# Seeking real-world networks that have an approximately linear structure

I'm currently looking into real-world networks which can be well approximated by interval graphs. It seems natural to suspect that networks that have constraints forcing them to be approximately physically linear could be well approximated by interval graphs.

For example, the highway system of the south island of New Zealand forms a network where geographical constraints force the network to have a natural linearity.

However, if I were to use this network, it looks like I would need to key in each of the highway intersections by hand.

In another attempt, I tried using the C. elegans neural network, thinking the physical linearity of the worm would force the network to be linear. Unfortunately, this research was thwarted by long head-to-tail neurons with large numbers of synapses (see my cogsci.SE question).

Question: Where can I access a real-world network which has an approximately linear structure (possibly due to some physical constraints)?

The network should be in a format that should be computer-readable.

• What are your criteria for "approximately linear"? I am afraid you have the algorithm to determine that (how approximate to linear it is) and you are looking for a network that you could test your algorithm on. So your question is more about finding a network which representation is released as machine-readable and your goal is to use its linear property. May 21, 2013 at 22:06
• I don't really have a formal criteria for approximately linear (which is why I tried to explain with examples). I suppose I do have an algorithm to test. But I'm not planning on using the network's linearity; the idea is to recover the linearity from the network structure alone. May 21, 2013 at 22:14
• Yeah, I don't really see how applying your algorithm to almost linear network will be interesting (comparison would be) but anyway, Trans-Canada Highways also are pretty linear. May 21, 2013 at 22:19