  Network intervention problems often benefit from selecting a highly-connected
node to perform interventions using these nodes, e.g. immunization. However, in
many network contexts, the structure of network connections is unknown, leading
to a challenge. We develop and examine the mathematical properties of two
distinct informationally light strategies, a novel global strategy and local
strategy, that yield higher degree nodes in virtually any network structure. We
further identify a novel network property called Inversity, whose sign
determines which of the two strategies, local or global, will be most effective
for a network. We demonstrate that local and global strategies obtain a
several-fold improvement in node degree relative to a random selection
benchmark for generated and real networks (including contact, affiliation and
online networks). In some networks, they achieve a 100-fold improvement. We
show how these new strategies can be used to control contagion of an epidemic
spreading across a set of village networks, finding that the strategies
developed here require far fewer ($<50\%$) nodes to be immunized, relative to
the random strategy baseline. Prior research has typically used the complete
network structure to choose nodes for optimal seeding. The relevant network is
often costly to collect, and is privacy-invasive, requiring knowing each
person's network neighbors, and might not be possible to obtain for
time-sensitive interventions. Our interventions are less invasive of individual
privacy, since each selected node only needs to nominate some network neighbors
for intervention, while mathematically guaranteed to provide better connected
nodes.
