The purpose of this paper is the expansion of the set-based model, namely an information retrieval model, with the use of graphs. The indexing process implements a graphical representation, while the querying and document representation are based on the classical set-based model. The root of the set-based model corresponds to the use of term sets to complete the querying process based on the terms of the query. However, in the weighting process, this paper presents a wholly different approach elaborating on algorithms that may clearly benefit the process based on the k-core decomposition of each single graph. The main focus will finally be the estimation and presentation of the most important nodes belonging to each graph. These intend to be regarded as keywords presenting the evaluation of their major influence.