Network anonymisation is an essential procedure in processing data structured as graphs to achieve non-identifiability of participating entities. This quality is particularly desirable among networks representing stakeholders whose identity should not be compromised for ethical or legal reasons or when such structures are publicly disclosed. Extensive use of sensitive graph-like data contributed to the development of anonymisation methods that vary in terms of performance given the network topology or imposed constraints. We present modifications to an existing greedy algorithm using equivalence classes and discuss the rationale behind them. The experimental results obtained on networks from various scientific fields indicate that algorithms taking into account the size of equivalence classes in edge evaluation can consistently outperform the existing greedy algorithm in terms of the solution quality for larger number of available deletions. The proposed improvements also lead to comparable running time.