Related papers: k-Core percolation on multiplex networks
The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model…
We consider the $k$-core decomposition of network models and Internet graphs at the autonomous system (AS) level. The $k$-core analysis allows to characterize networks beyond the degree distribution and uncover structural properties and…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understand the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with…
Many real complex systems cannot be represented by a single network, but due to multiple sub-systems and types of interactions, must be represented as a multiplex network. This is a set of nodes which exist in several layers, with each…
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical Erd\H{o}s-R\'enyi…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
In many complex systems, the interactions between objects span multiple aspects. Multiplex networks are accurate paradigms to model such systems, where each edge is associated with a type. A key graph mining primitive is extracting dense…
$k$-Core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of $k$-core percolation of random networks additionally exhibits critical behavior. Thus…
K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been…
K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For…
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 the edge deletion process of random graphs near a k-core percolation point. We find that the time-dependent number of edges in the process exhibits critically divergent fluctuations. We first show theoretically that the k-core…
The $k$-core of a graph is its largest subgraph with minimum degree at least $k$, a fundamental concept for uncovering hierarchical structures. In this paper, we establish a connection between the $k$-core and the high-order spectra of…
Neural networks are the pinnacle of Artificial Intelligence, as in recent years we witnessed many novel architectures, learning and optimization techniques for deep learning. Capitalizing on the fact that neural networks inherently…
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…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Core-periphery structure, the arrangement of a network into a dense core and sparse periphery, is a versatile descriptor of various social, biological, and technological networks. In practice, different core-periphery algorithms are often…
Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…