models. Furthermore, our pre-trained LGGM can be easily fine-tuned with graphs from target domains and demonstrate even better performance than those directly trained from scratch, behaving as a solid starting point for real-world customization. Inspired by Stable Diffusion, we further equip LGGM with the capability to generate graphs given text prompts (Text-to-Graph), such as the description of the network name and domain (i.e., "The power-1138-bus graph represents a network of buses in a power distribution system."), and network statistics (i.e., "The graph has a low average degree, suitable for modeling social media interactions."). This Text-to-Graph capability integrates the extensive world knowledge in the underlying language model, offering users fine-grained control of the generated graphs. We release the code, the model checkpoint, and the datasets at https://lggm-lg.github.io/.

Zhongmou He, Jing Zhu, Shengyi Qian et al.

Large Language Models (LLMs) have shown promising results on various language and vision tasks. Recently, there has been growing interest in applying LLMs to graph-based tasks, particularly on Text-Attributed Graphs (TAGs). However, most studies have focused on node classification, while the use of LLMs for link prediction (LP) remains understudied. In this work, we propose a new task on LLMs, where the objective is to leverage LLMs to predict missing links between nodes in a graph. This task evaluates an LLM's ability to reason over structured data and infer new facts based on learned patterns. This new task poses two key challenges: (1) How to effectively integrate pairwise structural information into the LLMs, which is known to be crucial for LP performance, and (2) how to solve the computational bottleneck when teaching LLMs to perform LP. To address these challenges, we propose LinkGPT, the first end-to-end trained LLM for LP tasks. To effectively enhance the LLM's ability to understand the underlying structure, we design a two-stage instruction tuning approach where the first stage fine-tunes the pairwise encoder, projector, and node projector, and the second stage further fine-tunes the LLMs to predict links. To address the efficiency challenges at inference time, we introduce a retrieval-reranking scheme. Experiments show that LinkGPT can achieve state-of-the-art performance on real-world graphs as well as superior generalization in zero-shot and few-shot learning, surpassing existing benchmarks. At inference time, it can achieve $10\times$ speedup while maintaining high LP accuracy.

Gaotang Li, Danai Koutra, Yujun Yan

We address the key challenge of size-induced distribution shifts in graph neural networks (GNNs) and their impact on the generalization of GNNs to larger graphs. Existing literature operates under diverse assumptions about distribution shifts, resulting in varying conclusions about the generalizability of GNNs. In contrast to prior work, we adopt a data-driven approach to identify and characterize the types of size-induced distribution shifts and explore their impact on GNN performance from a spectral standpoint, a perspective that has been largely underexplored. Leveraging the significant variance in graph sizes in real biological datasets, we analyze biological graphs and find that spectral differences, driven by subgraph patterns (e.g., average cycle length), strongly correlate with GNN performance on larger, unseen graphs. Based on these insights, we propose three model-agnostic strategies to enhance GNNs' awareness of critical subgraph patterns, identifying size-intensive attention as the most effective approach. Extensive experiments with six GNN architectures and seven model-agnostic strategies across five datasets show that our size-intensive attention strategy significantly improves graph classification on test graphs 2 to 10 times larger than the training graphs, boosting F1 scores by up to 8% over strong baselines.

Jiong Zhu, Aishwarya Reganti, Edward Huang et al.

Distributed training of GNNs enables learning on massive graphs (e.g., social and e-commerce networks) that exceed the storage and computational capacity of a single machine. To reach performance comparable to centralized training, distributed frameworks focus on maximally recovering cross-instance node dependencies with either communication across instances or periodic fallback to centralized training, which create overhead and limit the framework scalability. In this work, we present a simplified framework for distributed GNN training that does not rely on the aforementioned costly operations, and has improved scalability, convergence speed and performance over the state-of-the-art approaches. Specifically, our framework (1) assembles independent trainers, each of which asynchronously learns a local model on locally-available parts of the training graph, and (2) only conducts periodic (time-based) model aggregation to synchronize the local models. Backed by our theoretical analysis, instead of maximizing the recovery of cross-instance node dependencies -- which has been considered the key behind closing the performance gap between model aggregation and centralized training -- , our framework leverages randomized assignment of nodes or super-nodes (i.e., collections of original nodes) to partition the training graph such that it improves data uniformity and minimizes the discrepancy of gradient and loss function across instances. In our experiments on social and e-commerce networks with up to 1.3 billion edges, our proposed RandomTMA and SuperTMA approaches -- despite using less training data -- achieve state-of-the-art performance and 2.31x speedup compared to the fastest baseline, and show better robustness to trainer failures.

