Connectedness of users-items networks and recommender systems

Recommender systems have become an important issue in network science. Collaborative filtering and its variants are the most widely used approaches for building recommender systems, which have received great attention in both academia and industry. In this paper, we studied the relationship between recommender systems and connectivity of users-items bipartite network. This results in a novel recommendation algorithm. In our method recommended items are selected based on the eigenvector corresponding to the algebraic connectivity of the graph - the second smallest eigenvalue of the Laplacian matrix. Since recommending an item to a user equals to adding a new link to the users-items bipartite graph, the intuition behind the proposed approach is that the items should be recommended to the users such that the least increase in the connectedness of the network (i.e., the algebraic connectivity) is obtained. Through experiments on a number of benchmark datasets, we showed that the proposed connectivity-based recommendation method has comparable results to a number of commonly used recommendation methods. These results shed light on the relation between the evolution of users' behavior and network topology