TV-HGGs

Time-Varying Hyperbolic Geometric Graphs (TV-HGGs)

Previously we discovered a powerful and unique geometric framework explaining the ubiquitous common structure of complex networks and linking this structure to the optimality of their common functions. In this framework, network nodes are mapped to points in hyperbolic spaces, which lie beneath the observable topologies. The analysis of complex networks is then simplified significantly, as their discrete complex structure can be studied in purely geometric terms. This framework, known as hyperbolic geometric graphs (HGGs), has attracted a great deal of interest in mathematics, physics, computer science and biology. However, despite several years of research, our knowledge and understanding of network geometry is essentially still limited to static HGGs and methods that can only infer the geometry of network snapshots. But real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links, and there currently exists no principled theory that can model and predict their dynamics — a grand-challenge open problem in modern network theory. The main aim of this project was to address this challenge by mapping the general problem of predicting network dynamics to the specific problem of predicting the motion of nodes in their hidden hyperbolic spaces and developing models of time-varying hyperbolic geometric graphs.

Website: netsysci.cut.ac.cy/projects/tv-hggs/

Source Code: github.com/cosior/TV-HGG

Related Publications:

• Fundamental dynamics of popularity-similarity trajectories in real networks
• Topology and Geometry of the Third-Party Domains Ecosystem: Measurement and Applications