Related papers: Connected components in networks with higher-order…

Molecular interactions have widely been modelled as networks. The local wiring patterns around molecules in molecular networks are linked with their biological functions. However, networks model only pairwise interactions between molecules…

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…

In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium…

We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric…

In this paper we discuss the connected components of underlying graphs of halving lines' configurations. We show how to create a configuration whose underlying graph is the union of two given underlying graphs. We also prove that every…

We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…

Many empirical systems contain complex interactions of arbitrary size, representing, for example, chemical reactions, social groups, co-authorship relationships, and ecological dependencies. These interactions are known as higher-order…

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…

Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables optimal knowledge discovery by visually rendering co-occurences…

An ordered graph is a graph enhanced with a linear order on the vertex set. An ordered graph is a core if it does not have an order-preserving homomorphism to a proper subgraph. We say that $H$ is the core of $G$ if (i) $H$ is a core, (ii)…

Traditional functional connectivity based on functional magnetic resonance imaging (fMRI) can only capture pairwise interactions between brain regions. Hypergraphs, which reveal high-order relationships among multiple brain regions, have…

Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for…

Graph neural network, as a powerful graph representation technique based on deep learning, has shown superior performance and attracted considerable research interest. However, it has not been fully considered in graph neural network for…

Temporal Graph Neural Networks (TGNNs) have gained growing attention for modeling and predicting structures in temporal graphs. However, existing TGNNs primarily focus on pairwise interactions while overlooking higher-order structures that…

Psychiatric disorders have been traditionally conceptualized as latent conditions producing observable symptoms, but recent studies suggest that psychopathology may emerge from symptoms interactions. Psychometric networking model these…

Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…

Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…