Group interactions occur in various real-world contexts, e.g., co-authorship, email communication, and online Q&A. In each group, there is often a particularly significant member, around whom the group is formed. Examples include the first or last author of a paper, the sender of an email, and the questioner in a Q&A session. In this work, we discuss the existence of such individuals in real-world group interactions. We call such individuals group anchors and study the problem of identifying them. First, we introduce the concept of group anchors and the identification problem. Then, we discuss our observations on group anchors in real-world group interactions. Based on our observations, we develop Anchorradar, a fast and effective method for group anchor identification under realistic settings with label scarcity, i.e., when only a few groups have known anchors. Anchorradar is a semi-supervised method using information from groups both with and without known group anchors. Finally, through extensive experiments on thirteen real-world datasets, we demonstrate the empirical superiority of Anchorradar over various baselines w.r.t. accuracy and efficiency. In most cases, Anchorradar achieves higher accuracy in group anchor identification than all the baselines, while using 10.2x less training time than the fastest baseline and 43.6 x fewer learnable parameters than the most lightweight baseline on average.

Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., powerlaw degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain tractable to compute and control graph statistics. A common class of RGMs (e.g., Erdős-Rényi and stochastic Kronecker) outputs edge probabilities, so we need to realize (i.e., sample from) the output edge probabilities to generate graphs. Typically, the existence of each edge is assumed to be determined independently, for simplicity and tractability. However, with edge independency, RGMs provably cannot produce high subgraph densities and high output variability simultaneously. In this work, we explore RGMs beyond edge independence that can better reproduce common patterns while maintaining high tractability and variability. Theoretically, we propose an edge-dependent realization (i.e., sampling) framework called binding that provably preserves output variability, and derive closed-form tractability results on subgraph (e.g., triangle) densities. Practically, we propose algorithms for graph generation with binding and parameter fitting of binding. Our empirical results demonstrate that RGMs with binding exhibit high tractability and well reproduce common patterns, significantly improving upon edge-independent RGMs.

Higher-order interactions (HOIs) in complex systems, such as scientific collaborations, multi-protein complexes, and multi-user communications, are commonly modeled as hypergraphs, where each hyperedge (i.e., a subset of nodes) represents an HOI among the nodes. Given a hypergraph, hyperedge prediction aims to identify hyperedges that are either missing or likely to form in the future, and it has broad applications, including recommending interest-based social groups, predicting collaborations, and uncovering functional complexes in biological systems. However, the vast search space of hyperedge candidates (i.e., all possible subsets of nodes) poses a significant computational challenge, making naïve exhaustive search infeasible. As a result, existing approaches rely on either heuristic sampling to obtain constrained candidate sets or ungrounded assumptions on hypergraph structure to select promising hyperedges. In this work, we propose HyperSearch, a search-based algorithm for hyperedge prediction that efficiently evaluates unconstrained candidate sets, by incorporating two key components: (1) an empirically grounded scoring function derived from observations in real-world hypergraphs and (2) an efficient search mechanism, where we derive and use an anti-monotonic upper bound of the original scoring function (which is not anti-monotonic) to prune the search space. This pruning comes with theoretical guarantees, ensuring that discarded candidates are never better than the kept ones w.r.t. the original scoring function. In extensive experiments on 10 real-world hypergraphs across five domains, HyperSearch consistently outperforms state-of-the-art baselines, achieving higher accuracy in predicting new (i.e., not in the training set) hyperedges.

Combinatorial optimization (CO) is fundamental to several realworld applications, from logistics and scheduling to hardware design and resource allocation.Deep reinforcement learning (RL) has recently shown significant benefits in solving CO problems, reducing reliance on domain expertise and improving computational efficiency.However, the absence of a unified benchmarking framework leads to inconsistent evaluations, limits reproducibility, and increases engineering overhead, raising barriers to adoption for new researchers.To address these challenges, we introduce RL4CO, a unified and extensive benchmark with in-depth library coverage of 27 CO problem environments and 23 state-of-the-art baselines.Built on efficient software libraries and best practices in implementation, RL4CO features modularized implementation and flexible configurations of diverse environments, policy architectures, RL algorithms, and utilities with extensive documentation.RL4CO helps researchers build on existing successes while exploring and developing their own designs, facilitating the entire research process by decoupling science from heavy engineering.We finally provide extensive benchmark studies to inspire new insights and future work.RL4CO has already attracted numerous researchers in the community and is open-sourced at https://github.com/ai4co/rl4co 1 .

