CEU Electronic Theses and Dissertations, 2025
| Author | Blagojević, Luka |
|---|---|
| Title | Physical network structure and robustness |
| Summary | Physical networks are networks composed of interconnected, volume-occupying objects, embedded in three-dimensional space. For example, a biological neural network is composed of neurons, which are physical objects, connected via synaptic connections, thus forming a network. Due to technological advances, data describing the three-dimensional layout and network connectivity of physical networks is becoming increasingly available, which provides an opportunity to ask fundamental questions about the relationship between their physical and network structure. In my thesis, I contribute to the emerging field of physical network research by extending network science tools to incorporate physical structure and using these novel tools to characterize the structure and dynamics of empirical and model physical networks. In the first chapter, I introduce the topic, and the second chapter reviews the literature. The main results are presented in the following chapters. In Chapter 3, I extend the so-called meta-graph to analyze empirical physical networks. The meta-graph was originally introduced to capture physical conflicts in growing linear physical models (i.e., networks where nodes are spheres and links are straight cylinders). Here, I generalize the meta-graph to study the spatial proximity of general physical nodes and links. Applying this tool to empirical networks, I find a strong correlation between the layout and the combinatorial network describing the system, highlighting the need to study the co-evolution of networks and their physical shape. In the fourth chapter, I standardize and analyze 15 physical networks from different domains, each consisting of tube-like objects (links) connected at junction points (nodes). The networks are categorized into three types: lattice-like networks, trees, and linked trees; most nodes exhibit degrees of one or three. To characterize their layout, among other physical descriptors, I introduce a quantity that captures how physically confined links are, showing that while most links follow straight paths, some take winding trajectories through dense network regions. The shape and connectivity of these networks are intertwined: for some data sets, highly confined links tend to have high network centralities, confirming that important links in the network are also confined in space. In the fifth chapter, I investigate the robustness of networks against physical damage. To simulate spatially correlated damage, physical networks are tiled with equally sized boxes, which are sequentially removed. Whenever a tile is damaged, all links intersecting the tile are removed from the network, leading to a percolation transition. Using numerical simulations and analytical calculations, I systematically investigate how physical and network structures affect the location of this transition for both random and targeted tile removal. This thesis contributes to the emergent field of physical network theory, with the overarching goal of identifying principles valid for a wide class of physical networks. My results reveal that the shape and connectivity of physical networks are intertwined and that their interaction strongly affects their behavior. Therefore, to fully understand such systems, both physical and network structures must be taken into account. |
| Supervisor | Pósfai, Márton |
| Department | Network Science PhD |
| Full text | https://www.etd.ceu.edu/2025/blagojevic_luka.pdf |
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