  High-centrality nodes have disproportionate influence on the behavior of a
network; therefore controlling such nodes can efficiently steer the system to a
desired state. Existing multiplex centrality measures typically rank nodes
assuming the layers are qualitatively similar. Many real systems, however, are
comprised of networks heterogeneous in nature, for example, social networks may
have both agnostic and affiliative layers. Here, we use rank aggregation
methods to identify intervention targets in multiplex networks when the
structure, the dynamics, and our intervention goals are qualitatively different
for each layer. Our approach is to rank the nodes separately in each layer
considering their different function and desired outcome, and then we use Borda
count or Kemeny aggregation to identify a consensus ranking - top nodes in the
consensus ranking are expected to effectively balance the competing goals
simultaneously among all layers. To demonstrate the effectiveness of consensus
ranking, we apply our method to a degree-based node removal procedure such that
we aim to destroy the largest component in some layers, while maintaining
large-scale connectivity in others. For any multi-objective intervention,
optimal targets only exist in the Pareto-sense; we, therefore, use a weighted
generalization of consensus ranking to investigate the trade-off between the
competing objectives. We use a collection of model and real networks to
systematically investigate how this trade-off is affected by multiplex network
structure. We use the copula representation of the multiplex centrality
distributions to generate model multiplex networks with given rank
correlations. This allows use to separately manipulate the marginal centrality
distribution of each layer and the interdependence between the layers and to
independently investigate the role of the two using both analytical and
numerical methods.
