Welcome to the DK-Lab

The main focus of research at the DK-Lab is network theory. Research topics of particular interest to the lab are latent network geometry, maximum-entropy random graph ensembles, graph limits, random geometric graphs, graph curvature, causal sets, navigation in networks, and fundamentals of network dynamics. While research in the lab deals mainly with theoretical aspects of network science, the obtained theoretical results are often applied to real-world network data in a variety of applications.

Highlights of recent DK-Lab research with application flavor include:

• Curvature: Establishment of the first rigorous connection between graph curvature and space curvature, the former converging to the latter in the continuum limit
• Power laws: First rigorous formalization of impure power-law (degree) distributions, and the introduction of consistent methods to infer their exponents in real-world network data
• Routing: Design of optimal (as efficient as theoretically possible) routing and addressing schemes based on (geo)hyperbolic geometry for telecommunication networks and Internets of Things
• Brain: Demonstration that the spatiostructural organization of the human brain is nearly as needed for optimal routing of information between different parts of the brain
• Universe: Discovery that the large-scale structure and dynamics of our accelerating universe represented as a growing quantum-gravity network (a causal set), are asymptotically identical to the large-scale structure and growing dynamics of many complex networks, such as the brain or the Internet
• Hyperbolic geometry: Demonstration that scale-free degree distributions, strong clustering, community structure, and self-similarity of many real-world networks, naturally emerge from their latent hyperbolic or de Sitter geometries
• dk-series: Identification of a systematic series of properties for network analysis, akin to the Fourier or Taylor series in mathematical analysis, to quantify randomness in real networks, and to tell whether a particular structural property of a given real network is related to its particular function

More details concerning these and other projects are available in the research pages. The general philosophy motivating several projects in the lab is summarized in this opinion article.