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Network intervention problems often benefit from selecting a highly-connectednode to perform interventions using these nodes, e.g. immunization. However, inmany network contexts, the structure of network connections is unknown, leadingto a challenge. We develop and examine the mathematical properties of twodistinct informationally light strategies, a novel global strategy and localstrategy, that yield higher degree nodes in virtually any network structure. Wefurther identify a novel network property called Inversity, whose signdetermines which of the two strategies, local or global, will be most effectivefor a network. We demonstrate that local and global strategies obtain aseveral-fold improvement in node degree relative to a random selectionbenchmark for generated and real networks (including contact, affiliation andonline networks). In some networks, they achieve a 100-fold improvement. Weshow how these new strategies can be used to control contagion of an epidemicspreading across a set of village networks, finding that the strategiesdeveloped here require far fewer ($<50\%$) nodes to be immunized, relative tothe random strategy baseline. Prior research has typically used the completenetwork structure to choose nodes for optimal seeding. The relevant network isoften costly to collect, and is privacy-invasive, requiring knowing eachperson's network neighbors, and might not be possible to obtain fortime-sensitive interventions. Our interventions are less invasive of individualprivacy, since each selected node only needs to nominate some network neighborsfor intervention, while mathematically guaranteed to provide better connectednodes.

Interventions with Inversity in Unknown Networks Can Help Regulate Contagion