Related papers: What are higher-order networks?

Spatial dependency and spatial embedding are basic physical properties of many phenomena modeled by networks. The most indicated computational environment to deal with spatial information is to use Georeferenced Information System (GIS) and…

The acknowledged model for networks of collaborations is the hypergraph model. Nonetheless when it comes to be visualized hypergraphs are transformed into simple graphs. Very often, the transformation is made by clique expansion of the…

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only…

The analysis of the dynamics on complex networks is closely connected to structural features of the networks. Features like, for instance, graph-cores and node degrees have been studied ubiquitously. Here we introduce the D-spectrum of a…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

The structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit…

Consider two horizontal lines in the plane. A pair of a point on the top line and an interval on the bottom line defines a triangle between two lines. The intersection graph of such triangles is called a simple-triangle graph. This paper…

In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…

Graph are a ubiquitous data representation, as they represent a flexible and compact representation. For instance, the 3D structure of RNA can be efficiently represented as $\textit{2.5D graphs}$, graphs whose nodes are nucleotides and…

Graph Neural Networks (GNNs) are the first choice for learning algorithms on graph data. GNNs promise to integrate (i) node features as well as (ii) edge information in an end-to-end learning algorithm. How does this promise work out…

This article presents a survey of work on lifted graphical models. We review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We…

Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…

Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…

Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…

Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…

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…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level,…