  Probabilistic graphs are challenging to visualize using the traditional
node-link diagram. Encoding edge probability using visual variables like width
or fuzziness makes it difficult for users of static network visualizations to
estimate network statistics like densities, isolates, path lengths, or
clustering under uncertainty. We introduce Network Hypothetical Outcome Plots
(NetHOPs), a visualization technique that animates a sequence of network
realizations sampled from a network distribution defined by probabilistic
edges. NetHOPs employ an aggregation and anchoring algorithm used in dynamic
and longitudinal graph drawing to parameterize layout stability for uncertainty
estimation. We present a community matching algorithm to enable visualizing the
uncertainty of cluster membership and community occurrence. We describe the
results of a study in which 51 network experts used NetHOPs to complete a set
of common visual analysis tasks and reported how they perceived network
structures and properties subject to uncertainty. Participants' estimates fell,
on average, within 11% of the ground truth statistics, suggesting NetHOPs can
be a reasonable approach for enabling network analysts to reason about multiple
properties under uncertainty. Participants appeared to articulate the
distribution of network statistics slightly more accurately when they could
manipulate the layout anchoring and the animation speed. Based on these
findings, we synthesize design recommendations for developing and using
animated visualizations for probabilistic networks.
