Related papers: Percolation in Interdependent and Interconnected N…
Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak…
In the analysis of the robustness of multiplex networks, it is commonly assumed that a node is functioning only if its interdependent nodes are simultaneously functioning. According to this model, a multiplex network becomes more and more…
It was recently recognized that interdependencies among different networks can play a crucial role in triggering cascading failures and hence system-wide disasters. A recent model shows how pairs of interdependent networks can exhibit an…
The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of…
Modular networks, such as critical infrastructures, are often built from distinct, densely connected modules (e.g., cities) that are sparsely interconnected. When such networks are gradually and randomly disrupted under a percolation…
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…
The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially…
From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers).…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
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…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
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…
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…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
In reality, many real-world networks interact with and depend on other networks. We develop an analytical framework for studying interacting networks and present an exact percolation law for a network of $n$ interdependent networks (NON).…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…