Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence, it is natural to consider the question of finding dense subgraphs in a temporal network that are allowed to vary over time to a certain degree. In this paper, we search for dense subgraphs that have large pairwise Jaccard similarity coefficients. More formally, given a set of graph snapshots and a weight $\lambda$, we find a collection of dense subgraphs such that the sum of densities of the induced subgraphs plus the sum of Jaccard indices, weighted by $\lambda$, is maximized. We prove that this problem is NP-hard. To discover dense subgraphs with good objective value, we present an iterative algorithm which runs in $\mathcal{O}(n^2k^2 + m \log n + k^3 n)$ time per single iteration, and a greedy algorithm which runs in $\mathcal{O}(n^2k^2 + m \log n + k^3 n)$ time, where $k$ is the length of the graph sequence and $n$ and $m$ denote number of nodes and total number of edges respectively. We show experimentally that our algorithms are efficient, they can find ground truth in synthetic datasets and provide interpretable results from real-world datasets. Finally, we present a case study that shows the usefulness of our problem.
Learning graph embeddings is a crucial task in graph mining tasks. An effective graph embedding model can learn low-dimensional representations from graph-structured data for data publishing benefiting various downstream applications such as node classification, link prediction, etc. However, recent studies have revealed that graph embeddings are susceptible to attribute inference attacks, which allow attackers to infer private node attributes from the learned graph embeddings. To address these concerns, privacy-preserving graph embedding methods have emerged, aiming to simultaneously consider primary learning and privacy protection through adversarial learning. However, most existing methods assume that representation models have access to all sensitive attributes in advance during the training stage, which is not always the case due to diverse privacy preferences. Furthermore, the commonly used adversarial learning technique in privacy-preserving representation learning suffers from unstable training issues. In this paper, we propose a novel approach called Private Variational Graph AutoEncoders (PVGAE) with the aid of independent distribution penalty as a regularization term. Specifically, we split the original variational graph autoencoder (VGAE) to learn sensitive and non-sensitive latent representations using two sets of encoders. Additionally, we introduce a novel regularization to enforce the independence of the encoders. We prove the theoretical effectiveness of regularization from the perspective of mutual information. Experimental results on three real-world datasets demonstrate that PVGAE outperforms other baselines in private embedding learning regarding utility performance and privacy protection.
The decline in ecological connections signifies the potential extinction of species, which can be attributed to disruptions and alterations. The decrease in interconnections among species reflects their susceptibility to changes. For example, certain insects and plants that rely on exclusive interactions with a limited number of species, or even a specific species, face the risk of extinction if they lose these crucial connections. Currently, mining activities pose significant harm to natural ecosystems, resulting in various adverse environmental impacts. In this study, we utilized network science techniques to analyze the ecosystem in a graph-based structure, aiming to conserve the ecosystem affected by mining operations in the northern region of Scotland. The research encompasses identifying the most vital members of the network, establishing criteria for identifying communities within the network, comparing, and evaluating them, using models to predict secondary extinctions that occur when a species is removed from the network, and assessing the extent of network damage. Our study's novelty is utilizing network science approaches to investigate the biological data related to interactions between insects and plants.
Few-shot node classification, which aims to predict labels for nodes on graphs with only limited labeled nodes as references, is of great significance in real-world graph mining tasks. Particularly, in this paper, we refer to the task of classifying nodes in classes with a few labeled nodes as the few-shot node classification problem. To tackle such a label shortage issue, existing works generally leverage the meta-learning framework, which utilizes a number of episodes to extract transferable knowledge from classes with abundant labeled nodes and generalizes the knowledge to other classes with limited labeled nodes. In essence, the primary aim of few-shot node classification is to learn node embeddings that are generalizable across different classes. To accomplish this, the GNN encoder must be able to distinguish node embeddings between different classes, while also aligning embeddings for nodes in the same class. Thus, in this work, we propose to consider both the intra-class and inter-class generalizability of the model. We create a novel contrastive meta-learning framework on graphs, named COSMIC, with two key designs. First, we propose to enhance the intra-class generalizability by involving a contrastive two-step optimization in each episode to explicitly align node embeddings in the same classes. Second, we strengthen the inter-class generalizability by generating hard node classes via a novel similarity-sensitive mix-up strategy. Extensive experiments on few-shot node classification datasets verify the superiority of our framework over state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/COSMIC.
