Today, we have to cope with a great amount of data – BIG data problems. The main issues concerned about BIG data are sparing representation, time efficiency of data access and processing, as well as data mining and knowledge discovery. When dealing with the big amount of data, time is crucial. The most of time for data processing in the contemporary computer science is lost for a various search operation to access appropriate data. This paper presents how data collected in relational databases can be transformed into the associative neuronal graph structures, and how searching operations can be accelerated thanks to the use of aggregation and association of the stored data. To achieve an extraordinary efficiency in data access, this paper introduces new AVB+trees which together with Deep Associative Semantic Neuronal Graphs which can typically allow for constant time access to the stored data. The presented solution allows representing horizontal and vertical relations between data and stored objects, expanding possibilities of relational databases and replacing various search operations by the specific graph structure. Another contribution is the expansion of the aggregation of the duplicates to all data tables which contain the same attributes. In such a way, the presented associative structures simplify and speed up all searching operations in comparison to the classic solutions.