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Speed is a great concern in the recursive shortest spanning tree (RSST) algorithm as its applications are focused on image segmentation and video coding, in which a large amount of data is processed. Several efficient RSST algorithms have been proposed in the literature, but the linking properties are not properly addressed and used in these algorithms and they are intended to produce a truncated RSST. This paper categorizes the linking process into three classes based on link weights. These linking processes are defined as the linking process for link weight equal to zero (LPLW-Z), the linking process for link weight equal to one (LPLW-O), and the linking process for link weight equal to real number (LPLW-R). We study these linking properties and apply them to an efficient RSST algorithm. The proposed efficient RSST algorithm is novel, as it makes use of linking properties, and its resulting shortest spanning tree is truly identical to that produced by the conventional algorithm. Our experimental results show that the percentages of links for the three classes are 17%, 27%, and 58%, respectively. This paper proposes a prediction method for LPLW-O, as a result of which the vertex weight of the next region can be determined by comparing sizes of the merging regions. It is also demonstrated that the proposed LPLW-O with prediction approach is applicable to the multiple-stage merging. Our experimental results show that the proposed algorithm has a substantial improvement over the conventional RSST algorithm.