Before 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 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, and the recovery of topological properties from numerical kinetic properties simulating gene expression arrays .
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 and global pattern detection . This includes, for example , including, the detection of the connectivity phase transition leading to the emergence of giant components in Erd\"os-R\'enyi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression arrays .