Centrality Analysis in $d$ -Regular Directed Acyclic Random Networks and Its Applications in Top- $k$ Recommendations

Centrality analysis has been a very important research topic in online social networks. Traditionally, centrality analysis is carried out for a specific network. In this article, we conduct centrality analysis in random networks. For this, we consider the class of d-regular directed acyclic random networks generated by the configuration model. We consider two centralities: the PageRank and the in-component centrality (defined as the size of the in-component of a node). For the PageRank, we derive a closed-form solution in the complete directed acyclic network and show that it can be used as an approximation in a d-regular directed acyclic random network. For the in-component centrality, we derive upper bounds for its first moment and its second moment in a d-regular directed acyclic random network. These results have interesting applications in top-k recommendations. In particular, we propose a qualifying round algorithm that outputs a set of nodes to include the top-k nodes with high probability. Various experiments are conducted to show the effectiveness of the algorithm.