  We present a novel approach for computing a variant of eigenvector centrality
for multilayer networks with inter-layer constraints on node importance.
Specifically, we consider a multilayer network defined by multiple
edge-weighted, potentially directed, graphs over the same set of nodes with
each graph representing one layer of the network and no inter-layer edges. As
in the standard eigenvector centrality construction, the importance of each
node in a given layer is based on the weighted sum of the importance of
adjacent nodes in that same layer. Unlike standard eigenvector centrality, we
assume that the adjacency relationship and the importance of adjacent nodes may
be based on distinct layers. Importantly, this type of centrality constraint is
only partially supported by existing frameworks for multilayer eigenvector
centrality that use edges between nodes in different layers to capture
inter-layer dependencies. For our model, constrained, layer-specific
eigenvector centrality values are defined by a system of independent eigenvalue
problems and dependent pseudo-eigenvalue problems, whose solution can be
efficiently realized using an interleaved power iteration algorithm.
