I want to construct a Region Adjacency Graph from Handwritten word , after necessary image processing and connected component labeling ??

after necessary image processing like binarisation,thinning,connected component labeling. I am getting an image with different connected components, starting from background component having index 0, then 1,2,............ I want to construct region adjacency graph (RAG) from the image. Problem is background component is every where between the regions, I am getting graph in which all the regions are connected with single region that is background component labelled as 0.....How to construct the RAG without background component...