These functions score a drawing rather than the network it draws, so that a layout can be compared with another on the same network.
check_span() reports how many rows of nodes each tie crosses.
A layered layout should send most ties to the next row down,
and a long tie is one that skips rows to get where it is going.
check_offset() reports how far each tie travels sideways,
as a share of the width of the whole drawing.
A tie that drops straight down scores zero.
check_stress() reports how far the distances drawn
depart from the distances through the network.
A layout that draws two nodes twice as far apart as two others
should be drawing a path twice as long.
Source
Kruskal, Joseph B. 1964. "Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis", Psychometrika 29(1): 1-27. doi:10.1007/BF02289565
Arguments
- x
A plot, as
graphr()returns.
Value
check_span() returns one whole number for each tie,
with total and mean attributes holding the sum and the average.
check_offset() returns one number between 0 and 1 for each tie,
with a mean attribute.
check_stress() returns a single number of 0 or more,
with a scale attribute holding the factor the drawn distances were
scaled by, and a pairs attribute holding how many pairs were scored.
Details
check_span() and check_offset() answer different questions,
and a layered layout needs both answered.
check_span() asks whether the rows were well chosen,
and check_offset() asks whether the nodes were well placed within them.
The "layered" layout minimises each in turn, and its ranks and
alignment arguments choose how.
Which axis holds the rows is read from the plot,
as the axis on which the nodes take fewer distinct positions.
This is the y axis for "layered" and the x axis for "lineage",
so the same score can be compared across the two.
For a layout with no rows at all, such as "stress",
check_span() reports the distance in that axis' ranks,
which is not meaningful; the function is for layered layouts.
check_stress() applies to any layout, since every layout draws its
nodes some distance apart, and the score is the share of the path
distances that the drawn distances get wrong.
It is Kruskal's stress-1, so 0 is a perfect drawing,
and Kruskal read 20% as poor, 10% as fair, 5% as good,
and 2.5% as excellent.
Those figures were set for psychometric data rather than for networks,
which are harder: most pairs of nodes in a small-world network sit
two or three steps apart, and a plane holds few such distances at once,
so a score near 30% is ordinary and one near 5% is rare.
A layout that never set out to draw path distances,
such as "layered", "circle" or "configuration",
scores poorly by design.
The score belongs to the drawing rather than to the network,
which is what separates it from the share of distance variance
that graphr() reports beside it.
Draw one network two ways and the stress changes, since one drawing
holds its distances better than the other;
the share of variance does not, since two dimensions can hold
just as much of that network either way.
A network whose variance is held poorly sets a floor
that no layout gets under.
The drawn distances are scaled to the path distances before they are
compared, since a layout may place its nodes on any scale it likes,
and the ties are counted unweighted, as layout_scaling() counts them.
Where a network is disconnected, the pairs with no path between them
are left out of the score.
Examples
thrones <- manynet::to_uniplex(manynet::fict_thrones, "parent")
# The default graph is drawn once here, since each check reads the same plot.
drawn <- graphr(thrones)
# How long are the ties of the default layout?
attr(check_span(drawn), "total")
#> [1] 270
# How straight are they?
attr(check_offset(drawn), "mean")
#> [1] 0.03420039
# Compare with the layers igraph would have chosen:
# attr(check_span(graphr(thrones, ranks = "compact")), "total")
# Which layout draws the path distances best?
check_stress(graphr(manynet::ison_southern_women, layout = "scaling"))
#> [1] 0.3129352
#> attr(,"scale")
#> [1] 1.146146
#> attr(,"pairs")
#> [1] 992
check_stress(graphr(manynet::ison_southern_women, layout = "circle"))
#> [1] 0.5157822
#> attr(,"scale")
#> [1] 1.46639
#> attr(,"pairs")
#> [1] 992