[STAT/AP] Clara Stegehuis: Detecting geometry in scale free networks

04 November 2024 15:45 till 16:45 - Location: EEMCS Lecture Hall D@ta | Add to my calendar

Geometric network models formalize the natural idea that similar vertices are likely to connect. Therefore, geometric models capture many common structural properties of real-world networks. However, if one observes only the network connections, the presence of geometry is not always evident. Currently, triangle counts and clustering coefficients are the standard statistics to signal the presence of geometry. We show that triangle counts or clustering coefficients are insufficient because they fail to detect geometry induced by hyperbolic spaces, or in networks with power law degrees. We, therefore introduce different statistics, based on weighted subgraph counts that can even detect geometry in the 'weak geometry' regime, where the geometric effects converge to zero.