Ranking on Multipartite Graphs

Graphs are commonly used to model complex and large scaled structures. Friendship relations on a social platform, recommendations in big online marketplaces like e-bay or Amazon, or the link structure of the web, are examples for such structures. It is generally accepted (and appreciated) that these huge web structures tend to grow. But with a growing amount of stored data and higher complexity of the networks, one has to find new scalable analysing tools that supply reliable information about the vertices e.g. actors in these networks. Ranking algorithms are such tools that map each node to a specific weight due to its specific behaviour in the system. Ranking on multipartite graphs is of special interest. Such graphs can be used to model systems with typed elements, for example a university with lecturers, courses and students, or buyers and sellers in an online marketplace. In this thesis a new eigenvector based ranking-algorithm is proposed: theAn−Hn-Rank. It is designed to be applied on multipartite graphs with any number of types. First, the structure of multipartite graphs is examined, and the mathematical preliminaries are developed, on which the algorithm is based. The convergence of the algorithm is proven, and the algorithm is applied to gathered data.