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The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
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…
Power generation and distribution remains an important topic of discussion since the industrial revolution. As the system continues to grow, it needs to evolve both in infrastructure, robustness and its resilience to deal with failures. One…
In a complex system, perturbations propagate by following paths on the network of interactions among the system's units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very…
Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
Many geophysical processes can be modelled by using interconnected networks. The small-world network model has recently attracted much attention in physics and applied sciences. In this paper, we try to use and modify the small-world theory…
The robustness of complex networks with dependencies has been studied in recent years. However, previous studies focused on the robustness of networks composed of dependency links without network topology. In this study, we will analyze the…
Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network,…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…
We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…
The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the…
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 this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd\H{o}s-R\'{e}nyi networks, scale-free networks, and…
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…
We model the robustness against random failure or intentional attack of networks with arbitrary large-scale structure. We construct a block-based model which incorporates --- in a general fashion --- both connectivity and interdependence…
A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how…
The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a…