Fatemeh Vahedian, Ruiyu Li, Puja Trivedi et al.

Understanding the training dynamics of deep neural networks (DNNs) is important as it can lead to improved training efficiency and task performance. Recent works have demonstrated that representing the wirings of static graph cannot capture how DNNs change over the course of training. Thus, in this work, we propose a compact, expressive temporal graph framework that effectively captures the dynamics of many workhorse architectures in computer vision. Specifically, it extracts an informative summary of graph properties (e.g., eigenvector centrality) over a sequence of DNN graphs obtained during training. We demonstrate that our framework captures useful dynamics by accurately predicting trained, task performance when using a summary over early training epochs (<5) across four different architectures and two image datasets. Moreover, by using a novel, highly-scalable DNN graph representation, we also show that the proposed framework captures generalizable dynamics as summaries extracted from smaller-width networks are effective when evaluated on larger widths.

Puja Trivedi, Ekdeep Singh Lubana, Yujun Yan et al.

Unsupervised graph representation learning is critical to a wide range of applications where labels may be scarce or expensive to procure. Contrastive learning (CL) is an increasingly popular paradigm for such settings and the state-of-the-art in unsupervised visual representation learning. Recent work attributes the success of visual CL to use of task-relevant augmentations and large, diverse datasets. Interestingly, graph CL frameworks report strong performance despite using orders of magnitude smaller datasets and employing domain-agnostic graph augmentations (DAGAs). Motivated by this discrepancy, we probe the quality of representations learnt by popular graph CL frameworks using DAGAs. We find that DAGAs can destroy task-relevant information and harm the model's ability to learn discriminative representations. On small benchmark datasets, we show the inductive bias of graph neural networks can significantly compensate for this weak discriminability. Based on our findings, we propose several sanity checks that enable practitioners to quickly assess the quality of their model's learned representations. We further propose a broad strategy for designing task-aware augmentations that are amenable to graph CL and demonstrate its efficacy on two large-scale, complex graph applications. For example, in graph-based document classification, we show task-aware augmentations improve accuracy up to 20%.

Di Jin, Bunyamin Sisman, Hao Wei et al.

Multi-source entity linkage focuses on integrating knowledge from multiple sources by linking the records that represent the same real world entity. This is critical in high-impact applications such as data cleaning and user stitching. The state-of-the-art entity linkage pipelines mainly depend on supervised learning that requires abundant amounts of training data. However, collecting well-labeled training data becomes expensive when the data from many sources arrives incrementally over time. Moreover, the trained models can easily overfit to specific data sources, and thus fail to generalize to new sources due to significant differences in data and label distributions. To address these challenges, we present AdaMEL, a deep transfer learning framework that learns generic high-level knowledge to perform multi-source entity linkage. AdaMEL models the attribute importance that is used to match entities through an attribute-level self-attention mechanism, and leverages the massive unlabeled data from new data sources through domain adaptation to make it generic and data-source agnostic. In addition, AdaMEL is capable of incorporating an additional set of labeled data to more accurately integrate data sources with different attribute importance. Extensive experiments show that our framework achieves state-of-the-art results with 8.21% improvement on average over methods based on supervised learning. Besides, it is more stable in handling different sets of data sources in less runtime.

Jiong Zhu, Junchen Jin, Donald Loveland et al.

