In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we deal with a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. We state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.

翻译：在先前的论文中，我们引入了二分PageRank的概念，并推广了关于个性化PageRank中权威值在节点间流动极限的定理。本文旨在将这些结果扩展至多模态网络。具体而言，我们处理一种可用于描述多模态网络的超图类型，其中超链接连接来自每种模态的节点。我们针对此类图引入PageRank的推广形式，并定义可用于计算的相应随机游走模型。我们阐述并证明了在单个模态具有相同和不同阻尼因子情况下权威值流出极限的定理。