Cobweb of flows - The Visualization of Spatial Social Structure - page 175

method chosen. From seeing these pictures you could think you might draw
lines dividing the headwaters of the flow to define travel to work catchments.
Whether that is possible or not depends on how much flows cross over, how
many people travel in the same direction, how you measure flow and on how
many people travel at all.

6.4 Drawing the vortices

All the variations introduced by spatial, numerical and temporal
aggregation procedures operate on origin and destination data in an
almost more bewildering variety than they do on static data. ... we
summarise by trying to pick out the main bundles of arrows moving
between pairs of areal units. Thus it depends entirely what size,
shape and position of spatial units we use, what apparent bundles we
pick up.

(Forbes, 1984, p. 99)

The objects that have been discussed up to now have been vectors, single
attributes for sets of single areas - average direction and magnitude of flow.
These are all simply summaries. It can be better to attempt to draw the matrix,
not just a tangle of lines connecting all places between which people flow
but a picture that shows the static structure of the change in as much detail
as possible.
Lines can be used to show matrices of flow, as areas can be used to depict
scales of attributes. Lines have length, width, colour, direction (indicated by
arrowhead), and can be given order as they overlap. The first of these quali-
ties, length, conveys the strongest information, but is most difficult to use, as
the line links two places, and to alter its length would make that connection
ambiguous.
The best choice we have, which has most influence over the final image, is
whether to draw any particular line at all (Figures 6.9 and 6.10). With areas, this
is not a choice; there is a place for every area. With lines, there is only enough
space for a minority to be shown (between more than a couple of dozen places).
A line should be drawn between two places only if the flow between those places
is significant. But what is a significant flow?
There is a second and linked difficulty to determining which flows are worth
showing; this is the most serious effect of what some geographers call the modi-
fiable areal unit problem: the problem that the boundaries of each area influence
any statistics of that area. For mapping a simple variable the problem is largely
overcome by the use of many small areas and by using cartograms of the denom-
inator of the rate to be mapped. The problem is that the shapes, on the ground,
of the arbitrary areas between which flows are recorded will affect the number