Given a graph, a $k$-plex is a set of vertices in which each vertex is not adjacent to at most $k-1$ other vertices in the set. The maximum $k$-plex problem, which asks for the largest $k$-plex from the given graph, is an important but computationally challenging problem in applications such as graph mining and community detection. So far, there are many practical algorithms, but without providing theoretical explanations on their efficiency. We define a novel parameter of the input instance, $g_k(G)$, the gap between the degeneracy bound and the size of the maximum $k$-plex in the given graph, and present an exact algorithm parameterized by this $g_k(G)$, which has a worst-case running time polynomial in the size of the input graph and exponential in $g_k(G)$. In real-world inputs, $g_k(G)$ is very small, usually bounded by $O(\log{(|V|)})$, indicating that the algorithm runs in polynomial time. We further extend our discussion to an even smaller parameter $cg_k(G)$, the gap between the community-degeneracy bound and the size of the maximum $k$-plex, and show that without much modification, our algorithm can also be parameterized by $cg_k(G)$. To verify the empirical performance of these algorithms, we carry out extensive experiments to show that these algorithms are competitive with the state-of-the-art algorithms. In particular, for large $k$ values such as $15$ and $20$, our algorithms dominate the existing algorithms. Finally, empirical analysis is performed to illustrate the effectiveness of the parameters and other key components in the implementation.
Model pre-training on large text corpora has been demonstrated effective for various downstream applications in the NLP domain. In the graph mining domain, a similar analogy can be drawn for pre-training graph models on large graphs in the hope of benefiting downstream graph applications, which has also been explored by several recent studies. However, no existing study has ever investigated the pre-training of text plus graph models on large heterogeneous graphs with abundant textual information (a.k.a. large graph corpora) and then fine-tuning the model on different related downstream applications with different graph schemas. To address this problem, we propose a framework of graph-aware language model pre-training (GALM) on a large graph corpus, which incorporates large language models and graph neural networks, and a variety of fine-tuning methods on downstream applications. We conduct extensive experiments on Amazon's real internal datasets and large public datasets. Comprehensive empirical results and in-depth analysis demonstrate the effectiveness of our proposed methods along with lessons learned.
Given the success of Graph Neural Networks (GNNs) for structure-aware machine learning, many studies have explored their use for text classification, but mostly in specific domains with limited data characteristics. Moreover, some strategies prior to GNNs relied on graph mining and classical machine learning, making it difficult to assess their effectiveness in modern settings. This work extensively investigates graph representation methods for text classification, identifying practical implications and open challenges. We compare different graph construction schemes using a variety of GNN architectures and setups across five datasets, encompassing short and long documents as well as unbalanced scenarios in diverse domains. Two Transformer-based large language models are also included to complement the study. The results show that i) although the effectiveness of graphs depends on the textual input features and domain, simple graph constructions perform better the longer the documents are, ii) graph representations are especially beneficial for longer documents, outperforming Transformer-based models, iii) graph methods are particularly efficient at solving the task.
Large language models~(LLM) like ChatGPT have become indispensable to artificial general intelligence~(AGI), demonstrating excellent performance in various natural language processing tasks. In the real world, graph data is ubiquitous and an essential part of AGI and prevails in domains like social network analysis, bioinformatics and recommender systems. The training corpus of large language models often includes some algorithmic components, which allows them to achieve certain effects on some graph data-related problems. However, there is still little research on their performance on a broader range of graph-structured data. In this study, we conduct an extensive investigation to assess the proficiency of LLMs in comprehending graph data, employing a diverse range of structural and semantic-related tasks. Our analysis encompasses 10 distinct tasks that evaluate the LLMs' capabilities in graph understanding. Through our study, we not only uncover the current limitations of language models in comprehending graph structures and performing associated reasoning tasks but also emphasize the necessity for further advancements and novel approaches to enhance their graph processing capabilities. Our findings contribute valuable insights towards bridging the gap between language models and graph understanding, paving the way for more effective graph mining and knowledge extraction.
