Related papers: Connected components in networks with higher-order…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real…
Gy\'arf\'as famously showed that in every $r$-coloring of the edges of the complete graph $K_n$, there is a monochromatic connected component with at least $\frac{n}{r-1}$ vertices. A recent line of study by Conlon, Tyomkyn, and the second…
Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet,…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…
The conventional definition of hypergraph has two major issues: (1) there is not a standard definition of directed hypergraph and (2) there is not a formal definition of nested hypergraph. To resolve these issues, we propose a new…
Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for in networks with pairwise interactions, its effects in systems with higher-order…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and…
Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how the collective behavior of a system is influenced by the microscopic organization of its…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
A hypergraph is a generalization of an ordinary graph, and it naturally represents group interactions as hyperedges (i.e., arbitrary-sized subsets of nodes). Such group interactions are ubiquitous in many domains: the sender and receivers…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…
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…