igraph-help
[Top][All Lists]

## [igraph] planar vs. non-planar graph indices

 From: Alisa Coffin Subject: [igraph] planar vs. non-planar graph indices Date: Mon, 28 Apr 2008 13:05:24 -0400

Hello igraph list,

As a newbie to the igraph world, I am struggling to understand the differences between non-planar and planar graphs and the indices used to measure them. I found an seemingly good article on Wikipedia that describes planar graphs and the mathematical criteria of planarity. However, now I am wondering about some of the indices in igraph.

In particular, I was looking at the graph.density index and wondering if this calculation is for a planar or non-planar graph, or does it matter? I didn't find any mention in the igraph manual about assumptions of planarity. Did I just miss it? Are there indices in igraph that would apply exclusively to planar or non-planar graphs as the case may be?

I am applying this analysis to the study of the structure of transportation networks which, in the case of roads, have been mostly analyzed as planar graphs. For me, this brings up questions about how to deal with structures such as bridges and tunnels in the system. Graph theoretic measures of transportation systems include indices, such as the alpha and gamma indices that consider both planar and non-planar graph structures by specifying different algorithms depending on the planarity of the graph (see for example Hagget, P. and Chorley R.J. Network Analysis in Geography).

I am a bit stuck here, so any help from the community would be greatly appreciated.

Thank you,
Alisa.

--
Alisa Coffin, PhD. Candidate
Department of Geography
University of Florida
Gainesville, FL 32611