There has been rapid growth in biomedical literature, yet capturing the heterogeneity of the bibliographic information of these articles remains relatively understudied. Although graph mining research via heterogeneous graph neural networks has taken center stage, it remains unclear whether these approaches capture the heterogeneity of the PubMed database, a vast digital repository containing over 33 million articles. We introduce PubMed Graph Benchmark (PGB), a new benchmark dataset for evaluating heterogeneous graph embeddings for biomedical literature. The benchmark contains rich metadata including abstract, authors, citations, MeSH terms, MeSH hierarchy, and some other information. The benchmark contains three different evaluation tasks encompassing systematic reviews, node classification, and node clustering. In PGB, we aggregate the metadata associated with the biomedical articles from PubMed into a unified source and make the benchmark publicly available for any future works.
Researchers of temporal networks (e.g., social networks and transaction networks) have been interested in mining dynamic patterns of nodes from their diverse interactions. Inspired by recently powerful graph mining methods like skip-gram models and Graph Neural Networks (GNNs), existing approaches focus on generating temporal node embeddings sequentially with nodes' sequential interactions. However, the sequential modeling of previous approaches cannot handle the transition structure between nodes' neighbors with limited memorization capacity. Detailedly, an effective method for the transition structures is required to both model nodes' personalized patterns adaptively and capture node dynamics accordingly. In this paper, we propose a method, namely Transition Propagation Graph Neural Networks (TIP-GNN), to tackle the challenges of encoding nodes' transition structures. The proposed TIP-GNN focuses on the bilevel graph structure in temporal networks: besides the explicit interaction graph, a node's sequential interactions can also be constructed as a transition graph. Based on the bilevel graph, TIP-GNN further encodes transition structures by multi-step transition propagation and distills information from neighborhoods by a bilevel graph convolution. Experimental results over various temporal networks reveal the efficiency of our TIP-GNN, with at most 7.2\% improvements of accuracy on temporal link prediction. Extensive ablation studies further verify the effectiveness and limitations of the transition propagation module. Our code is available at \url{https://github.com/doujiang-zheng/TIP-GNN}.
The explosive growth of cyber attacks nowadays, such as malware, spam, and intrusions, caused severe consequences on society. Securing cyberspace has become an utmost concern for organizations and governments. Traditional Machine Learning (ML) based methods are extensively used in detecting cyber threats, but they hardly model the correlations between real-world cyber entities. In recent years, with the proliferation of graph mining techniques, many researchers investigated these techniques for capturing correlations between cyber entities and achieving high performance. It is imperative to summarize existing graph-based cybersecurity solutions to provide a guide for future studies. Therefore, as a key contribution of this paper, we provide a comprehensive review of graph mining for cybersecurity, including an overview of cybersecurity tasks, the typical graph mining techniques, and the general process of applying them to cybersecurity, as well as various solutions for different cybersecurity tasks. For each task, we probe into relevant methods and highlight the graph types, graph approaches, and task levels in their modeling. Furthermore, we collect open datasets and toolkits for graph-based cybersecurity. Finally, we outlook the potential directions of this field for future research.
Along with the rapid evolution of mobile communication technologies, such as 5G, there has been a drastically increase in telecom fraud, which significantly dissipates individual fortune and social wealth. In recent years, graph mining techniques are gradually becoming a mainstream solution for detecting telecom fraud. However, the graph imbalance problem, caused by the Pareto principle, brings severe challenges to graph data mining. This is a new and challenging problem, but little previous work has been noticed. In this paper, we propose a Graph ATtention network with COst-sensitive BOosting (GAT-COBO) for the graph imbalance problem. First, we design a GAT-based base classifier to learn the embeddings of all nodes in the graph. Then, we feed the embeddings into a well-designed cost-sensitive learner for imbalanced learning. Next, we update the weights according to the misclassification cost to make the model focus more on the minority class. Finally, we sum the node embeddings obtained by multiple cost-sensitive learners to obtain a comprehensive node representation, which is used for the downstream anomaly detection task. Extensive experiments on two real-world telecom fraud detection datasets demonstrate that our proposed method is effective for the graph imbalance problem, outperforming the state-of-the-art GNNs and GNN-based fraud detectors. In addition, our model is also helpful for solving the widespread over-smoothing problem in GNNs. The GAT-COBO code and datasets are available at https://github.com/xxhu94/GAT-COBO.
