Pósfai Márton (Central European University)

Az előadás kivonata: Physical networks are spatially embedded complex networks composed of nodes and links that are physical objects which cannot overlap. Examples of physical networks range from neural networks and networks of bio-molecules to computer chips and disordered meta-materials. It is hypothesized that the unique features of physical networks, such as the non-trivial shape of nodes and links and volume exclusion affect their network structure and function. However, the traditional toolset of network science cannot capture these properties, calling for a suitable generalization of network theory. Here, I present recent efforts to understand the impact of physicality through two classes of analytically tractable models: (i) linear physical networks (LPN), which construct networks from straight cylinders [1,2], and (ii) a network-of-network model (NoN) that construct physical networks from random walk trajectories [3]. Using a variety of analytical tools, I characterize, for example, the onset of physical effects and the emergence of a jamming transition in LPNs, showing that physicality impacts the network structure even when the total volume of the links is negligible. I also show that in the NoN model physicality induces heterogeneity in both the physical and the network properties and that the two become strongly correlated. I study the dynamics on physical networks by characterizing the network’s Laplacian spectrum, and we show that the Laplacian of the combinatorial network $Q_G$ is not sufficient to describe the dynamics on physical networks and that the physical layout must be taken into account as $V^{−1/2} Q_G V^{−1/2}$ where $V$ is a diagonal matrix containing the volume of the nodes. Overall, our model demonstrates that in the presence of volume exclusion, traditional methods of network science are not sufficient to characterize the structure of physical networks and the dynamics on them.

[1] Pósfai, Márton, et al. "Impact of physicality on network structure." Nature Physics (2023): 1-8.
[2] Bonamassa, I., et al. "Bundling by volume exclusion in non-equilibrium spaghetti." arXiv preprint arXiv:2401.02579 (2024).
[3] Pete, Gábor, et al. "A network-of-networks model for physical networks." arXiv preprint arXiv:2306.01583 (2023).