nwport

Network portrait is matrix $B$ constructed from a graph such that $B_{l,k}$ is the number of nodes having $k$ nodes at a distance $l$. It encodes a lot of the network's structural properties.

Network portraits offer a great way to compare networks both visually and numerically.

This repository represents the research work done in proceedings of Idea's 2021 Scientific School: Mathematics, Theoretical Physics and Mathematical Methods of Data Analysis in Neuroscience (link).

We study network portraits of model networks, C. elegans connectomes and human brain connectomes:

• Properties of different networks' portraits
• Comparison of networks based on Jensen-Shannon Divergence metric defined using network portraits
• Resistance to randomization
• Attacks on networks: dynamics & properties
• How portraits reflect other network properties
• Reconstructing the graph by its portrait: approaches & uniqueness

The work is inspired by Bagrow & Bollt, 2019.

View project's final presentation.

Inside

• Network portrait implementation
• Support for directed & undirected graphs
• Network portrait heatmap plots
• Calculation of KL-divergence & Jensen-Shannon divergence
• Portraits of model (regular & random) networks
• Animations of model network portraits across parameter ranges
• Implementation of attacks on networks (gradual node removal) in different modes

Data

• Model networks:
  • Erdős–Rényi
  • Random Regular
  • Barabási–Albert
  • Watts–Strogatz
• Human brain connectomes courtesy of the PIT Bioinformatics group;
• C. Elegans connectomes courtesy of Neurodata.