Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs
E. Roberts, T. Schlitt, A. Coolen
Journal of Physics A 44, 275002 (2011)
#graphtheory#machinelearning#statisticalphysics
Our approach gives a rigorous quantitative method for prioritising network properties.
We generate new mathematical tools with which to quantify the macroscopic topological structure of large directed networks. This is achieved via a statistical mechanical analysis of constrained maximum entropy ensembles of directed random graphs with prescribed joint distributions for in- and out-degrees and prescribed degree–degree correlation functions. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies and complexities of these ensembles, and for information-theoretic distances. The results are applied to data on gene regulation networks.
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Geometric phases and cyclic isotropic cosmologies
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Photonic Maxwell’s demon
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Coupling news sentiment with web browsing data improves prediction of intra-day price dynamics
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Subcritical U-Bootstrap percolation models have non-trivial phase transitions
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Quantifying noise in mass spectrometry and yeast two-hybrid protein interaction detection experiments
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Journal of the Royal Society Interface
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Spin systems on hypercubic Bethe lattices: a Bethe–Peierls approach
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Structures and stability of calcium and magnesium carbonates at mantle pressures
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Journal of Physics A
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