Before revision:   Our algorithmic information methodology therefore provides a rigorous framework enabling  fundamental assessment and comparison between different methods for reducing the complexity of networks while preserving key structures in the networks thereby facilitating the identification of such core processes .
After revision:  However, the approach shows that network motif analysis excels at preserving the relative algorithmic information content of a network, hence validating and generalizing the remarkable fact that despite their inherent combinatorial possibilities, local regularities preserve information to such an extent that essential properties are fully recoverable across different networks to determine their family group to which they belong to (eg genetic vs social network). Our algorithmic information methodology therefore provides a rigorous framework enabling fundamental assessment and comparison between different methods for reducing the complexity of networks while preserving key structures in the networks thereby facilitating the identification of such core processes .