# Real-world examples of unweighted directed graphs

Social Networks, Internet Traffic, Citation Networks, Transportation Networks, and Biological Networks exemplify real-world instances of unweighted directed graphs. Within these domains, the Graph Fourier Transform (GFT) serves as a fundamental tool for processing graph signals. Nonetheless, the asymmetry of adjacency matrices in directed graphs frequently hinders their diagonalizability, thus impeding the development of an appropriate GFT. Despite these challenges, extensive research endeavors have resulted in diverse approaches for GFT. To gauge their efficacy, access to real-world examples of unweighted directed graphs with publicly available datasets online would be exceptionally advantageous.

Q. Are there any real-world examples of (unweighted) directed graphs whose datasets are available on the web?

• P.S. I think this question is fine for MathOverflow. I have long believed that the MO community ought to be more accommodating of applied math questions. Apr 13 at 13:36

Two other graph repositories in the same vein as The network repository, that I like because they allow to search specifically for graphs with particular properties (such as directedness):

• Great, so helpful.
– ABB
Apr 19 at 15:41
• Indeed, it is the most complete source that I have ever faced!
– ABB
Apr 20 at 9:17

Disclaimer: I am not an applied mathematician at all and I found this just via some basic Goolging. But the "Stanford Large Network Dataset Collection" (https://snap.stanford.edu/data/) looks interesting and might be what you're after.

• It is wonderful and absolutely helpful.
– ABB
Apr 14 at 10:49

It's been recognized that adjacency matrix approaches to forming a spectral graph theory is problematic. It's been rediscovered that Eckmann's Combinatorial Hodge theory removes the problems and gives a topologically principles way to think about graph Laplacians. This recognition has apparently developed independently in numerous applied fields such as finite element methods using discrete differential forms, graph signal processing, etc.

A very nice review of combinatorial Hodge theory and its spectral theory of graphs is:

Graphs, Simplicial Complexes and Hypergraphs: Spectral Theory and Topology Mulas, Raffaella; Horak, Danijela; Jost, J.

A few examples of oriented graphs can be found as part of USC's GraSP library. The graph folder contains a number of directed examples:

https://github.com/GraSP-toolbox/GraSP/tree/master/Graphs

The Gleich's boost graph library contains further examples (in fact the Minnesota road system example oft used as a graph signal processing example originates from here):

https://www.cs.purdue.edu/homes/dgleich/packages/matlab_bgl/index.html

The network repository (Rossi & Ahmed) is a substantial repository I haven't used yet, but should contain a wealth of datasets of interest:

https://graphdatasets.com/