Related papers: Beyond directed hypergraphs: heterogeneous hypergr…
This paper studies observability for non-uniform hypergraphs with inputs and outputs. To capture higher-order interactions, we define a canonical non-homogeneous dynamical system with nonlinear outputs on hypergraphs. We then construct…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
We develop novel hierarchical reciprocal graphical models to infer gene networks from heterogeneous data. In the case of data that can be naturally divided into known groups, we propose to connect graphs by introducing a hierarchical prior…
In finite group theory, studying the prime graph of a group has been an important topic for almost the past half-century. Recently, prime graphs of solvable groups have been characterized in graph theoretical terms only. This now allows the…
The ongoing need for effective epidemic modeling has driven advancements in capturing the complex dynamics of infectious diseases. Traditional models, such as Susceptible-Infected-Recovered, and graph-based approaches often fail to account…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
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…
Hypergraphs provide a natural way to represent higher-order interactions among multiple entities. While undirected hypergraphs have been extensively studied, the case of directed hypergraphs, which can model oriented group interactions,…
Numerical reasoning over texts, such as addition, subtraction, sorting and counting, is a challenging machine reading comprehension task, since it requires both natural language understanding and arithmetic computation. To address this…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important since it reveals which hypergraph properties cannot be…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs.…
Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.