# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 57: Networks: From Topology to Dynamics IV (joint session DY/SOE)

### DY 57.2: Vortrag

### Freitag, 31. März 2023, 09:45–10:00, ZEU 250

**Discovering hidden layers in quantum graphs** — Łukasz Gajewski, •Julian Sienkiewicz, and Janusz Hołyst — Faculty of Physics, Warsaw University of Technology, Warsaw, Poland

Finding hidden layers in complex networks is an important and nontrivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multilayer system exist and, if so, their extent, i.e., how many unknown layers are there. Assuming that the only information available is the time evolution of wave propagation on a single layer of a network, it is indeed possible to uncover that which is hidden by merely observing the dynamics. We present evidence on both synthetic and real-world networks that the frequency spectrum of the wave dynamics can express distinct features in the form of additional frequency peaks. These peaks exhibit dependence on the number of layers taking part in the propagation and thus allowing for the extraction of said number. We show that, in fact, with sufficient observation time, one can fully reconstruct the row-normalized adjacency matrix spectrum. We compare our propositions to a machine learning approach using a wave packet signature method modified for the purposes of multilayer systems.