Adversarial attacks are allegedly unnoticeable. Prior studies have designed attack noticeability measures on graphs, primarily using statistical tests to compare the topology of original and (possibly) attacked graphs. However, we observe two critical limitations in the existing measures. First, because the measures rely on simple rules, attackers can readily enhance their attacks to bypass them, reducing their attack ''noticeability'' and, yet, maintaining their attack performance. Second, because the measures naively leverage global statistics, such as degree distributions, they may entirely overlook attacks until severe perturbations occur, letting the attacks be almost ''totally unnoticeable.''

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.

How can we find meaningful clusters in a graph robustly against noise edges? Graph clustering (i.e., dividing nodes into groups of similar ones) is a fundamental problem in graph analysis with applications in various fields. Recent studies have demonstrated that graph neural network (GNN) based approaches yield promising results for graph clustering. However, we observe that their performance degenerates significantly on graphs with noise edges, which are prevalent in practice. In this work, we propose MetaGC for robust GNN-based graph clustering. MetaGC employs a decomposable clustering loss function, which can be rephrased as a sum of losses over node pairs. We add a learnable weight to each node pair, and MetaGC adaptively adjusts the weights of node pairs using meta-weighting so that the weights of meaningful node pairs increase and the weights of less-meaningful ones (e.g., noise edges) decrease. We show empirically that MetaGC learns weights as intended and consequently outperforms the state-of-the-art GNN-based competitors, even when they are equipped with separate denoising schemes, on five real-world graphs under varying levels of noise. Our code and datasets are available at https://github.com/HyeonsooJo/MetaGC.

Graphs are a powerful mathematical model, and they are used to represent real-world structures in various fields. In many applications, real-world structures with high connectivity and robustness are preferable. For enhancing the connectivity and robustness of graphs, two operations, adding edges and anchoring nodes, have been extensively studied. However, merging nodes, which is a realistic operation in many scenarios (e.g., bus station reorganization, multiple team formation), has been overlooked. In this work, we study the problem of improving graph cohesiveness by merging nodes. First, we formulate the problem mathematically using the size of the k-truss, for a given k, as the objective. Then, we prove the NP-hardness and non-modularity of the problem. After that, we develop BATMAN, a fast and effective algorithm for choosing sets of nodes to be merged, based on our theoretical findings and empirical observations. Lastly, we demonstrate the superiority of BATMAN over several baselines, in terms of speed and effectiveness, through extensive experiments on fourteen real-world graphs.

Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the connections between node pairs sharing a neighbor, and it has extensive applications in various domains. Hypergraphs, an extension of graphs, are designed to represent group relations. However, to the best of our knowledge, there has been no examination regarding the transitivity of real-world group interactions. In this work, we investigate the transitivity of group interactions in real-world hypergraphs. We first suggest intuitive axioms as necessary characteristics of hypergraph transitivity measures. Then, we propose a principled hypergraph transitivity measure HyperTrans, which satisfies all the proposed axioms, with a fast computation algorithm Fast-HyperTrans. After that, we analyze the transitivity patterns in real-world hypergraphs distinguished from those in random hypergraphs. Lastly, we propose a scalable hypergraph generator THera. It reproduces the observed transitivity patterns by leveraging community structures, which are pervasive in real-world hypergraphs. Our code and datasets are available at https://github.com/kswoo97/hypertrans.

Simplicial complexes are higher-order combinatorial structures which have been used to represent real-world complex systems. In this paper, we concentrate on the local patterns in simplicial complexes called simplets, a generalization of graphlets. We formulate 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 the 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. Finally, 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.