We present a new clustering metric, based on a random graph model and a ratio cut concept. The minimization of the proposed clustering cost can be transformed to a uniform multicommodity flow problem by adding artificial weight functions, which can be solved by a multicommodity flow-based algorithm with high complexity. We devise a probabilistic flow injection approach which drastically reduces the complexity of the flow-based algorithm. Experimental results show that this algorithm generates promising results with respect to the proposed metric.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>