Graph incremental learning (GIL), which continuously updates graph models by sequential knowledge acquisition, has garnered significant interest recently. However, existing GIL approaches focus on task-incremental and class-incremental scenarios within a single domain. Graph domain-incremental learning (Domain-IL), aiming at updating models across multiple graph domains, has become critical with the development of graph foundation models (GFMs), but remains unexplored in the literature. In this paper, we propose Graph Domain-Incremental Learning via Knowledge Dientanglement and Preservation (GraphKeeper), to address catastrophic forgetting in Domain-IL scenario from the perspectives of embedding shifts and decision boundary deviations. Specifically, to prevent embedding shifts and confusion across incremental graph domains, we first propose the domain-specific parameter-efficient fine-tuning together with intra- and inter-domain disentanglement objectives. Consequently, to maintain a stable decision boundary, we introduce deviation-free knowledge preservation to continuously fit incremental domains. Additionally, for graphs with unobservable domains, we perform domain-aware distribution discrimination to obtain precise embeddings. Extensive experiments demonstrate the proposed GraphKeeper achieves state-of-the-art results with 6.5%~16.6% improvement over the runner-up with negligible forgetting. Moreover, we show GraphKeeper can be seamlessly integrated with various representative GFMs, highlighting its broad applicative potential.

The widespread application of graph data in various high-risk scenarios has increased attention to graph anomaly detection (GAD). Faced with real-world graphs that often carry node descriptions in the form of raw text sequences, termed text-attributed graphs (TAGs), existing graph anomaly detection pipelines typically involve shallow embedding techniques to encode such textual information into features, and then rely on complex self-supervised tasks within the graph domain to detect anomalies. However, this text encoding process is separated from the anomaly detection training objective in the graph domain, making it difficult to ensure that the extracted textual features focus on GAD-relevant information, seriously constraining the detection capability. How to seamlessly integrate raw text and graph topology to unleash the vast potential of cross-modal data in TAGs for anomaly detection poses a challenging issue. This paper presents a novel end-to-end paradigm for text-attributed graph anomaly detection, named CMUCL. We simultaneously model data from both text and graph structures, and jointly train text and graph encoders by leveraging cross-modal and uni-modal multi-scale consistency to uncover potential anomaly-related information. Accordingly, we design an anomaly score estimator based on inconsistency mining to derive node-specific anomaly scores. Considering the lack of benchmark datasets tailored for anomaly detection on TAGs, we release 8 datasets to facilitate future research. Extensive evaluations show that CMUCL significantly advances in text-attributed graph anomaly detection, delivering an 11.13% increase in average accuracy (AP) over the suboptimal.

The present paper considers a finite sequence of graphs, e.g., coming from technological, biological, and social networks, each of which is modelled as a realization of a graph-valued random variable, and proposes a methodology to identify possible changes in stationarity in its generating stochastic process. In order to cover a large class of applications, we consider a general family of attributed graphs, chatacterized by a possible variable topology (edges and vertices) also in the stationary case. A Change Point Method (CPM) approach is proposed, that (i) maps graphs into a vector domain; (ii) applies a suitable statistical test; (iii) detects the change --if any-- according to a confidence level and provides an estimate for its time of occurrence. Two specific CPMs are proposed: one detecting shifts in the distribution mean, the other addressing generic changes affecting the distribution. We ground our proposal with theoretical results showing how to relate the inference attained in the numerical vector space to the graph domain, and vice versa. Finally, simulations on epileptic-seizure detection problems are conducted on real-world data providing evidence for the CPMs effectiveness.

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs have been proposed, they only consider simple nonlinear activation functions in their layers, such as rectifiers or squashing functions. In this paper, we investigate the use of graph convolutional networks (GCNs) when combined with more complex activation functions, able to adapt from the training data. More specifically, we extend the recently proposed kernel activation function, a non-parametric model which can be implemented easily, can be regularized with standard $\ell_p$-norms techniques, and is smooth over its entire domain. Our experimental evaluation shows that the proposed architecture can significantly improve over its baseline, while similar improvements cannot be obtained by simply increasing the depth or size of the original GCN.

Graphs provide a powerful means for representing complex interactions between entities. Recently, new deep learning approaches have emerged for representing and modeling graph-structured data while the conventional deep learning methods, such as convolutional neural networks and recurrent neural networks, have mainly focused on the grid-structured inputs of image and audio. Leveraged by representation learning capabilities, deep learning-based techniques can detect structural characteristics of graphs, giving promising results for graph applications. In this paper, we attempt to advance deep learning for graph-structured data by incorporating another component: transfer learning. By transferring the intrinsic geometric information learned in the source domain, our approach can construct a model for a new but related task in the target domain without collecting new data and without training a new model from scratch. We thoroughly tested our approach with large-scale real-world text data and confirmed the effectiveness of the proposed transfer learning framework for deep learning on graphs. According to our experiments, transfer learning is most effective when the source and target domains bear a high level of structural similarity in their graph representations.

In this paper we present a novel geometric method for the problem of global pairwise alignment of protein-protein interaction (PPI) networks. A PPI network can be viewed as a node-edge graph and its alignment often needs to solve some generalized version of the subgraph isomorphism problem which is notoriously challenging and NP-hard. All existing research has focused on designing algorithms with good practical performance. In this paper we propose a two-step algorithm for the global pairwise PPI network alignment which consists of a Geometric Step and an MCMF Step. Our algorithm first applies a graph embedding technique that preserves the topological structure of the original PPI networks and maps the problem from graph domain to geometric domain, and computes a rigid transformation for one of the embedded PPI networks so as to minimize its Earth Mover's Distance (EMD) to the other PPI network. It then solves a Min-Cost Max-Flow problem using the (scaled) inverse of sequence similarity scores as edge weight. By using the flow values from the two steps (i.e., EMD and Min-Cost Max-Flow) as the matching scores, we are able to combine the two matching results to obtain the desired alignment. Unlike other popular alignment algorithms which are either greedy or incremental, our algorithm globally optimizes the problem to yield an alignment with better quality.