Real world applications of graph limits

Question

It is well known that the area of graph limits (initiated by Lovász and coauthors) had provided a very powerful framework to deal with problems arising, for instance, in extremal combinatorics and Ramsey Theory.

As the main philosophy of the area is to deal with huge graphs, my question is the following: are there already "real-world" research applications of all this methodology. For instance, in explicit large networks (brain, computer networks, biological networks, ...)?

I will be happy to see some applications (namely, papers) using these techniques "far away" from mathematics.

Answer 1

The first paragraph of the preface of Lovasz's book Large networks and graph limits says they were motivated in part by applications to quantum computers, statistical physics, and models for the internet. Later, he mentions applications to property testing in computer science, via statistics on graphs. Quantum graphs are discussed in detail in chapter 6, but the connection to quantum computation is not spelled out.

In the first chapter he lists many real-world examples of huge graphs, including the internet, social networks, ecological networks, interactions between proteins, the human brain, chemical bonds in crystals, computer chip design. But none of these are mentioned anywhere else in the book, except crystals (mentioned in section 2.2 in connection with the Ising model and magnetization). PageRank is never mentioned.

Another way to answer your question is to search Google Scholar for papers that cite this book. Doing that, I find 1200 papers. Google scholar lets you search within the citing articles. Doing that yields a few papers you might be interested in, and I suspect there are more.

Biology:

• Auxin transport model for leaf venation
• Efficient Agony Based Transfer Learning Algorithms for Survival Forecasting
• Genetic Fine-Mapping With Dense Linkage Disequilibrium Blocks
• Mean field limits of co-evolutionary heterogeneous networks
• Structure and dynamics of molecular networks: A novel paradigm of drug discovery: A comprehensive review
• A unified view of generative models for networks: models, methods, opportunities, and challenges

Epidemiology:

• Optimal vaccination: Various (counter) intuitive examples
• Generating Plausible Large-Scale Instances for Optimal Control Problems in Network Epidemic Models
• Introduction to networks and diseases
• Mathematics of Epidemics on Networks

Social networks:

• Iterated Models For Social Networks

Neuroscience:

• Continuous representations of brain connectivity using spatial point processes
• Brain Connectome Network Properties Visualization