Related papers: k-core (bootstrap) percolation on complex networks…
The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model…
Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices and are interesting in their own right with ordinary percolation exhibiting not one, but two, phase transitions. We study four constraint percolation…
Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least $r$ active neighbors. Such process, originally studied on regular structures, has been recently investigated also in…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
An analytical approach to calculating bond percolation thresholds, sizes of $k$-cores, and sizes of giant connected components on structured random networks with non-zero clustering is presented. The networks are generated using a…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…
Bootstrap percolation is an often used model to study the spread of diseases, rumors, and information on sparse random graphs. The percolation process demonstrates a critical value such that the graph is either almost completely affected or…
In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system.…
We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the sudden emergence of the 3- and 4-cores…
We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
The organisation of a network in a maximal set of nodes having at least $k$ neighbours within the set, known as $k$-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $k$-shells…
The use of machine learning techniques in classical and quantum systems has led to novel techniques to classify ordered and disordered phases, as well as uncover transition points in critical phenomena. Efforts to extend these methods to…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…