2020/05/27 by Carlo Vittorio Cannistraci, Cannistraci, Carlo Vittorio, Alessandro Muscoloni +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Physical sciences #Fractal and DNA sequence analysis #Physics and Society (physics.soc-ph) #Slime Mold and Myxomycetes Research #Social and Information Networks (cs.SI) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2005.13255
openalex publication_date 2020/05/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of geometrical congruence is considered the reason for nearly maximally efficient greedy navigation of hyperbolic networks. Here, we propose a complex network measure termed geometrical congruence (GC) and we show that there might exist different TSP, whose projections (pTSP) in the hyperbolic space largely diverge, and significantly differ from the respective geodesics. We discover that, contrary to current belief, hyperbolic networks do not demonstrate in general geometrical congruence and efficient navigability which, in networks generated with nPSO model, seem to emerge only for power-law exponent close to 2. We conclude by showing that GC measure can impact also real networks analysis, indeed it significantly changes in structural brain connectomes grouped by gender or age.