Related papers: Percolation in real multiplex networks
Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a…
In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths…
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore,…
Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that community structure is ubiquitous among various social networks. Thus, studying…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
Suppose each site independently and randomly chooses some sites around it, and it is weakly (strongly) connected with them (if there choose each other). What is the probability that the weak (strong) connected cluster is infinite? We…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
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…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
Network reconstruction is fundamental to understanding the dynamical behaviors of the networked systems. Many systems, modeled by multiplex networks with various types of interactions, display an entirely different dynamical behavior…
In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…
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…
Many works have studied the Internet topology, but few have investigated the question of how it evolves over time. This paper focuses on the Internet routing IP-level topology and proposes a first step towards realistic modeling of its…
K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using…