Abstract: For there exist routing decision making difficulties and weak precision of path eigenvalues in graph outline extraction with reachable path decision as its core,the MST growth algorithms are proposed to hierarchically extract graph outline.The topological structure of graph routing is partitioned into two parts,including intra-domain routing and inter-domain routing.By recombining coherent paths of no-dominated points,the weighted undirected graph with dominated points as its nodes is established in intra-domain routing.And based on MST of the undirected graph,utilizing the unique reachability between any two trees nodes,the MST growth algorithms are constructed in inter-domain routing.Then,the entire graph outline is extracted with the above processes achieved.An example and a practical application validate the feasibility and effectiveness of the proposed algorithms.