The big graph database model provides strong modeling for complex applications and efficient querying. However, it is still a big challenge to find all exact matches of a query graph in a big graph database, which is known as the subgraph isomorphism problem. The current subgraph isomorphism approaches are built on Ullmann's idea of focusing on the strategy of pruning out the irrelevant candidates. Nevertheless, the existing pruning techniques need much more improvement to efficiently handle complex queries. Moreover, many of those existing algorithms need large indices requiring extra memory consumption. Motivated by these, we introduce a new subgraph isomorphism algorithm, named as BB-Graph, for querying big graph databases efficiently without requiring a large data structure to be stored in main memory. We test and compare our proposed BB-Graph algorithm with two popular existing approaches, GraphQL and Cypher. Our experiments are done on three different data sets; (1) a very big graph database of a real-life population database, (2) a graph database of a simulated bank database, and (3) the publicly available World Cup big graph database. We show that our solution performs better than those algorithms mentioned here for most of the query types experimented on these big databases.