  Node-link diagrams are widely used to visualise networks. However, even the
best network layout algorithms ultimately result in 'hairball' visualisations
when the graph reaches a certain degree of complexity, requiring simplification
through aggregation or interaction (such as filtering) to remain usable. Until
now, there has been little data to indicate at what level of complexity
node-link diagrams become ineffective or how visual complexity affects
cognitive load. To this end, we conducted a controlled study to understand
workload limits for a task that requires a detailed understanding of the
network topology---finding the shortest path between two nodes. We tested
performance on graphs with 25 to 175 nodes with varying density. We collected
performance measures (accuracy and response time), subjective feedback, and
physiological measures (EEG, pupil dilation, and heart rate variability). To
the best of our knowledge, this is the first network visualisation study to
include physiological measures. Our results show that people have significant
difficulty finding the shortest path in high-density node-link diagrams with
more than 50 nodes and even low-density graphs with more than 100 nodes. From
our collected EEG data we observe functional differences in brain activity
between hard and easy tasks. We found that cognitive load increased up to a
certain level of difficulty after which it decreased, likely because
participants had given up. We also explored the effects of global network
layout features such as size or number of crossings, and features of the
shortest path such as length or straightness on task difficulty. We found that
global features generally had a greater impact than those of the shortest path.
