Thanks for the helpful comments, David. I'm in the funny position of having decided to talk about "climate network theory" and Ludescher's paper, and now being rather skeptical of both. But I think the best approach is to be honest at the start, and say something like:
> Instead of talking about what I was probably invited to talk about - abstract aspects of network theory - I decided to learn about climate networks and talk about those. My colleagues in the Azimuth Project and I put some work into this subject, and this is what I've learned so far.
> Perhaps you could survey the existing applications in climate network theory,
I'm not sure there are "applications" yet, except for Ludescher _et al_'s attempt to use them for El Niño prediction. This is part of my dissatisfaction.
So far it seems people have mainly been using climate networks to take a new look at climate data. They've made some mildly interesting _discoveries_, which I would not call "applications".
My vague plan is to:
1) Explain the ENSO - the El Niño Southern Oscillation - and why it's important.
2) Talk about the rather fascinating and important idea of [teleconnections](https://en.wikipedia.org/wiki/Teleconnection): roughly, patterns of highly correlated weather between distant locations. The most famous teleconnection is ENSO, but there are others.
3) Summarize some attempts to objectively search for teleconnections in weather data. This is a pattern recognition question - something NIPS people will like. In many of these attempts, the ENSO shows up as the most powerful teleconnection. I should mention some of the runners-up.
4) Explain the main ideas of network theory as used by researchers in climate networks. This is the sort of network theory that people use when talking about "complex networks" - it's basically the analysis of statistical properties of large **weighted graphs**: graphs with positive numbers labelling their edges. (It's not the same as what _I_ usually mean by network theory, though my idea of network theory _includes_ this.)
5) Talk about attempts to use network theory to find teleconnections. There's an idea called the [backbone of the climate network](http://arxiv.org/abs/1002.2100), the sub-network consisting of sites having the strongest link strengths.
6) Talk about the idea that El Niños "break climate links" around the world.
7) Describe and critique Ludescher _et al_'s attempt to predict El Nños by looking for increased link strengths between the El Niño basin and other parts of the Pacific.
This is certainly enough stuff for an hour. It will take work to make it really clear and exciting. But it seems like a reasonably interesting subject even if nobody quite knows what to make of it yet. I'm not going to try to "sell" climate networks.