  In many real network systems, nodes usually cooperate with each other and
form groups, in order to enhance their robustness to risks. This motivates us
to study a new type of percolation, group percolation, in interdependent
networks under attacks. In this model, nodes belonging to the same group
survive or fail together. We develop a theoretical framework for this novel
group percolation and find that the formation of groups can improve the
resilience of interdependent networks significantly. However, the percolation
transition is always of first order, regardless of the distribution of group
sizes. As an application, we map the interdependent networks with
inter-similarity structures, which attract many attentions very recently, onto
the group percolation and confirm the non-existence of continuous phase
transitions.
