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Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
Inspired by the study of loose cycles in hypergraphs, we define the \emph{loose core} in hypergraphs as a structure which mirrors the close relationship between cycles and $2$-cores in graphs. We prove that in the $r$-uniform binomial…
We study curvature-driven edge reweighting for community recovery in the balanced two-block stochastic block model. Given a graph G with initial weights equal to the adjacency matrix, we iteratively update edge weights using Lin-Lu-Yau…
Background: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way…
The widespread relevance of increasingly complex networks requires methods to extract meaningful coarse-grained representations of such systems. For undirected graphs, standard community detection methods use criteria largely based on…
Timestamped relational datasets consisting of records between pairs of entities are ubiquitous in data and network science. For applications like peer-to-peer communication, email, social network interactions, and computer network security,…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
Localizing the source of graph diffusion phenomena, such as misinformation propagation, is an important yet extremely challenging task. Existing source localization models typically are heavily dependent on the hand-crafted rules.…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…
Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…
We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…
We present the first comprehensive analysis of temporal settings for directed temporal graphs, fully resolving their hierarchy with respect to support, reachability, and induced-reachability equivalence. These notions, introduced by…
With growing emphasis on privacy regulations, machine unlearning has become increasingly critical in real-world applications such as social networks and recommender systems, many of which are naturally represented as graphs. However,…
Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models…
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…