We survey and introduce concepts and tools  at the intersection of information theory and network biology. 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. 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 and thus a robust definition of graph complexity.
We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global 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. 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 labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.
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located
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local and global
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networks at the intersection of local and global pattern detection. This includes, for example, the detection of the connectivity phase transition leading to the
data. We show examples such as the
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labelled and unlabelled
labeled and unlabeled
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labelled
labeled
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the Kolmogorov complexity of the unlabelled graph
its unlabeled Kolmogorov complexity