Before revision:  In this paper we propose a null model based  approach to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control method that does not suffer from these computational costs .
After revision:  In this paper we propose a null model based approach to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control method that does not suffer from the computational costs associated to resampling and permutation based approaches .