Related papers: The nature of hypergraph $k$-core percolation prob…
The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…
The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network…
Hypergraph is a data structure that enables us to model higher-order associations among data entities. Conventional graph-structured data can represent pairwise relationships only, whereas hypergraph enables us to associate any number of…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
Learning from structured data is a core machine learning task. Commonly, such data is represented as graphs, which normally only consider (typed) binary relationships between pairs of nodes. This is a substantial limitation for many domains…
The RNA inverse folding problem, a key challenge in RNA design, involves identifying nucleotide sequences that can fold into desired secondary structures, which are critical for ensuring molecular stability and function. The inherent…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…
We address the problem of defining connected components in hypergraphs, which are models for systems with higher-order interactions. For graphs with dyadic interactions, connected components are defined in terms of paths connecting nodes…
Let V denote a set of N vertices. To construct a "hypergraph process", create a new hyperedge at each event time of a Poisson process; the cardinality K of this hyperedge is random, with arbitrary probability generating function r(x),…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
Learning expressive representations for high-dimensional yet sparse features has been a longstanding problem in information retrieval. Though recent deep learning methods can partially solve the problem, they often fail to handle the…
Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is…
Eigenvector centrality is a standard network analysis tool for determining the importance of (or ranking of) entities in a connected system that is represented by a graph. However, many complex systems and datasets have natural multi-way…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
An edge labeling of a graph distinguishes neighbors by sets (multisets, resp.), if for any two adjacent vertices $u$ and $v$ the sets (multisets, resp.) of labels appearing on edges incident to $u$ and $v$ are different. In an analogous way…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is…
We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by…
Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…