Graph filters that transform prior node values to posterior scores via edge propagation often support graph mining tasks affecting humans, such as recommendation and ranking. Thus, it is important to make them fair in terms of satisfying statistical parity constraints between groups of nodes (e.g., distribute score mass between genders proportionally to their representation). To achieve this while minimally perturbing the original posteriors, we introduce a filter-aware universal approximation framework for posterior objectives. This defines appropriate graph neural networks trained at runtime to be similar to filters but also locally optimize a large class of objectives, including fairness-aware ones. Experiments on a collection of 8 filters and 5 graphs show that our approach performs equally well or better than alternatives in meeting parity constraints while preserving the AUC of score-based community member recommendation and creating minimal utility loss in prior diffusion.
We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of drawing large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common "hairball" look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.
As one of the most popular GNN architectures, the graph attention networks (GAT) is considered the most advanced learning architecture for graph representation and has been widely used in various graph mining tasks with impressive results. However, since GAT was proposed, none of the existing studies have provided systematic insight into the relationship between the performance of GAT and the number of layers, which is a critical issue in guiding model performance improvement. In this paper, we perform a systematic experimental evaluation and based on the experimental results, we find two important facts: (1) the main factor limiting the accuracy of the GAT model as the number of layers increases is the oversquashing phenomenon; (2) among the previous improvements applied to the GNN model, only the residual connection can significantly improve the GAT model performance. We combine these two important findings to provide a theoretical explanation that it is the residual connection that mitigates the loss of original feature information due to oversquashing and thus improves the deep GAT model performance. This provides empirical insights and guidelines for researchers to design the GAT variant model with appropriate depth and well performance. To demonstrate the effectiveness of our proposed guidelines, we propose a GAT variant model-ADGAT that adaptively selects the number of layers based on the sparsity of the graph, and experimentally demonstrate that the effectiveness of our model is significantly improved over the original GAT.
Graph contrastive learning has become a powerful technique for several graph mining tasks. It learns discriminative representation from different perspectives of augmented graphs. Ubiquitous in our daily life, singed-directed graphs are the most complex and tricky to analyze among various graph types. That is why singed-directed graph contrastive learning has not been studied much yet, while there are many contrastive studies for unsigned and undirected. Thus, this paper proposes a novel signed-directed graph contrastive learning, SDGCL. It makes two different structurally perturbed graph views and gets node representations via magnetic Laplacian perturbation. We use a node-level contrastive loss to maximize the mutual information between the two graph views. The model is jointly learned with contrastive and supervised objectives. The graph encoder of SDGCL does not depend on social theories or predefined assumptions. Therefore it does not require finding triads or selecting neighbors to aggregate. It leverages only the edge signs and directions via magnetic Laplacian. To the best of our knowledge, it is the first to introduce magnetic Laplacian perturbation and signed spectral graph contrastive learning. The superiority of the proposed model is demonstrated through exhaustive experiments on four real-world datasets. SDGCL shows better performance than other state-of-the-art on four evaluation metrics.
