The structural characteristics of a network are uniquely determined by its adjacency matrix, which encodes the complete information about the interactions between a system's components. However, in physical networks, like the brain or the vascular system, the network's three-dimensional layout also affects the system's structure and function. Therefore, when analyzing physical networks, it is important to take the physical embedding of the network into account. We lack, however, the tools to systematically analyze and interpret the physical embedding topology of networks combined with their structural topology. In this thesis, we aim at exploring the unique features of physical networks and developing network theories that are tailored for describing and explaining properties of physical networks. We also analyze real-world physical networks, especially focusing on the Drosophila larval brain system. We first find the best method to build a network from the given data of neuron embedding in the Drosophila larval brain, which is applicable to other similar physical systems. Next, we apply our developed theories on physical networks to the Drosophila brain network and analyze various properties of the network to gain insights of the system.

Committee:

1.  Albert-Laszlo Barabasi, Network Science Institute, Northeastern University, Boston, MA 02115, Department of Physics, Northeastern University, Boston, MA 02115, Department of Network and Data Science, Central European University, Budapest 1051, Hungary.

2.  Alessandro Vespignani, Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA USA.

3.  Sam Scarpino, Santa Fe Institute, Santa Fe, NM 87501, Pandemic Prevention Institute, The Rockefeller Foundation, Washington, D.C. 20037, Network Science Institute, Northeastern University, Boston, MA 02115, Department of Physics, Northeastern University, Boston, MA 02115, Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405.

4. Emma Towlson, Department of Computer Science, University of Calgary, Calgary, Alberta, T2N 1N4, Canada.