There's a chapter titled "Graph Theory' dedicated to graphs and their usage, in my book 'A handbook of mathematical models with python'. This chapter could have been named 'Graphs' or 'Networks' instead, just to imply the simplicity of its content. :)

To know about graph data structures and how they serve as inputs to GNNs (deep learning models), please read chapter 6 of the book.

Studying a protein with an elastic network model that includes coarse-grained Gaussian network model (GNM) and atomic anisotropic network model (ANM): https://www.pnas.org/doi/full/10.1073/pnas.0902159106

-> Elastic network model (coarse-grained model) to study protein dynamics:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6320916/

-> My work on anisotropic model:

https://link.springer.com/article/10.1186/s13628-017-0034-9 https://www.sciencedirect.com/science/article/abs/pii/S0025556417303140

Wikipedia reference: https://en.wikipedia.org/wiki/Anisotropic_Network_Model

Studying protein dynamics with python: http://prody.csb.pitt.edu/tutorials/enm_analysis/

OTHER USE CASES

-> Find most optimal (flight) routes in terms of distance and airtime using Dijkstra algorithm from (weighted) graphs

More on Dijkstra algorithm for a graph geodesic: https://mathworld.wolfram.com/DijkstrasAlgorithm.html

-> Create knowledge graphs (directed) from unstructured data and visualize with different layouts: https://www.kaggle.com/code/ranja7/knowledge-graphs-networkx-layouts

-> Do social network analysis with graphs from your data of connections/contacts on social site

-> There are operations research problems (routing etc.) that can be solved utilizing network science.