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Since abdominal blood vessels have complicated branching structures, understanding them is important to perform abdominal surgeries. In this paper, we propose a method for automated analysis of branching structures of abdominal arteries and hepatic portal system. A blood vessel region is expressed as a tree structure. Likelihoods of candidate anatomical names for each branch in the tree structure is computed by utilizing a machine learning-based method. Possible branching patterns are expressed as a graph whose edges are assigned weights based on the likelihoods of the branches in the tree structure. The directed spanning tree of the graph represents a branching pattern. The optimum branching pattern is obtained by computing the directed maximum spanning tree. Each branch in the tree structure is labeled anatomical names based on the branching pattern. 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