We introduce concepts and tools at the intersection of information theory and network biology. 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  . We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labelled and unlabelled graphs and prove that the Kolmogorov complexity of a labelled graph is a good approximation of the Kolmogorov complexity of the unlabelled graph.
We introduce concepts and tools at the intersection of information theory and network biology. 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 . We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labelled and unlabelled graphs and prove that the Kolmogorov complexity of a labelled graph is a good approximation of the Kolmogorov complexity of the unlabelled graph.
R
Kolmogorov complexity
compressibility
D
(e.g. graph motifs)
A
, and the recovery of topological properties from numerical kinetic properties simulating gene expression arrays