[R] connection network - influence of site

[Guillaume Blanchet]

Dear R users,

I'm trying to construct a distance matrix based on a nb object 
created by spdep where sites must have a larger influence in one 
direction then in the other.

Here is an example to better illustrate what I need:

Let say I have the following Gabriel connection network


library(spdep)
library(ade4)
data(orbatid)

nbgab<-graph2nb(gabrielneigh(as.matrix(oribatid$xy)))
plot(nbgab,oribatid$xy)

text(oribatid$xy,as.character(1:70),pos=1) # site number
arrows(-0.3,0,-0.3,10) # gradient direction


In that example, site 1 shouldn't influence site 2 (so it should have 
a distance if 0 in the distance matrix). However site 1 should 
influence site 7 (1 in the distance matrix), it should also influence 
site 12 and 10 (2 in the distance matrix), and site 13,14,17 and 20 
(3 in the distance matrix) and so on for every site. Also, the 
smallest number of "jumps" from one site to the other has to be 
considered (e.g. 1 to 20 can be connected through 3 links (1 -> 7 -> 
10 -> 20) or through 4 links (1 -> 7 ->  12 -> 13 -> 20)).

Considering the gradient, it has to be noted that the distance matrix 
will be asymmetric (e.g. site 7 doesn't influence site 1).

This needs to be done for various connection network, going from 
regular grid (rook connections) to networks such as the one presented 
above.

Can it be done ? If it can, I would be very happy for some one to 
give me a hand. And if it has already been done I would be glad to be 
pointed in the right direction.


Thanks in advance !!

Guillaume Blanchet