Related papers: k-Core percolation on multiplex networks
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
Due to the increasing discovery and implementation of networks within all disciplines of life, the study of subgraph connectivity has become increasingly important. Motivated by the idea of community (or sub-graph) detection within 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…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…
The notion of a core is generalized to multiway networks. To determine the multiway cores, we adapted already-known algorithms for determining the generalized cores in one-mode and two-mode networks. A new node property, node diversity has…
The k-core of a graph is its maximal subgraph with minimum degree at least k, and the core value of a vertex u is the largest k for which u is contained in the k-core of the graph. Among cohesive subgraphs, k-core and its variants have…
Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell…
In social network analysis, the size of the k-core, i.e., the maximal induced subgraph of the network with minimum degree at least k, is frequently adopted as a typical metric to evaluate the cohesiveness of a community. We address the…
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold $\lambda_c$ for the emergence of a non-trivial k-core in the random graph $G(n,\lambda/n)$, and…
We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary…
Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both…
A key graph mining primitive is extracting dense structures from graphs, and this has led to interesting notions such as $k$-cores which subsequently have been employed as building blocks for capturing the structure of complex networks and…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…
The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
The $k$-core of a graph is the maximal subgraph in which every node has degree at least~$k$, the shell index of a node is the largest $k$ such that the $k$-core contains the node, and the degeneracy of a graph is the largest shell index of…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…