Related papers: Critical phenomena in heterogeneous k-core percola…
Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research,…
Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…
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…
Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms are often…
Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a…
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…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
The models of $k$-core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, several newly discovered…
We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical $(u,v)$ flower network. Using the renormalization-group like procedure, we derive the recursion relations for the percolating…
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…
We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical…
The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…
In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, $k$-core percolation, bootstrap percolation, the…
To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
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…
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…