In graph networks, graph structural analytics such as betweenness centrality has played an important role in finding the most central vertices in graph data. Hence, betweenness centrality has been heavily applied to discover the most important genes with respect to multiple diseases in biomedicine research. Considering color as a property of graph data to represent different categories for the nodes and edges in the graph, we may investigate the betweenness centrality of each colored subgraph composed of a specific color. However, as investigators may be interested in querying betweenness centrality on multiple combinations of the colored subgraphs, the total execution time on all the subgraphs may be excessively long, considering all the possible combinations. In addition, the performance could be worse when the size of the graph grows larger. In this research, we propose an approach to computing betweenness centrality by incorporating node colors and edge colors. We propose that the node with the highest betweenness centrality can be computed for a very large and colored graph by decomposing the graph into colored subgraphs and merging the result from the base cases. Furthermore, we compare our approach with the conventional approaches in the experiments, and we demonstrate that our scalable approach is more efficient when finding the global backbone node with the highest betweenness centrality.