Fundamental network science

formalized representations of the geometry of multi-dimensional networks

Foundational network science research includes: study of topological data analysis on graphs, reinforcement learning on complex networks, graph embedding and representation learning, scalable algorithms for mining graphs, and anomaly detection. We are also working on a collection of studies developing rigorous approaches to latent-geometric network models, maximum entropy ensembles of random graphs, and their navigability, with applications ranging from neuroscience to quantum gravity and cosmology.

Featured publications

A wealth of discovery built on the Human Genome Project — by the numbers

Alexander J. Gates, Deisy Morselli Gysi, Manolis Kellis & Albert-László Barabási
Nature
February 10, 2021

Network geometry

Marián Boguñá, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Ángeles Serrano
Nature Reviews Physics
January 29, 2021

Link prediction with hyperbolic geometry

Maksim Kitsak, Ivan Voitalov, and Dmitri Krioukov
Phys. Rev. Research
October 21, 2020

Recent publications

Ollivier-Ricci curvature convergence in random geometric graphs

Pim van der Hoorn, William J. Cunningham, Gabor Lippner, Carlo Trugenberger, and Dmitri Krioukov
Physics Review Research
March 5, 2021

A wealth of discovery built on the Human Genome Project — by the numbers

Alexander J. Gates, Deisy Morselli Gysi, Manolis Kellis & Albert-László Barabási
Nature
February 10, 2021

Network geometry

Marián Boguñá, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Ángeles Serrano
Nature Reviews Physics
January 29, 2021

Clustering in a hyperbolic model of complex networks

Nikolaos Fountoulakis, Pim van der Hoorn, Tobias Müller, and Markus Schepers
Electronic Journal of Probability
January 25, 2021

Generalized word shift graphs: a method for visualizing and explaining pairwise comparisons between texts

Ryan J. Gallagher, Morgan R. Frank, Lewis Mitchell, Aaron J. Schwartz, Andrew J. Reagan, Christopher M. Danforth & Peter Sheridan Dodds
SpringerOpen
January 19, 2021
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Featured project

In our project on Scalable Graph Distances, we explore measurements of graph distance in metric spaces, which are required for many graph mining tasks (eg, clustering, anomaly detection). This project explores a formal mathematical foundation covering a family of graph distance measures that overcome common limitations, such as their inability to scale up to millions of nodes and reliance on heuristics. In another collection of studies on latent geometry, we rigorously establish conditions for a given (real) network to have latent geometry. This geometry can then be reliably used in applications ranging from explaining the structure of (optimal) information flows in the brain to providing new approaches to the dark energy problem in cosmology.

Major funders

NSF, Army Research Office