Kijung Shin

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs. This has led to a proliferation of specialized hypergraph centrality measures, but the field remains fragmented and lacks a unifying framework. This article addresses this gap by providing the first systematic survey of 39 distinct measures. We introduce a novel taxonomy classifying them as (1) structural (topology-based), (2) functional (impact on system dynamics), or (3) contextual (incorporating external features). We also present an experimental assessment comparing their empirical similarity and computation time. Finally, we discuss applications, establishing a coherent roadmap for future research in this area.

In many real-world scenarios, interactions happen in a group-wise manner with multiple entities, and therefore, hypergraphs are a suitable tool to accurately represent such interactions. Hyperedges in real-world hypergraphs are not composed of randomly selected nodes but are instead formed through structured processes. Consequently, various hypergraph generative models have been proposed to explore fundamental mechanisms underlying hyperedge formation. However, most existing hypergraph generative models do not account for node attributes, which can play a significant role in hyperedge formation. As a result, these models fail to reflect the interactions between structure and node attributes. To address the issue above, we propose NoAH , a stochastic hypergraph generative model for attributed hypergraphs. NoAH utilizes the core–fringe node hierarchy to model hyperedge formation as a series of node attachments and determines attachment probabilities based on node attributes. We further introduce NoAHFit , a parameter learning procedure that fits NoAH to a given real-world hypergraph so that generated hypergraphs reproduce structural and attribute-related patterns. Through experiments on nine datasets across four different domains, we show that NoAH with NoAHFit achieves the best overall average rank among the nine evaluated hypergraph generative models when evaluated across six structure–attribute interplay metrics. Moreover, we discuss variants of NoAH for different types of node attributes, including binary, categorical, and continuous attributes. For cases without pre-existing node attributes, we extend NoAH and NoAHFit to jointly learn latent node attributes together with the parameters of NoAH and use the learned attributes for generation.

AI agents are rapidly evolving from isolated personal assistants into networked actors that interact with one another at scale. We envision the emergence of AI agent societies, with their own social and economic dynamics, as a new research frontier. We argue that AI agent societies should be studied as a distinct object of inquiry: neither simply larger collections of individual agents nor merely simulations of human society. To formalize this perspective, we propose four core properties that a valid AI agent society should satisfy: individualized objectives, rules and governance, autonomy, and scale and complexity. Building on this framework, we identify four classes of societal behaviors worth studying in AI agent societies: economic behaviors, behaviors under conflict-of-interest, unsafe and unethical behaviors, and system-level behaviors. We then outline key technical challenges—including property parameterization, parameter balancing, and robust implementation—and argue that progress on these challenges could enable scientifically informative and practically useful models of AI agent societies. Finally, we revisit existing multi-agent systems through the lens of the proposed core properties, show that they instantiate only subsets of them, and discuss implications for platform design, evaluation, and governance.