We bridge two research directions on graph neural networks (GNNs), by formalizing the relation between heterophily of node labels (i.e., connected nodes tend to have dissimilar labels) and the robustness of GNNs to adversarial attacks. Our theoretical and empirical analyses show that for homophilous graph data, impactful structural attacks always lead to reduced homophily, while for heterophilous graph data the change in the homophily level depends on the node degrees. These insights have practical implications for defending against attacks on real-world graphs: we deduce that separate aggregators for ego- and neighbor-embeddings, a design principle which has been identified to significantly improve prediction for heterophilous graph data, can also offer increased robustness to GNNs. Our comprehensive experiments show that GNNs merely adopting this design achieve improved empirical and certifiable robustness compared to the best-performing unvaccinated model. Additionally, combining this design with explicit defense mechanisms against adversarial attacks leads to an improved robustness with up to 18.33% performance increase under attacks compared to the best-performing vaccinated model.

Tara Safavi, Danai Koutra

Relational knowledge bases (KBs) are commonly used to represent world knowledge in machines. However, while advantageous for their high degree of precision and interpretability, KBs are usually organized according to manually-defined schemas, which limit their expressiveness and require significant human efforts to engineer and maintain. In this review, we take a natural language processing perspective to these limitations, examining how they may be addressed in part by training deep contextual language models (LMs) to internalize and express relational knowledge in more flexible forms. We propose to organize knowledge representation strategies in LMs by the level of KB supervision provided, from no KB supervision at all to entity- and relation-level supervision. Our contributions are threefold: (1) We provide a high-level, extensible taxonomy for knowledge representation in LMs; (2) Within our taxonomy, we highlight notable models, evaluation tasks, and findings, in order to provide an up-to-date review of current knowledge representation capabilities in LMs; and (3) We suggest future research directions that build upon the complementary aspects of LMs and KBs as knowledge representations.

Jing Zhu, Xingyu Lu, Mark Heimann et al.

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.

Yujun Yan, Milad Hashemi, Kevin Swersky et al.

In node classification tasks, graph convolutional neural networks (GCNs) have demonstrated competitive performance over traditional methods on diverse graph data. However, it is known that the performance of GCNs degrades with increasing number of layers (oversmoothing problem) and recent studies have also shown that GCNs may perform worse in heterophilous graphs, where neighboring nodes tend to belong to different classes (heterophily problem). These two problems are usually viewed as unrelated, and thus are studied independently, often at the graph filter level from a spectral perspective. We are the first to take a unified perspective to jointly explain the oversmoothing and heterophily problems at the node level. Specifically, we profile the nodes via two quantitative metrics: the relative degree of a node (compared to its neighbors) and the node-level heterophily. Our theory shows that the interplay of these two profiling metrics defines three cases of node behaviors, which explain the oversmoothing and heterophily problems jointly and can predict the performance of GCNs. Based on insights from our theory, we show theoretically and empirically the effectiveness of two strategies: structure-based edge correction, which learns corrected edge weights from structural properties (i.e., degrees), and feature-based edge correction, which learns signed edge weights from node features. Compared to other approaches, which tend to handle well either heterophily or oversmoothing, we show that {our model, GGCN}, which incorporates the two strategies performs well in both problems.

Tara Safavi, Jing Zhu, Danai Koutra

Codifying commonsense knowledge in machines is a longstanding goal of artificial intelligence. Recently, much progress toward this goal has been made with automatic knowledge base (KB) construction techniques. However, such techniques focus primarily on the acquisition of positive (true) KB statements, even though negative (false) statements are often also important for discriminative reasoning over commonsense KBs. As a first step toward the latter, this paper proposes NegatER, a framework that ranks potential negatives in commonsense KBs using a contextual language model (LM). Importantly, as most KBs do not contain negatives, NegatER relies only on the positive knowledge in the LM and does not require ground-truth negative examples. Experiments demonstrate that, compared to multiple contrastive data augmentation approaches, NegatER yields negatives that are more grammatical, coherent, and informative -- leading to statistically significant accuracy improvements in a challenging KB completion task and confirming that the positive knowledge in LMs can be "re-purposed" to generate negative knowledge.

