Related papers: Higher-order percolation processes on multiplex hy…
Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting…
Motivated by the bootstrap percolation process for graphs, we define a new, high-order generalisation to $k$-uniform hypergraphs, in which we infect $j$-sets of vertices for some integer $1\le j \le k-1$. We investigate the smallest…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
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…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
Background: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way…
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…
Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems raging from the brain to high-order social networks.…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a…
The largest eigenvalue of the matrix describing a network's contact structure is often important in predicting the behavior of dynamical processes. We extend this notion to hypergraphs and motivate the importance of an analogous eigenvalue,…
Hypergraphs effectively model higher-order relationships in natural phenomena, capturing complex interactions beyond pairwise connections. We introduce a novel hypergraph message passing framework inspired by interacting particle systems,…