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Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
We study the giant component problem slightly above the critical regime for percolation on Poissonian random graphs in the scale-free regime, where the vertex weights and degrees have a diverging second moment. Critical percolation on…
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional…
We consider percolation on high-dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show that typically the largest component is of order logarithmic in the number of vertices.…
In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses $k \ge 1$ incident edges, whose weight is then increased by 1. The choice of this $k$-tuple occurs…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. We consider the the path-loss plus fading model of wireless signal…
In this article, we consider an anisotropic finite-range bond percolation model on $\mathbb{Z}^2$. On each horizontal layer $\{(x,i): x \in \mathbb{Z}\}$ we have edges $\langle(x, i),(y, i)\rangle$ for $1 \leq |x - y| \leq N$. There are…
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
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 a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced,…
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…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…