# Network Capacity Bound for Personalized PageRank in Multimodal Networks

## TL;DR

This paper extends the concept of Personalized PageRank to multimodal hypergraph networks, providing theoretical bounds on authority flow and a generalized PageRank model for such complex structures.

## Contribution

It introduces a generalized PageRank for multimodal hypergraphs and proves theorems on authority flow limits under various damping factor conditions.

## Key findings

- Theorems on authority flow limits in multimodal networks.
- A generalized PageRank model for hypergraph structures.
- Analysis of damping factor effects on authority distribution.

## Abstract

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.