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Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, $k$-core percolation, bootstrap percolation, the…
We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits,…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…
We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior…
In this paper we introduce a variant of the honeycomb lattice in which we create defects by randomly exchanging adjacent bonds, producing a random tiling with a distribution of polygon edges. We study the percolation properties on these…
In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of $M$ networks (one per layer) where each is a subgraph of a foundational network $G$. Each layer network is the…
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…
We propose a method to make a highly clustered complex network within the configuration model. Using this method, we generated highly clustered random regular networks and analyzed the properties of them. We show that highly clustered…
We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network…
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…
We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether…
The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks…
Recent renormalization group results predict non self averaging behaviour at criticality for relevant disorder. However, we find strong self averaging(SA) behaviour in the critical region of a quenched Ising model on an ensemble of…
High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…