Before revision:  We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different  aspects of synthetic and biological networks at the intersection of local and global pattern detection. This includes, for example, the detection of the connectivity phase transition leading to the emergence of giant components in Erdos-Renyi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data.
After revision:  We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdos-Renyi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data.