重心法、邊路徑法與新邊路徑位序法在三階正規階層結構圖上之比較分析

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Abstract

In the recent year, we have a significant effect making use of the concept diagram or the learning hierarchy map to confer concept learning. Kozo Sugiyama proposed BCM in 1981, not only to promote technology of analysis but also to increase the practicability and readability of hierarchical graph. A modified BCM developed by Tsai reduced time spend on discussion when the identical Barycenter.

Liu proposed EM and EOM in 2004, had been highly regarded among the scholars studying hierarchy. Thus, our purpose is to improved of EOM and then on effects of BCM, EM and NEOM for reducing the crossed edges in proper hierarchical graphs of three layers.

Our results are as follows. Assume that G is a proper hierarchical graph of three layers and has the same indegrees in the 2nd and 3rd layers.

1. We obtain 10 graphs in which the number of the crossed edges reduced by BCM, EM and NEOM respectively has the following relation; BCM < EM < NEOM. 2. We obtain 10 graphs in which the number of the crossed edges reduced by BCM, EM and NEOM respectively has the following relation; BCM < NEOM < EM. 3. We obtain 208 graphs in which the number of the crossed edges reduced by BCM, EM and NEOM respectively has the following relation; BCM < EM = NEOM. 4. We obtain 2 graphs in which the number of the crossed edges reduced by BCM, EM and NEOM respectively has the following relation; BCM = EM < NEOM. 5. We obtain 446 graphs in which the number of the crossed edges reduced by BCM, EM and NEOM respectively has the following relation; BCM = EM = NEOM. 6. The graph obtained by BCM has the minimal number of the crossed edges for

all proper hierarchical graphs of three layers.

Keywords: BCM, EM, NEOM, crossed edges, proper hierarchical graphs. ii

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