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. 2020 Feb 10;11:811. doi: 10.1038/s41467-020-14600-w

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© The Author(s) 2020, corrected publication 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Flow centrality measure. The source nodes (blue) are connected to the target nodes (red) preferentially through high flow centrality nodes (green). b Flow centrality score calculation. 1000 samples are generated through the randomization scheme explained in Methods section. For each node, its FC score is compared with its corresponding values in the random samples and a z-score is obtained, defined as flow centrality score (FCS). c Flow central paths are selected among the shortest paths between asthma and COPD seed genes. The selection condition is that all the intermediate genes in the paths have a FCS >2. Two sets of 10,000 random paths are extracted (Type A, length-preserved, and Type B, endpoints-preserved), for a total of three sets of paths. d starting from each sets of network paths, GO annotations and GEO expression data, the sequential similarity and sequential coexpression values are calculated and compared.