  Consider spies infiltrating a network or dissidents secretly organising under
a dictatorship. Such scenarios can be cast as adversarial social network
analysis problems involving nodes connecting while evading network analysis
tools, e.g., centrality measures or community detection algorithms. While most
works consider unilateral actions of an evader, we define a network formation
game. Here, several newcomers attempt to rewire the existing social network, to
become directly tied with the high centrality players, while keeping their own
centrality small. This extends the network formation literature, including the
Jackson and Wolinsky model, by considering additional strategies and new
utility functions. We algorithmically demonstrate that the pairwise Nash stable
networks (\PANS) constitute a lattice, where the stronger \PANS{} lattice is
nested in the weaker \PANS. We also prove that inclusion in \PANS{} implies
less utility for everyone. Furthermore, we bound the social efficiency of
\PANS{} and directly connect efficiency to the strength of \PANS. Finally, we
characterise the \PANS{} in practically important settings, deriving tight
efficiency bounds. Our results suggest the hiders how to interconnect stably
and efficiently. Additionally, the results let us detect infiltrated networks,
enhancing the social network analysis tools. Besides the theoretical
development, this is applicable to fighting terrorism and espionage.
