Three-dimensional shape and connectivity of physical networks

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We contribute to this effort by standardizing and analyzing 15 data sets from different domains. Treating junction points as nodes and connections between them as links, we divide the networks into three categories: lattice-like networks, trees, and linked trees. We find that the degree distribution of physical networks is bounded, with most nodes having degrees one or three. Characterizing the physical properties of links, we show that links have an elongated shape and tend to follow a nearly straight trajectory, while a small fraction of links follow a winding path. These typical node and link properties must be reflected by physical network models. We also measure how confined a link is in space by comparing its trajectory to a randomized null-model, showing that links that are central in the abstract network tend to be physically confined by their neighbors. The fact that the shape and connectivity of the physical networks are intertwined highlights that their three-dimensional layout must be taken into account to understand the evolution and function of physical networks. Below is a figure from the paper explaining how link confinement measure is computed:

arXiv link: https://arxiv.org/abs/2211.13265

Technical project overview

This project is divided into four different parts:

1. data - I perform data processing of physical network skeletons, where I perform skeleton healing and remove redundancies in the physical structure.

2. basic_measures - I consider physical aspects of my data, so I analyze their fractal dimension and space-filling properties (physical density).

3. abstract_network- With a graph structure to work with, I perform standard network analysis (degree distribution and motifs).

4. link_confinement_measure - I apply collision detection algorithms to compute a link-level measure of local confinement.

Data

All processed datasets are available upon request, as I cannot host them on GitHub. If you are interested in the data before processing, please take a look at the subsections below:

Individual biological neuron datasets

Raw SWC format data is available:

https://neuromorpho.org/neuron_info.jsp?neuron_name=20Nov2007-3-ON-OFF - zebrafish_neuron

https://neuromorpho.org/neuron_info.jsp?neuron_name=VPM_1 - rat_neuron

https://neuromorpho.org/neuron_info.jsp?neuron_name=H16-06-010-01-03-04-01_566350716_m - human_neuron

https://neuromorpho.org/neuron_info.jsp?neuron_name=Dec15IR2e_y_morph - monkey_neuron

Fruit fly biological neural network datasets

To access the original fruit-fly data, you will need to use the Python library provided by the Janelia project, which you can install from https://pypi.org/project/neuprint-python/

Neuron data is downloaded from here: https://neuromorpho.org/