Chapter 6

Relations, Networks, Flows

In this chapter the focus is squarely on networks (which mathematicians confusingly insist on calling graphs) and their potential for more relational understandings of space in giscience. As much of the code associated with the figures in this chapter shows, handling such structure elegantly is not something existing geospatial tools do well.

Links for Chapter 6

The number of possible shortest paths, i.e., pairs of vertices, choosable from a graph of any given size is given by the numbers in integer sequence A000522.

Figures 6.5 and 6.6 Reduced world city network viewed various ways

This page includes python code derived from the code that was used to generate these figures. Again, you will see just how troublesome the limitations of existing platforms…

Figure 6.7 World trade network communities

Here is a colour version of this figure, which is a lot easier to make sense of than the black and white version in print.

Figure 6.10 The small world rewiring process

The figure in the book shows only three rewiring steps for the sake of space. Here we show 11 with increasing probability of rewiring at each step of 0.05.

Figure 6.11 The small world rewiring process in two dimensions

Here the small world network phenomenon based on ‘rewiring’ is shown for a two-dimensional lattice. This particular network structure is less studied than might be expected…

Figure 6.12 A simple graph drawn nine different ways

The main difference here is that the output is in colour, which might make it easier to see what’s going on.

Figure 6.14 Relative time map of the Santa Barbara street network

This started out as the notebook developed by Geoff Boeing available here although by now it has been very heavily modified!

© 2023 David O’Sullivan