Related papers: Percolation in Interdependent and Interconnected N…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…
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…
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…
Recent work in the area of interdependent networks has focused on interactions between two systems of the same type. However, an important and ubiquitous class of systems are those involving monitoring and control, an example of…
Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the…
We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
We study the mutual percolation of two interdependent lattice networks ranging from two to seven dimensions, denoted as $D$. We impose that the length of interdependent links connecting nodes in the two lattices be less than or equal to a…
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
We consider connectivity properties of certain i.i.d. random environments on $\Z^d$, where at each location some steps may not be available. Site percolation and oriented percolation can be viewed as special cases of the models we consider.…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
Infrastructure systems, such as power, transportation, telecommunication, and water systems, are composed of multiple components which are interconnected and interdependent to produce and distribute essential goods and services. So, the…