Projects
Under construction…
Physical Networks
Physical networks are networks of tangible objects, 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 reconstruction by ML/AI have recently made it possible to obtain detailed three-dimensional maps of such complex systems, providing new opportunities for studying physical networks.
In recent years, the physical embedding of networks has been shown to give rise to emergent phenomena, including entanglement [(Liu, Dehmamy, and Barabási 2021), (Glover and Barabási 2024)], bundling (Bonamassa et al. 2024), jamming (Pósfai et al. 2024), and correlations between node degree and node volume (Pete et al. 2024).
For my PhD thesis, I am exploring the spectral and topological properties of physical networks, as well as the dynamical processes that unfold on them.
Higher-Order Networks
Triadic interactions are higher-order, three-body interactions in which a node modulates the edge between two other nodes. Such interactions are ubiquitous in real-world systems, such as glia cells in the brain regulate synaptic connectivity between neurons.
Fractal Scale-Free Networks
A network is fractal (with respect to shortest-path lengths) if the minimum number of subgraphs (boxes) of diameter l_{\textup{B}} required to cover the network scales as \begin{equation} N_{\textup{B}}(l_{\textup{B}}) \sim l_{\textup{B}}^{-D_{\textup{f}}} \end{equation} where D_{\textup{f}} is the fractal dimension of the network (Song, Havlin, and Makse 2005). In fractal networks, the average path lengths also scales as the power of the network size, \begin{equation} \langle l \rangle \sim N^{1/D_{\textup{f}}}. \end{equation} While many empirical networks exhibit the small-world property, where the average path lengths scales logarithmically with the number of nodes (corresponding to the absence of characteristic scales, i.e., D_{\textup{f}} \to \infty), the fractal property can still hold at length scales shorter than the network’s characteristic size. Detecting this scaling through shortest paths, however, is often challenging because most real networks lack a sufficiently large diameter.
Fractal networks are of particular interest because their structure gives rise to distinctive features, such as long-range degree correlations manifested in hub repulsion (Rozenfeld et al. 2008).