Related papers: Uncovering the hidden core-periphery structure in …
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…
Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the…
A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…
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…
Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…
Network embedding is a fervid topic in current networks science and observes that most real complex systems can be embedded in hidden metrics space and emerge as the geometrical property, where the geometric distance between nodes…
We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…
In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
In this paper we devise a generative random network model with core-periphery properties whose core nodes act as sublinear dominators, that is, if the network has $n$ nodes, the core has size $o(n)$ and dominates the entire network. We show…
At rest, human brain functional networks display striking modular architecture in which coherent clusters of brain regions are activated. The modular account of brain function is pervasive, reliable, and reproducible. Yet, a complementary…
We show that the community structure of a network can be used as a coarse version of its embedding in a hidden space with hyperbolic geometry. The finding emerges from a systematic analysis of several real-world and synthetic networks. We…
Real-world networks exhibit universal structural properties such as sparsity, small-worldness, heterogeneous degree distributions, high clustering, and community structures. Geometric network models, particularly Random Hyperbolic Graphs…
Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics -- a grand-challenge open problem. Here, we show…
Understanding key structural properties of large scale networks are crucial for analyzing and optimizing their performance, and improving their reliability and security. Here we show that these networks possess a previously unnoticed…
Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is…
Meso-scale structures are network features where nodes with similar properties are grouped together instead of being treated individually. In this work, we provide formal and mathematical definitions of three such structures: assortative…