In a real-time transaction processing system, Minka is utilizing Neo4j to model transactions as graphs, which allows for efficient and fast processing of financial information. Prior to adopting Neo4j, the system used relational databases but found them to be slow due to the need to join tables to find connected nodes. The use of Neo4j's index-free adjacency feature has greatly improved performance by allowing for direct connections between nodes without the need for joins. Minka's experience with Neo4j has enabled the company to push the boundaries of what is possible in real-time transaction processing, including faster data migration and more efficient query execution. As the company continues to scale, they are exploring the use of full graphs in AuraDB and envisioning a future where multiple transaction-processing clusters are connected to facilitate fast and secure transactions across different regions. The developer sees a vast potential for graph technology in solving complex problems and modeling connections between seemingly unrelated entities, which is reflected in their enthusiasm for Neo4j and its applications.