Related papers: Percolation on random networks with arbitrary k-co…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
The degree of a vertex in a hypergraph is defined as the number of edges incident to it. In this paper we study the $k$-core, defined as the maximal induced subhypergraph of minimum degree $k$, of the random $r$-uniform hypergraph…
We introduce random-kernel networks, a multilayer extension of random feature models where depth is created by deterministic kernel composition and randomness enters only in the outermost layer. We prove that deeper constructions can…
The concept of k-core in complex networks plays a key role in many applications, e.g., understanding the global structure, or identifying central/critical nodes, of a network. A malicious attacker with jamming ability can exploit the…
Modeling how networks change under structural perturbations can yield foundational insights into network robustness, which is critical in many real-world applications. The largest connected component is a popular measure of network…
We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components…
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…
As one of the most well-studied cohesive subgraph models, the $k$-core is widely used to find graph nodes that are ``central'' or ``important'' in many applications, such as biological networks, social networks, ecological networks, and…
The type of malicious attack inflicting on networks greatly influences their stability under ordinary percolation in which a node fails when it becomes disconnected from the giant component. Here we study its generalization, $k$-core…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
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…
Graph models have long been used in lieu of real data which can be expensive and hard to come by. A common class of models constructs a matrix of probabilities, and samples an adjacency matrix by flipping a weighted coin for each entry.…
We study the problem of finding the smallest set of nodes in a network whose removal results in an empty $k$-core; where the $k$-core is the sub-network obtained after the iterative removal of all nodes of degree smaller than $k$. This…
An independent set may not contain both a vertex and one of its neighbours. This basic fact makes the uniform distribution over independent sets rather special. We consider the hard-core model, an essential generalization of the uniform…
Decomposing a graph into a hierarchical structure via $k$-core analysis is a standard operation in any modern graph-mining toolkit. $k$-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address…
We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently generates a random network from a given expected degree sequence. The revision was to replace the approximated edge probability between a pair of nodes with a…
Decomposing hypergraphs is a key task in hypergraph analysis with broad applications in community detection, pattern discovery, and task scheduling. Existing approaches such as $k$-core and neighbor-$k$-core rely on vertex degree…