Hyperbolic geometry of Kuramoto oscillator networks

Hyperbolic Geometry of Complex Networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conver...

On Hyperbolic Geometry Structure of Complex Networks

Various real world phenomena can be modeled by a notion called complex network. Much effort has been devoted into understanding and manipulating this notion. Recent research hints that complex networks have an underlying hyperbolic geometry that gives them navigability, a highly desirable property observed in many complex networks. In this internship, a parameter called δ-hyperbolicity, which i...

Hyperbolic Geometry

The Synchronization of Kuramoto Oscillator Networks: Forecasting Financial Index Critical Points

Organizations can be modeled as complex systems. Here we consider complex economic organizations such as the stock exchange and show that the Kuramoto equation is a suitable model to forecast maxima or minima of the financial signals.

Fast generation of complex networks with underlying hyperbolic geometry

Complex networks have become increasingly popular for modeling various real-world phenomena. Realistic generative network models are important in this context as they avoid privacy concerns of real data and simplify complex network research regarding data sharing, reproducibility, and scalability studies. We investigate a model creating geometric graphs in hyperbolic space. Previous work provid...