Given a large graph with few node labels, how can we (a) identify whether there is generalized network-effects (GNE) or not, (b) estimate GNE to explain the interrelations among node classes, and (c) exploit GNE efficiently to improve the performance on downstream tasks? The knowledge of GNE is valuable for various tasks like node classification, and targeted advertising. However, identifying GNE such as homophily, heterophily or their combination is challenging in real-world graphs due to limited availability of node labels and noisy edges. We propose NetEffect, a graph mining approach to address the above issues, enjoying the following properties: (i) Principled: a statistical test to determine the presence of GNE in a graph with few node labels; (ii) General and Explainable: a closed-form solution to estimate the specific type of GNE observed; and (iii) Accurate and Scalable: the integration of GNE for accurate and fast node classification. Applied on real-world graphs, NetEffect discovers the unexpected absence of GNE in numerous graphs, which were recognized to exhibit heterophily. Further, we show that incorporating GNE is effective on node classification. On a million-scale real-world graph, NetEffect achieves over 7 times speedup (14 minutes vs. 2 hours) compared to most competitors.
This paper proposes a graph-based approach to representing spatio-temporal trajectory data that allows an effective visualization and characterization of city-wide traffic dynamics. With the advance of sensor, mobile, and Internet of Things (IoT) technologies, vehicle and passenger trajectories are being increasingly collected on a massive scale and are becoming a critical source of insight into traffic pattern and traveller behaviour. To leverage such trajectory data to better understand traffic dynamics in a large-scale urban network, this study develops a trajectory-based network traffic analysis method that converts individual trajectory data into a sequence of graphs that evolve over time (known as dynamic graphs or time-evolving graphs) and analyses network-wide traffic patterns in terms of a compact and informative graph-representation of aggregated traffic flows. First, we partition the entire network into a set of cells based on the spatial distribution of data points in individual trajectories, where the cells represent spatial regions between which aggregated traffic flows can be measured. Next, dynamic flows of moving objects are represented as a time-evolving graph, where regions are graph vertices and flows between them are treated as weighted directed edges. Given a fixed set of vertices, edges can be inserted or removed at every time step depending on the presence of traffic flows between two regions at a given time window. Once a dynamic graph is built, we apply graph mining algorithms to detect change-points in time, which represent time points where the graph exhibits significant changes in its overall structure and, thus, correspond to change-points in city-wide mobility pattern throughout the day (e.g., global transition points between peak and off-peak periods).
The SARS-CoV-2 coronavirus is the cause of the COVID-19 disease in humans. Like many coronaviruses, it can adapt to different hosts and evolve into different lineages. It is well-known that the major SARS-CoV-2 lineages are characterized by mutations that happen predominantly in the spike protein. Understanding the spike protein structure and how it can be perturbed is vital for understanding and determining if a lineage is of concern. These are crucial to identifying and controlling current outbreaks and preventing future pandemics. Machine learning (ML) methods are a viable solution to this effort, given the volume of available sequencing data, much of which is unaligned or even unassembled. However, such ML methods require fixed-length numerical feature vectors in Euclidean space to be applicable. Similarly, euclidean space is not considered the best choice when working with the classification and clustering tasks for biological sequences. For this purpose, we design a method that converts the protein (spike) sequences into the sequence similarity network (SSN). We can then use SSN as an input for the classical algorithms from the graph mining domain for the typical tasks such as classification and clustering to understand the data. We show that the proposed alignment-free method is able to outperform the current SOTA method in terms of clustering results. Similarly, we are able to achieve higher classification accuracy using well-known Node2Vec-based embedding compared to other baseline embedding approaches.
Link prediction on dynamic graphs is an important task in graph mining. Existing approaches based on dynamic graph neural networks (DGNNs) typically require a significant amount of historical data (interactions over time), which is not always available in practice. The missing links over time, which is a common phenomenon in graph data, further aggravates the issue and thus creates extremely sparse and dynamic graphs. To address this problem, we propose a novel method based on the neural process, called Graph Sequential Neural ODE Process (GSNOP). Specifically, GSNOP combines the advantage of the neural process and neural ordinary differential equation that models the link prediction on dynamic graphs as a dynamic-changing stochastic process. By defining a distribution over functions, GSNOP introduces the uncertainty into the predictions, making it generalize to more situations instead of overfitting to the sparse data. GSNOP is also agnostic to model structures that can be integrated with any DGNN to consider the chronological and geometrical information for link prediction. Extensive experiments on three dynamic graph datasets show that GSNOP can significantly improve the performance of existing DGNNs and outperform other neural process variants.