Related papers: An Analytical Solution to the $k$-core Pruning Pro…
We introduce a $k$-leaf removal algorithm as a generalization of the so-called leaf removal algorithm. In this pruning algorithm, vertices of degree smaller than $k$, together with their first nearest neighbors and all incident edges are…
Multi-layer networks or multiplex networks are generally considered as the networks that have the same set of vertices but different types of edges. Multi-layer networks are especially useful when describing the systems with several kinds…
The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…
We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and…
We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by…
Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…
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…
We induce the NonBacktracking Expansion Branch method to analyze the k-core pruning process on the monopartite graph G which does not contain any self-loop or multi-edge. Different from the traditional approaches like the generating…
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…
The $k$-core decomposition in a graph is a fundamental problem for social network analysis. The problem of $k$-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on $k$-core…
Core decomposition is a fundamental operator in network analysis. In this paper, we study the problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed $(k, h)$-core, is a maximal…
Given an undirected graph, the $k$-core is a subgraph in which each node has at least $k$ connections. This is widely used in graph analytics to identify core subgraphs within a larger graph. The sequential $k$-core decomposition algorithm…
The resilience of a complex interconnected system concerns the size of the macroscopic functioning node clusters after external perturbations based on a random or designed scheme. For a representation of the interconnected systems with…
Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking…
The $k$-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least $k$ other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of $k$-core, which we…
The $k$-core decomposition is a fundamental primitive in many machine learning and data mining applications. We present the first distributed and the first streaming algorithms to compute and maintain an approximate $k$-core decomposition…
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…
In complex networks, many elements interact with each other in different ways. A hypergraph is a network in which group interactions occur among more than two elements. In this study, first, we propose a method to identify influential…
Core decomposition is a classic technique for discovering densely connected regions in a graph with large range of applications. Formally, a $k$-core is a maximal subgraph where each vertex has at least $k$ neighbors. A natural extension of…
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community…