Jiong Zhu, Ryan A. Rossi, Anup Rao et al.

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

Di Jin, Sungchul Kim, Ryan A. Rossi et al.

We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting the temporal dependencies, and generalizing existing embedding methods for such data. While previous work on dynamic modeling and embedding has focused on representing a stream of timestamped edges using a time-series of graphs based on a specific time-scale (e.g., 1 month), we propose the notion of an $ε$-graph time-series that uses a fixed number of edges for each graph, and show its superiority over the time-scale representation used in previous work. In addition, we propose a number of new temporal models based on the notion of temporal reachability graphs and weighted temporal summary graphs. These temporal models are then used to generalize existing base (static) embedding methods by enabling them to incorporate and appropriately model temporal dependencies in the data. From the 6 temporal network models investigated (for each of the 7 base embedding methods), we find that the top-3 temporal models are always those that leverage the new $ε$-graph time-series representation. Furthermore, the dynamic embedding methods from the framework almost always achieve better predictive performance than existing state-of-the-art dynamic node embedding methods that are developed specifically for such temporal prediction tasks. Finally, the findings of this work are useful for designing better dynamic embedding methods.

Tara Safavi, Danai Koutra

We present CoDEx, a set of knowledge graph completion datasets extracted from Wikidata and Wikipedia that improve upon existing knowledge graph completion benchmarks in scope and level of difficulty. In terms of scope, CoDEx comprises three knowledge graphs varying in size and structure, multilingual descriptions of entities and relations, and tens of thousands of hard negative triples that are plausible but verified to be false. To characterize CoDEx, we contribute thorough empirical analyses and benchmarking experiments. First, we analyze each CoDEx dataset in terms of logical relation patterns. Next, we report baseline link prediction and triple classification results on CoDEx for five extensively tuned embedding models. Finally, we differentiate CoDEx from the popular FB15K-237 knowledge graph completion dataset by showing that CoDEx covers more diverse and interpretable content, and is a more difficult link prediction benchmark. Data, code, and pretrained models are available at https://bit.ly/2EPbrJs.

Jiong Zhu, Yujun Yan, Lingxiao Zhao et al.

We investigate the representation power of graph neural networks in the semi-supervised node classification task under heterophily or low homophily, i.e., in networks where connected nodes may have different class labels and dissimilar features. Many popular GNNs fail to generalize to this setting, and are even outperformed by models that ignore the graph structure (e.g., multilayer perceptrons). Motivated by this limitation, we identify a set of key designs -- ego- and neighbor-embedding separation, higher-order neighborhoods, and combination of intermediate representations -- that boost learning from the graph structure under heterophily. We combine them into a graph neural network, H2GCN, which we use as the base method to empirically evaluate the effectiveness of the identified designs. Going beyond the traditional benchmarks with strong homophily, our empirical analysis shows that the identified designs increase the accuracy of GNNs by up to 40% and 27% over models without them on synthetic and real networks with heterophily, respectively, and yield competitive performance under homophily.

Yujun Yan, Kevin Swersky, Danai Koutra et al.

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data distributions that are outside of their restricted training sets, namely larger inputs and unseen data. We study these generalization issues at the level of numerical subroutines that comprise common algorithms like sorting, shortest paths, and minimum spanning trees. First, we observe that transformer-based sequence-to-sequence models can learn subroutines like sorting a list of numbers, but their performance rapidly degrades as the length of lists grows beyond those found in the training set. We demonstrate that this is due to attention weights that lose fidelity with longer sequences, particularly when the input numbers are numerically similar. To address the issue, we propose a learned conditional masking mechanism, which enables the model to strongly generalize far outside of its training range with near-perfect accuracy on a variety of algorithms. Second, to generalize to unseen data, we show that encoding numbers with a binary representation leads to embeddings with rich structure once trained on downstream tasks like addition or multiplication. This allows the embedding to handle missing data by faithfully interpolating numbers not seen during training.

