Related papers: Higher-Order Components Dictate Higher-Order Conta…
The co-evolution of structure and dynamics, known as adaptivity, is a fundamental property in various systems and drives diverse emergent behaviors. However, the adaptivity in previous works is primarily stemmed from pairwise situations,…
Complex contagions describe diffusion of behaviors in a social network in settings where spreading requires the influence by two or more neighbors. In a $k$-complex contagion, a cluster of nodes are initially infected, and additional nodes…
The emergence of collective behaviors in networks of dynamical units in pairwise interaction has been explained as the effect of diffusive coupling. How does the presence of higher-order interaction impact the onset of spontaneous or…
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…
A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such…
Evolutionary game theory has provided substantial contributions to explain the emergence of cooperation under unfavourable conditions in ecology, economics, and the social sciences. Recently, inspired by newly available empirical evidence…
Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as…
Higher-order interactions can dramatically reshape collective dynamics, yet how their microscopic organization controls macroscopic critical behavior remains unclear. Here we develop a new theory to study contagion dynamics on hypergraphs…
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…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size $t$ to belong to the hypergraph depends of a…
The microscopic organization of dynamical systems coupled via higher-order interactions plays a pivotal role in understanding their collective behavior. In this paper, we introduce a framework for systematically investigating the impact of…
We present exact solutions for the size of the giant connected component (GCC) of graphs composed of higher-order homogeneous cycles, including weak cycles and cliques, following bond percolation. We use our theoretical result to find the…
Complex systems, represented as dynamic networks, comprise of components that influence each other via direct and/or indirect interactions. Recent research has shown the importance of using Higher-Order Networks (HONs) for modeling and…
Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…
We consider connected components in $k$-uniform hypergraphs for the following notion of connectedness: given integers $k\ge 2$ and $1\le j \le k-1$, two $j$-sets (of vertices) lie in the same $j$-component if there is a sequence of edges…
In this paper, we study the high-order phase transition in random $r$-uniform hypergraphs. For a positive integer $n$ and a real $p\in [0,1]$, let $H:=H^r(n,p)$ be the random $r$-uniform hypergraph with vertex set $[n]$, where each $r$-set…
Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more…
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…