Physical Networks
Physical networks are networks of tangible components, in which nodes and edges are embedded in physical space and subject to constraints such as volume exclusion [(Dehmamy, Milanlouei, and Barabási 2018)]. Examples include biological neural networks, vascular systems, porous media, and granular materials. Advances in imaging technologies and accelerated 3D reconstruction by ML/AI have enabled to obtain detailed three-dimensional maps of such complex systems, providing new opportunities to study general organizing principles for tangible complex systems.
While the physical layout of networks has been shown to give rise to emergent structural properties, such as entanglement [Glover and Barabási (2024)], bundling (Bonamassa et al. 2025), jamming (Pósfai et al. 2024), and correlations between node degree and node volume (Pete et al. 2024), it remains elusive how these would impact dynamical processes that unfold on physical networks.
For my PhD thesis, I am exploring the spectral and topological properties of physical networks and their dynamical implications through physical Laplacian, a vertex-weighted graph Laplacian for physical networks derived in (Pete et al. 2024) as \begin{align} \mathbf{Q}_{\textrm{P}} = \mathbf{V}^{-1/2} \mathbf{Q}_{\textrm{G}} \mathbf{V}^{-1/2} \end{align} where \mathbf{G_{\textrm{G}}} is the combinatorial graph Laplacian and \mathbf{V}=\mathrm{diag}(v_1, \dots, v_{N}) is the diagonal volume matrix.
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