Tara Safavi, Danai Koutra, Edgar Meij

Little is known about the trustworthiness of predictions made by knowledge graph embedding (KGE) models. In this paper we take initial steps toward this direction by investigating the calibration of KGE models, or the extent to which they output confidence scores that reflect the expected correctness of predicted knowledge graph triples. We first conduct an evaluation under the standard closed-world assumption (CWA), in which predicted triples not already in the knowledge graph are considered false, and show that existing calibration techniques are effective for KGE under this common but narrow assumption. Next, we introduce the more realistic but challenging open-world assumption (OWA), in which unobserved predictions are not considered true or false until ground-truth labels are obtained. Here, we show that existing calibration techniques are much less effective under the OWA than the CWA, and provide explanations for this discrepancy. Finally, to motivate the utility of calibration for KGE from a practitioner's perspective, we conduct a unique case study of human-AI collaboration, showing that calibrated predictions can improve human performance in a knowledge graph completion task.

Ryan A. Rossi, Di Jin, Sungchul Kim et al.

Structural roles define sets of structurally similar nodes that are more similar to nodes inside the set than outside, whereas communities define sets of nodes with more connections inside the set than outside. Roles based on structural similarity and communities based on proximity are fundamentally different but important complementary notions. Recently, the notion of structural roles has become increasingly important and has gained a lot of attention due to the proliferation of work on learning representations (node/edge embeddings) from graphs that preserve the notion of roles. Unfortunately, recent work has sometimes confused the notion of structural roles and communities (based on proximity) leading to misleading or incorrect claims about the capabilities of network embedding methods. As such, this paper seeks to clarify the misconceptions and key differences between structural roles and communities, and formalize the general mechanisms (e.g., random walks, feature diffusion) that give rise to community or role-based structural embeddings. We theoretically prove that embedding methods based on these mechanisms result in either community or role-based structural embeddings. These mechanisms are typically easy to identify and can help researchers quickly determine whether a method preserves community or role-based embeddings. Furthermore, they also serve as a basis for developing new and improved methods for community or role-based structural embeddings. Finally, we analyze and discuss applications and data characteristics where community or role-based embeddings are most appropriate.

Di Jin, Mark Heimann, Ryan Rossi et al.

Identity stitching, the task of identifying and matching various online references (e.g., sessions over different devices and timespans) to the same user in real-world web services, is crucial for personalization and recommendations. However, traditional user stitching approaches, such as grouping or blocking, require quadratic pairwise comparisons between a massive number of user activities, thus posing both computational and storage challenges. Recent works, which are often application-specific, heuristically seek to reduce the amount of comparisons, but they suffer from low precision and recall. To solve the problem in an application-independent way, we take a heterogeneous network-based approach in which users (nodes) interact with content (e.g., sessions, websites), and may have attributes (e.g., location). We propose node2bits, an efficient framework that represents multi-dimensional features of node contexts with binary hashcodes. node2bits leverages feature-based temporal walks to encapsulate short- and long-term interactions between nodes in heterogeneous web networks, and adopts SimHash to obtain compact, binary representations and avoid the quadratic complexity for similarity search. Extensive experiments on large-scale real networks show that node2bits outperforms traditional techniques and existing works that generate real-valued embeddings by up to 5.16% in F1 score on user stitching, while taking only up to 1.56% as much storage.

Saba A. Al-Sayouri, Ekta Gujral, Danai Koutra et al.

Graph representations have increasingly grown in popularity during the last years. Existing representation learning approaches explicitly encode network structure. Despite their good performance in downstream processes (e.g., node classification, link prediction), there is still room for improvement in different aspects, like efficacy, visualization, and interpretability. In this paper, we propose, t-PINE, a method that addresses these limitations. Contrary to baseline methods, which generally learn explicit graph representations by solely using an adjacency matrix, t-PINE avails a multi-view information graph, the adjacency matrix represents the first view, and a nearest neighbor adjacency, computed over the node features, is the second view, in order to learn explicit and implicit node representations, using the Canonical Polyadic (a.k.a. CP) decomposition. We argue that the implicit and the explicit mapping from a higher-dimensional to a lower-dimensional vector space is the key to learn more useful, highly predictable, and gracefully interpretable representations. Having good interpretable representations provides a good guidance to understand how each view contributes to the representation learning process. In addition, it helps us to exclude unrelated dimensions. Extensive experiments show that t-PINE drastically outperforms baseline methods by up to 158.6% with respect to Micro-F1, in several multi-label classification problems, while it has high visualization and interpretability utility.

