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. 2015 Mar 31;16(1):63. doi: 10.1186/s13059-015-0624-2

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© Cheng et al.; licensee BioMed Central. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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The schematic diagram of the hierarchy score maximization algorithm. In hierarchical networks, the downward, upward, and horizontal edges are shown in red, blue, and black colors, respectively. (A) The definition of hierarchy score. (B) A simulated annealing algorithm for inferring the hierarchical structure by maximizing the hierarchy score. (C) The procedure to calculate the probability of nodes in different hierarchy levels. Simulated annealing procedure is performed for k runs and in each run a hierarchical structure is inferred by maximizing the hierarchy score. The frequency of each node in these k hierarchical networks is calculated to obtain a probabilistic hierarchical network. Discretized hierarchical network is obtained by assigning nodes to the level with highest frequency.