Related papers: Multi-scale structure and topological anomaly dete…
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…
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…
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core…
Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA, 108, 3838 (2011)], using simulations, that scale-free networks with "onion structure" are very robust against targeted high degree attacks. The onion structure is a…
We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection,…
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…
The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
The use of machine learning techniques in classical and quantum systems has led to novel techniques to classify ordered and disordered phases, as well as uncover transition points in critical phenomena. Efforts to extend these methods to…
Network robustness is a measure a network's ability to survive adversarial attacks. But not all parts of a network are equal. K-cores, which are dense subgraphs, are known to capture some of the key properties of many real-life networks.…
All networks can be analyzed at multiple scales. A higher scale of a network is made up of macro-nodes: subgraphs that have been grouped into individual nodes. Recasting a network at higher scales can have useful effects, such as decreasing…
We study core-periphery structure in networks using inference methods based on a flexible network model that allows for traditional onion-like cores within cores, but also for hierarchical tree-like structures and more general non-nested…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…
In Social Network Analysis (SNA), k-core decomposition is used to detect hierarchical shells in networks. The application of the K-core decomposition to a network of keywords allows us to represent the conceptual structure of a research…
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the…
We uncover the global organization of clustering in real complex networks. As it happens with other fundamental properties of networks such as the degree distribution, we find that real networks are neither completely random nor ordered…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…