  Data collection often involves the partial measurement of a larger system. A
common example arises in collecting network data: we often obtain network
datasets by recording all of the interactions among a small set of core nodes,
so that we end up with a measurement of the network consisting of these core
nodes along with a potentially much larger set of fringe nodes that have links
to the core. Given the ubiquity of this process for assembling network data, it
is crucial to understand the role of such a `core-fringe' structure.
  Here we study how the inclusion of fringe nodes affects the standard task of
network link prediction. One might initially think the inclusion of any
additional data is useful, and hence that it should be beneficial to include
all fringe nodes that are available. However, we find that this is not true; in
fact, there is substantial variability in the value of the fringe nodes for
prediction. Once an algorithm is selected, in some datasets, including any
additional data from the fringe can actually hurt prediction performance; in
other datasets, including some amount of fringe information is useful before
prediction performance saturates or even declines; and in further cases,
including the entire fringe leads to the best performance. While such variety
might seem surprising, we show that these behaviors are exhibited by simple
random graph models.
