Networks are defined by local, node-level connections that give rise to globally rich structures. The relationship between local and global scales has been a central focus in network science, leading to characteristic network measures such as density, degree heterogeneity, clustering, and community structure. In this dissertation, I investigate how local rules govern the emergence of large-scale network properties and structures.

The first two projects focus on physical networks, where nodes and links occupy physical space, often leading to entangled configurations. This physicality introduces unique constraints and unexplored questions in network science. In the first project, I introduce a new metric, the average crossing number, to quantify the entanglement of physical networks. I demonstrate how key network characteristics—derived from both the adjacency matrix and node positions—control the degree of entanglementIn the second project, I explore how repeated network structures emerge in nature from a set of local rules. By combining node-level rules with inherent design principles, I aim to identify the mechanisms required to successfully design a target network from a predefined set of nodes.

In the third project, I shift focus to the limitations of reconstructing networks from node-level dynamics, as captured by time-series data. Using common network models with controlled statistics—such as density and degree heterogeneity—I investigate when and how node-level signals are sufficient or insufficient to capture the underlying network structure. This project provides new insights into the biases and challenges of network reconstruction, offering a critical perspective on the interpretability of inferred networks and highlighting the interplay between local dynamics and global structure.

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