People Prefer Less Stress and Fewer Crossings - Graph Drawing - page 522

People Prefer Less Stress and Fewer Crossings

Markus Chimani 1 , Patrick Eades 2 , Peter Eades 2 , Seok-Hee Hong 2 , Weidong Huang 3 ,
Karsten Klein 2 , Michael Marner 4 , Ross T. Smith 4 ,andBruce H. Thomas 4

1 University of Osnabr uck, Germany
[e-mail]
2 University of Sydney, Australia
[e-mail],
{ peter.eades,seokhee.hong,karsten.klein } @sydney.edu.au
3 University of Tasmania, Australia
[e-mail]
4 University of South Australia, Adelaide, Australia
{ michael.marner,ross.smith,bruce.thomas } @unisa.edu.au

Human experiments in Graph Drawing,such as the seminal papers of Purchase et al. [1],
have concentrated on tasks ,such as path-tracing. Here we report the first results in an
ongoing series of experiments to investigate the geometric properties of graph drawings
that users prefer . The specific experiment described in this poster investigates the impact
of edge crossings and stress in straight-line drawingsonhuman preference. Ourresults
suggest a positive preference for drawings with less stress and fewer crossings.

Experiment. Seventy nine subjects were recruited; subjects were about 50% Computer
Science students and 50% Cognitive Science at the University of Osnabr uck. After
standard introductory material, subjects were shown a sequence of ten “instances”. Each
instance consisted of a screen containing apairofgraph drawings. The subject was
asked to click on which one of the pair they prefer. A typical screenshot is in Fig.1.The
data set used in the experiment comes from publicly available graph sets, including the
Hachul library, Walshaw'sGraphPartitioning Archive, and sets of randomly generated
biconnected and scale free graphs (using the OGDF generators). We used a total of 118
graphs, ranging in size from small (25 nodes and 29 edges) to moderately large (8000
nodes and 15580 edges). For each graph in the data set, fourdrawingswerecomputed
using a force-directed method; these fourdrawings varied in stress and crossings. For
each instance of the experiment, a graph was randomly selected from the data set, and
two drawingsofthefourdrawingsofthatgraph were randomly selected and displayed
as in Fig.1.Thesubject was then asked to click on the drawing that he/she prefers.

Results. The subject preferred the drawing with less (scaled 1 ) stress in 57% of all (790)
instances, and preferred the drawing with fewer crossings in 65% of all instances. We
found that preference for lower stress drawings increases with (scaled) stress ratio ,that
is, the ratio of the stress between the two drawings presented to the user, to a maxi-
mum of 70% of instances when stress ratio is greater than 4. Curiously, the percentage