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.

翻译：我们提出了一种新方法，用于计算具有层间节点重要性约束的多层网络中的特征向量中心性变体。具体而言，考虑一个由多个加权有向图（可能为有向图）定义的多层网络，这些图共享同一节点集，每个图代表网络的一个层，且层间无连边。与标准特征向量中心性构建类似，给定层中每个节点的重要性基于该层内相邻节点重要性的加权和。但与标准特征向量中心性不同，我们允许邻接关系及其相邻节点的重要性基于不同层。值得注意的是，现有基于跨层节点连边捕获层间依赖性的多层特征向量中心性框架仅部分支持此类中心性约束。在我们的模型中，受约束的层特异性特征向量中心性值由独立特征值问题与依赖伪特征值问题构成的方程组定义，可通过交错幂迭代算法高效求解。