In this paper we propose an adaptive local pruning method for association rules. Our method exploits the exact mapping between a certain class of association rules, namely those whose consequents are singletons and backward directed hypergraphs (B-Graphs). The hypergraph which represents the association rules is called an Association Rules Network(ARN). Here we present a simple example of an ARN. In the full paper we prove several properties of the ARN and apply the results of our approach to two popular data sets.