Related papers: Dynamics of "comb-of-comb" networks
Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
We consider a new model for complex networks whose underlying mechanism is extending dense subgraphs. In the frustum model, we iteratively extend cliques over discrete-time steps. For many choices of the underlying parameters, graphs…
Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
Multilayer networks have been the subject of intense research during the last few years, as they represent better the interdependent nature of many real world systems. Here, we address the question of describing the three different…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological…
Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and…
Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
Precise timing of spikes and temporal locking are key elements of neural computation. Here we demonstrate how even strongly heterogeneous, deterministic neural networks with delayed interactions and complex topology can exhibit periodic…
Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…