Thanks Roger.

Given my programming experience, at this point in time I am not able to move
forward programming gabriel graph construction with alternative distance
measures. If anyone is interested, a quicker work around for me at this time
is to integrate R with the use of the batch command line functionality of
the program Passage (Pattern Analysis, Spatial Statistics and Geographic
Exegesis). Among other capabilities, Passage can create a suite of graph
types based on any type of distance measure.

ilona

On Tue, Apr 6, 2010 at 6:09 AM, Roger Bivand <Roger.Bivand@nhh.no> wrote:

> On Mon, 5 Apr 2010, Ilona Naujokaitis-Lewis wrote:
>
>  Hello everyone,
>>
>> I am working on the problem of creating alternative types of graphs (i.e.
>> networks) based on alternative distance measures and then comparing
>> topological differences between them.  Specifically I am constructing
>> graphs
>> created using euclidean distances versus genetic distances. These
>> different
>> distance measures are used to create alternative graphs as they represent
>> the links (or edges) between the nodes (vertices).
>> I would like to compare 3 types of graphs:
>> 1. Complete (saturated graphs where all nodes are connected to one
>> another)
>> 2. Gabriel graphs,
>> 3. minimum spanning trees
>>
>> I can build complete and minimum spanning trees using both distance types
>> as
>> weights for the links. For the minimum spanning tree situation, this
>> creates
>> 2 very different looking graphs. I am currently not able to create Gabriel
>> graphs using an alternative to Euclidean distance as links between nodes.
>> Although, gabriel graphs are a type of planar graph, it is my
>> understanding
>> that one should be able to construct Gabriel graphs based on alternative
>> distance measures. In the population genetics software it is possible to
>> do
>> this. The result is generally 2 Gabriel graphs where the links between
>> nodes
>> are in different locations (i.e. the graphs should not look identical). I
>> would like to do this in R but am running into trouble as the Garbriel
>> functions seem to only use coordinates as inputs. I have looked into the
>> following packages: spdep (spatial neighbour applications), igraph,
>> spatgraphs, ade4.
>>
>> The data I have are:
>> 1. coordinates of nodes (vertices)
>> 2. pairwise distance matrix of genetic and euclidean distance between
>> nodes
>>
>> Here is a small bit of code using some simulated data.
>>
>> # Create coordinate data
>> x <- round(runif(20,1,10),1)
>> y <- round(runif(20,5,10),1)
>> xy <- cbind(x,y)
>> # Create gabriel graph based on Euclidean distance
>> col.gab <- graph2nb(gabrielneigh(xy))
>> plot(col.gab,xy)
>>
>>
>> # create a matrix of weights: in my case this represents measures of
>> genetic
>> distance between each pair of nodes
>> # diagonal = 0
>> # lower and upper matrix parts have identical values
>> genetic <- matrix(0,nrow=20,ncol=20)
>> genetic <- matrix(rnorm(500, 0.5, 0.25),nrow=20,ncol=20)
>> genetic[lower.tri(genetic)] <- genetic[upper.tri(genetic)]
>> diag(genetic)<-c(rep(0,length(genetic[1,])))
>>
>>
>> Weighting the links after the Gabriel graph is created based on Euclidean
>> distance does not make sense for me.
>> If anyone has an idea of how I might try and create Gabriel graphs based
>> on
>> a distance measure that is not Euclidean, I would love to hear it.
>>
>> Thanks in advance for everyone's help.
>>
>
> In an earlier thread relevant to this topic, it was suggested that syntheic
> coordinates could be extracted from multidimensional scaling of the
> non-Euclidean distance matrix. You could try this, and judge how far from
> what you need you land by doing complete and MST on the synthetic
> coordinates for comparison. If this shows that the synthetic coordinates are
> no use, you'll be obliged to program your own Gabriel function for
> user-supplied distances. If you'd like to contribute such a function back, I
> think others would be grateful.
>
> Hope this helps,
>
> Roger
>
>
>> I am currently using R (v.2.10.1) on Windows XP.
>>
>> Ilona Naujokaitis-Lewis, PhD student
>>
>>
>>
> --
> Roger Bivand
> Economic Geography Section, Department of Economics, Norwegian School of
> Economics and Business Administration, Helleveien 30, N-5045 Bergen,
> Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
> e-mail: Roger.Bivand@nhh.no
>
>


-- 
Ilona Naujokaitis-Lewis
ilona.naujo.lewis@gmail.com
phone: 647.668.6239

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