Projects
Under construction…
Physical Networks
Physical networks are networks of tangible objects, i.e., nodes and edges are embedded in a physical space under physical constraints including but not limited to volume exclusion [(Dehmamy, Milanlouei, and Barabási 2018)]. Examples of physical networks include biological neural networks, vascular networks, porous media, granular materials, to name just a few [(Blagojević and Pósfai 2024)]. The recent advances of imaging techniques and machine learning have significantly improved the availablity of three-dimensional maps of complex physical systems, which motivates the study of physical networks.
Over the recent years, the physicality of the network has been shown to result in the emergent properties such as entanglement [(Liu, Dehmamy, and Barabási 2021), (Glover and Barabási 2024)], bundling (Bonamassa et al. 2024), jamming (Pósfai et al. 2024), and degree-volume correlations (Pete et al. 2024).
For my PhD thesis, I am investigating the spectral and topological properties of physical networks, as well as dynamical processes on physical networks.
Higher-Order Networks
Triadic interactions are three-body (higher-order) interactions in which a node regulates an edge between two other nodes positively or negatively. Such interactions are ubiquitous in real-world networks, such as glia cells in the brain that regulate the 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 a given 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-law of the network size, i.e., \begin{equation} \langle l \rangle \sim N^{1/D_{\textup{f}}}. \end{equation} While many empirical networks are shown to be small-world, in which the average path lengths scales as logarithm of the number of nodes, i.e., D_{\textup{f}} \to \infty, the fractality can still be valid in length scale shorter than the characteristic length scale of the network (although it is difficult to observe the scaling in terms of shortest path lengths, as most of the networks do not have long enough diameter).
Networks with fractal structure exhibit intriguing properties, such as the long-range degree correlations in the form of hub repulsion (Rozenfeld et al. 2008).