Related papers: Weak Multiplex Percolation
The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent…
We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
Complex systems are characterized by multiple spatial and temporal scales. A natural framework to capture their multiscale nature is that of multilayer networks, where different layers represent distinct physical processes that often…
The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast…
We study entanglement distribution in quantum complex networks where nodes are connected by bipartite entangled states. These networks are characterized by a complex structure, which dramatically affects how information is transmitted…
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
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…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
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…
Distinct channels of interaction in a complex networked system define network layers, which co-exist and co-operate for the system's function. Towards realistic modeling and understanding such multiplex systems, we introduce and study a…
Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex…
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…
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…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Many real-world complex systems across natural, social, and economical domains consist of manifold layers to form multiplex networks. The multiple network layers give rise to nonlinear effect for the emergent dynamics of systems.…
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
Identifying the most influential spreaders is important to understand and control the spreading process in a network. As many real-world complex systems can be modeled as multilayer networks, the question of identifying important nodes in…