Related papers: Hierarchical models of rigidity percolation
Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
Drawing inspiration from real world interacting systems we study a system consisting of two networks that exhibit antagonistic and dependent interactions. By antagonistic and dependent interactions, we mean, that a proportion of functional…
We introduce a model of percolation induced by disorder, where an initially homogeneous network with links of equal weight is disordered by the introduction of heterogeneous weights for the links. We consider a pair of nodes i and j to be…
We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then,…
Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
We investigate the heterogeneity of outcomes of repeated instances of percolation experiments in complex networks using a message passing approach to evaluate heterogeneous, node dependent probabilities of belonging to the giant or…
Percolation theory investigates systems of interconnected units, their resilience to damage and their propensity to propagation. For random networks we can solve the percolation problems analytically using the generating function formalism.…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…
Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent…
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize…
Neural network methods are increasingly applied to solve phase transition problems, particularly in identifying critical points in non-equilibrium phase transitions, offering more convenience compared to traditional methods. In this paper,…
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand…
Despite the huge interest in network resilience to stress, most of the studies have concentrated on internal stress damaging network structure (e.g., node removals). Here we study how networks respond to environmental stress deteriorating…