I have a large directed graph, and I try to access every edge for this digraph. The problem is to minimize the number of the access (a connected subgraph is counted as one access). And it reduces to count the minimum number of connected subgraph that covers the whole digraph.
Is there any existing study or algorithm in this area?

I found some related topic such as finding the largest Eulerian subgraph, but it is different to find the minimum number of subgraphs.