Network theory is today a central topic in computational systems biology as a framework to understand and reconstruct relations among biological components. For example, constructing networks from a gene expression dataset provides a set of possible hypotheses explaining connections among genes, vital knowledge to advancing our understanding of URLanisms as systems. Here we briefly survey aspects 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  biological networks at the interplay of local and global pattern detection  . We provide approximations to the algorithmic probability and Kolmogorov complexity of motifs connected to the asymptotic topological propertiesof networks .
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 .
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Network theory is today a central topic in computational systems biology as a framework to understand and reconstruct relations among biological components. For example, constructing networks from a gene expression dataset provides a set of possible hypotheses explaining connections among genes, vital knowledge to advancing our understanding of URLanisms as systems. Here we briefly survey aspects
We introduce concepts and tools
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synthetic and
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interplay of local
intersection of local (e.g. graph motifs)
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, including, the detection of the connectivity phase transition leading to the emergence of giant components in Erd\"os-R\'enyi random graphs
R
approximations to the
exact theoretical calculations, numerical approximations and error estimations of entropy,
R
of motifs connected to the asymptotic topological propertiesof networks
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