Modern manufacturing arena necessitates the need for responsiveness by practicing agile manufacturing (AM) principles. AM imposes the transformation of the manufacturing organisation so as to respond to dynamic market changes. This article focuses towards the application of graph theory (GT) for conceptual modelling the agile system and to compute the dependencies among the individual agile enabler, criteria and attributes as a top-down approach. Using GT approach, digraphs were systematically constructed for agile enablers and variable permanent matrix values were computed for different scenarios and the relative importance of agility enablers were determined. The permanent values of Management responsibility enabler and technology enabler are found to be 920 (minimum) and 3529 × 1014, respectively for the existing situation, whereas for the practically base case situation, it was found to be 1185 (minimum) and 5081.17 × 1014 (maximum), respectively. The Comprehensive Agility Index was found to be 1.3996 × 1045, which can be even used to benchmark with other best-in-class agile organisations. © 2013 Taylor and Francis.