The world is full of networks. We're part of them, our infrastructure is full of them, and there are even networks within our bodies (e.g. made from neurons). This summer the mathematician Richard Montgomery won a prestigious EMS Prize at the European Congress of Mathematics (ECM) for his work on the pure maths of networks, also known as graph theory. In this episode of Maths on the move Richard tells us about an amazing result he helped to prove to great acclaim, known as Ringel's conjecture, and why it's interesting to take graphs to the extreme. You might also want to read this article about Richard's work. To find out more about the event at the Isaac Newton Institute in honour of Tim Gowers, which is mentioned in the podcast, see here. This content was produced with kind support from the London Mathematical Society.