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Let [Formula: see text] be a directed graph associated with a weight [Formula: see text]. For an edge-cut [Formula: see text] of [Formula: see text], the average weight of [Formula: see text] is denoted and defined as [Formula: see text]. An optimal edge-cut with average weight is an edge-cut [Formula: see text] such that [Formula: see text] is maximum among all edge-cuts (or minimum, symmetrically). In this paper, a polynomial algorithm for this problem is proposed for finding an optimal edge-cut in a rooted tree separating the root and the set of all leafs. This algorithm enables us to develop an automatic clustering method with more accurate detection of community output.more » « less
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