Related papers: Emergent Complex Network Geometry
This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly…
Graphical models are frequently used to represent topological structures of various complex networks. Current criteria to assess different models of a network mainly rely on how close a model matches the network in terms of topological…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying…
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
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 past decade has seen tremendous growth in the field of Complex Social Networks. Several network generation models have been extensively studied to develop an understanding of how real world networks evolve over time. Two important…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabasi-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing…