Before revision:  We show that Shannon's information entropy, Kolmogorov complexity and algorithmic probability quantify different aspects of synthetic and biological networks at the intersection of local (e.g. graph motifs) and global pattern detection, including, the detection of the connectivity phase transition leading to the emergence of giant components in Erd\"os-R\'enyi random graphs  .
After revision:  We show that Shannon's information entropy, compressibility and algorithmic probability quantify different aspects of synthetic and biological networks at the intersection of local (e.g. graph motifs) and global pattern detection, including, the detection of the connectivity phase transition leading to the emergence of giant components in Erd\"os-R\'enyi random graphs .