Related papers: Multi-scale structure and topological anomaly dete…
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…
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 Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k-edge swapping MCMC…
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…
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree…
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…
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…
Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…
We introduce and use k-shell decomposition to investigate the topology of the Internet at the AS level. Our analysis separates the Internet into three sub-components: (a) a nucleus which is a small (~100 nodes) very well connected globally…
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 widely used to identify the center of a large network, it is a pruning process in which the nodes with degrees less than $k$ are recursively removed. Although the simplicity and effectiveness of this method…
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
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…
The analysis of the dynamics on complex networks is closely connected to structural features of the networks. Features like, for instance, graph-cores and node degrees have been studied ubiquitously. Here we introduce the D-spectrum of a…
A vast variety of biological, social, and economical networks shows topologies drastically differing from random graphs; yet the quantitative characterization remains unsatisfactory from a conceptual point of view. Motivated from the…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
Many networks can be usefully decomposed into a dense core plus an outlying, loosely-connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
Graph clustering or community detection constitutes an important task for investigating the internal structure of graphs, with a plethora of applications in several domains. Traditional techniques for graph clustering, such as spectral…