Saba A. Al-Sayouri, Danai Koutra, Evangelos E. Papalexakis et al.

The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning algorithms aim to preserve local and global network structure by identifying node neighborhood notions. However, many existing algorithms generate embeddings that fail to properly preserve the network structure, or lead to unstable representations due to random processes (e.g., random walks to generate context) and, thus, cannot generate to multi-graph problems. In this paper, we propose RECS, a novel, stable graph embedding algorithmic framework. RECS learns graph representations using connection subgraphs by employing the analogy of graphs with electrical circuits. It preserves both local and global connectivity patterns, and addresses the issue of high-degree nodes. Further, it exploits the strength of weak ties and meta-data that have been neglected by baselines. The experiments show that RECS outperforms state-of-the-art algorithms by up to 36.85% on multi-label classification problem. Further, in contrast to baselines, RECS, being deterministic, is completely stable.

Yike Liu, Tara Safavi, Abhilash Dighe et al.

While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data are thus becoming vital for extracting actionable insights. In particular, while data summarization techniques have been studied extensively, only recently has summarizing interconnected data, or graphs, become popular. This survey is a structured, comprehensive overview of the state-of-the-art methods for summarizing graph data. We first broach the motivation behind, and the challenges of, graph summarization. We then categorize summarization approaches by the type of graphs taken as input and further organize each category by core methodology. Finally, we discuss applications of summarization on real-world graphs and conclude by describing some open problems in the field.

Yike Liu, Neil Shah, Danai Koutra

How do graph clustering techniques compare with respect to their summarization power? How well can they summarize a million-node graph with a few representative structures? Graph clustering or community detection algorithms can summarize a graph in terms of coherent and tightly connected clusters. In this paper, we compare and contrast different techniques: METIS, Louvain, spectral clustering, SlashBurn and KCBC, our proposed k-core-based clustering method. Unlike prior work that focuses on various measures of cluster quality, we use vocabulary structures that often appear in real graphs and the Minimum Description Length (MDL) principle to obtain a graph summary per clustering method. Our main contributions are: (i) Formulation: We propose a summarization-based evaluation of clustering methods. Our method, VOG-OVERLAP, concisely summarizes graphs in terms of their important structures which lead to small edge overlap, and large node/edge coverage; (ii) Algorithm: we introduce KCBC, a graph decomposition technique, in the heart of which lies the k-core algorithm (iii) Evaluation: We compare the summarization power of five clustering techniques on large real graphs, and analyze their compression performance, summary statistics and runtimes.

Wolfgang Gatterbauer, Stephan Günnemann, Danai Koutra et al.

How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels of their neighbors and appropriate assumptions of homophily ("birds of a feather flock together") or heterophily ("opposites attract"). One of the most widely used methods for this kind of inference is Belief Propagation (BP) which iteratively propagates the information from a few nodes with explicit labels throughout a network until convergence. One main problem with BP, however, is that there are no known exact guarantees of convergence in graphs with loops. This paper introduces Linearized Belief Propagation (LinBP), a linearization of BP that allows a closed-form solution via intuitive matrix equations and, thus, comes with convergence guarantees. It handles homophily, heterophily, and more general cases that arise in multi-class settings. Plus, it allows a compact implementation in SQL. The paper also introduces Single-pass Belief Propagation (SBP), a "localized" version of LinBP that propagates information across every edge at most once and for which the final class assignments depend only on the nearest labeled neighbors. In addition, SBP allows fast incremental updates in dynamic networks. Our runtime experiments show that LinBP and SBP are orders of magnitude faster than standard