Related papers: Percolation in heterogeneous spatial networks with…
Almost all network research has been focused on the properties of a single network that does not interact and depends on other networks. In reality, many real-world networks interact with other networks. Here we develop an analytical…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
We study the critical behavior for percolation on inhomogeneous random networks on $n$ vertices, where the weights of the vertices follow a power-law distribution with exponent $\tau \in (2,3)$. Such networks, often referred to as…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice $\mathbb{Z}^d$, $d\ge1$, because it fulfills several stylized facts observed in large…
Distributions of the size of the largest component, in particular the large-deviation tail, are studied numerically for two graph ensembles, for Erdoes-Renyi random graphs with finite connectivity and for two-dimensional bond percolation.…
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…
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,…
Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…
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…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…
We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for…
The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale…
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
The margins within the geographic range of species are often specific in terms of ecological and evolutionary processes, and can strongly influence the species' reaction to climate change. One of the frequently observed features at range…
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…