Research
Current projects
Physical networks
How physical constraints impact network structure and dynamics, including how degree-volume disorder controls Laplacian eigenmode localization (Yamamoto, Bonamassa, and Pósfai 2026b, 2026a).
Current focusLaplacian eigenmode localization, diffusion, synchronization
Scaling theory for networks
Scaling laws and critical phenomena for networks with heterogeneous topologies (Yamamoto and Yakubo 2023; Yakubo, Shimojo, and Yamamoto 2024).
Current focusCrossover · percolation criticality
Network synchronization
How network structure and physical heterogeneity organize collective order in experimentally realized oscillator systems.
Current focusModular synchronization · spin oscillators
Past project
The completed projects are listed below. For a full list of publications, see the publications page.
Bifractality of fractal scale-free networks
We showed that fractal scale-free networks are characterized by two distinct local fractal dimensions: one governing neighborhoods around hubs and another governing regions far from them. Our analytical and numerical results suggest that such bifractality is generic, leading us to conjecture that any network combining scale-free connectivity with fractal structure exhibits this behavior. (Yamamoto and Yakubo 2023).
Random walks on bifractal networks
Building on bifractality, we showed that a random walk’s walk dimension remains position-independent, whereas the spectral dimension splits into two local values.
The result connects structural bifractality to transport properties: local structural scaling remains visible in return-to-origin probabilities (Yakubo, Shimojo, and Yamamoto 2024).
Mining triadic interactions
We considered diffusive dynamics in networks with triadic interactions in which a node can influence the connection between two other nodes. We demonstrated that such interactions can be mined from conditional correlations and mutual information between node triplets (Niedostatek et al. 2025).