Now it comes a bigger problem. Due to budget constraint, you only have sampled all of the nodes within a rectangular plot. They are the total 100 nodes you have in Unlimited-Networks (I).

This constraint suggests that we do not have an entire network – there would be more nodes outside the plot of which data we are unable to obtain. This is unfortunate as an incomplete network would just affect concerned analyses. To solve this problem, one may think to hypothetically generate nodes outside the plot, perhaps based on the spatial pattern of the nodes inside the plot. Here, nevertheless, I am going to propose an alternative solution. We will simply use the information we have in hand to approach the reality.

Let’s say the spatial coordinates of the four corners of the plot are, respectively, (-240, -270), (240, -270), (-240, 270), (240, 270).

There would be some nodes located within distance d to one of the four rectangular plot boundaries. Insert visualization If this is the case, the nodes themselves and the nodes they share the same compartments with should be removed as they potentially are connected to the unknown nodes outside the plot.

To deal with this issue, we can write another function. I will apply the fundamental matrix of Markov Chain as it works really fast and accurately generates compartments within networks. For now, I save the effort of explaining why this works. A thorough explanation will appear in a R package or an academic paper.

nt_inv <- function(d) {
    DM <- dist[] < d
    diag(DM) = 0
    I <- diag(1, nrow=nrow(dist), ncol=ncol(dist))
    D <- sapply(1:nrow(dist), function(z) DM[,z]/(z+1)) 
    inv <- solve(I-D)
    return(inv)
    }

This function gives us a 100 x 100 matrix signaling whether any two nodes are within the same compartment. For each pair of two nodes i and j in the same compartment, nt_inv(d)[i,j] will be a non-zero value. Otherwise, nt_inv(d)[i,j] will be zero. In addition, nt_inv(d)[i,i] for i in 1 to 100 will be always one.

This helps understand the compartment of each node, a basis for further coding. Continue