A directed hypergraph, which consists of nodes and hyperarcs, is a higher-order data structure that naturally models directional group interactions (e.g., chemical reactions of molecules). Although there have been extensive studies on local structures of (directed) graphs in the real world, those of directed hypergraphs remain unexplored. In this work, we focus on measurements, findings, and applications related to local structures of directed hypergraphs, and they together contribute to a systematic understanding of various real-world systems interconnected by directed group interactions. Our first contribution is to define 91directed hypergraphlets(DHGs), which disjointly categorize directed connections and overlaps among four node sets that compose two incident hyperarcs. Our second contribution is to develop exact and approximate algorithms for counting the occurrences of each DHGs. Our last contribution is to characterize 11 real-world directed hypergraphs and individual hyperarcs in them using the occurrences of DHGs, which reveals clear domain-based local structural patterns. Our experiments demonstrate that our DHG-based characterization gives up to$12\%$and$33\%$better performances on hypergraph clustering and hyperarc prediction, respectively, than baseline characterization methods. Moreover, we show that CODA-A, which is our proposed approximate algorithm, is up to$36\times$faster than its competitors with similar characterization quality.

The problem of predicting node properties (e.g., node classes) in graphs has received significant attention due to its broad range of applications. Graphs from real-world datasets often evolve over time, with newly emerging edges and dynamically changing node properties, posing a significant challenge for this problem. In response, temporal graph neural networks (TGNNs) have been developed to predict dynamic node properties from a stream of emerging edges. However, our analysis reveals that most TGNN-based methods are (a) far less effective without proper node features and, due to their complex model architectures, (b) vulnerable to distribution shifts. In this paper, we propose SPLASH, a simple yet powerful method for predicting node properties on edge streams under distribution shifts. Our key contributions are as follows: (1) we propose feature augmentation methods and an automatic feature selection method for edge streams, which improve the effectiveness of TGNNs, (2) we propose a lightweight MLP-based TGNN architecture that is highly efficient and robust under distribution shifts, and (3) we conduct extensive experiments to evaluate the accuracy, efficiency, generalization, and qualitative performance of the proposed method and its competitors on dynamic node classification, dynamic anomaly detection, and node affinity prediction tasks across seven real-world datasets.

Continual Learning (CL) is the process of learning ceaselessly a sequence of tasks. Most existing CL methods deal with independent data (e.g., images and text) for which many benchmark frameworks and results under standard experimental settings are available. Compared to them, however, CL methods for graph data (graph CL) are relatively underexplored because of (a) the lack of standard experimental settings, especially regarding how to deal with the dependency between instances, (b) the lack of benchmark datasets and scenarios, and (c) high complexity in implementation and evaluation due to the dependency. In this paper, regarding (a) we define four standard incremental settings (task-, class-, domain-, and time-incremental) for node-, link-, and graph-level problems, extending the previously explored scope. Regarding (b), we provide 35 benchmark scenarios based on 24 real-world graphs. Regarding (c), we develop BeGin , an easy and fool-proof framework for graph CL. BeGin is easily extended since it is modularized with reusable modules for data processing, algorithm design, and evaluation. Especially, the evaluation module is completely separated from user code to eliminate potential mistakes. Regarding benchmark results, we cover \(3\times\) more combinations of incremental settings and levels of problems than the latest benchmark. All assets for the benchmark framework are publicly available at https://github.com/ShinhwanKang/BeGin .

Abstract Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we focus on the local patterns in simplicial complexes called simplets, a generalization of graphlets. We study the problem of counting simplets of a given size in a given simplicial complex. For this problem, we extend a sampling algorithm based on color coding, from graphs to simplicial complexes, with essential technical novelty. We theoretically analyze our proposed algorithm named SC3, showing its correctness, unbiasedness, convergence, and time/space complexity. Through extensive experiments on sixteen real-world datasets, we show the superiority of SC3 in terms of accuracy, speed, and scalability, compared to the baseline methods. We use the counts given by SC3 for simplicial complex analysis, especially for characterization, which is further used for simplicial complex clustering, where SC3 shows a strong ability of characterization with domain-based similarity. Additionally, we explore a variant of simplet counting (specifically, estimating the relative counts of simplets) under realistic scenarios where the entire simplicial complex is not provided at once but can only be partially accessed, for instance, through a limited number of API calls. For such scenarios, we propose a random-walk-based sampling algorithm, SCRW, and analyze its theoretical properties. In our experiments, SCRW requires, on average, $$16.5\times $$ 16.5 × less memory than SC3, while the speed-accuracy trade-offs provided by the two methods are comparable.