Related papers: Directed extended-range percolation
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
We study the sensitivity of directed complex networks to the addition and pruning of edges and vertices and introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network…
We study the critical behavior of various geometrical and transport properties of percolation in 6 dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up…
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…
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicist's point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality…
Motivated by the importance of geometric information in real systems, a new model for long-range correlated percolation in link-adding networks is proposed with the connecting probability decaying with a power-law of the distance on the…
Many real-world infrastructures, from sensor and road networks to power grids, are spatially embedded and anisotropic, with constraints on the maximum number of links each node can establish. Such systems can be represented as anisotropic…
We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{reciprocal} connections whose probabilities depend on the age…
Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…
In a Monte Carlo study the conductivity of two-dimensional random stick systems is investigated from the percolation threshold up to ten times the percolation threshold density. We propose a model explicitly depending on the stick density…
Segment Routing is a recent network technology that helps optimizing network throughput by providing finer control over the routing paths. Instead of routing directly from a source to a target, packets are routed via intermediate waypoints.…
Message-passing theories have proved to be invaluable tools in studying percolation, non-recurrent epidemics and similar dynamical processes on real-world networks. At the heart of the message-passing method is the nonbacktracking matrix…
Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…
Connectedness percolation phenomena in two-dimensional packings of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption (RSA) off-lattice model with preferential…
Reciprocal arcs represent the lowest order cycle possible to find in directed graphs without self-loops. Representing also a measure of feed-back between vertices, it is interesting to understand how reciprocal arcs influence other…
Given a complex network, its \emph{L-}paths correspond to sequences of $L+1$ distinct nodes connected through $L$ distinct edges. The \emph{L-}conditional expansion of a complex network can be obtained by connecting all its pairs of nodes…
Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological…
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…