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Background  Graph-based analysis (GBA) of genome-scale metabolic networks has revealed system-level structures such as the bow-tie connectivity that describes the overall mass flow in a network. However, many pathways obtained by GBA are biologically impossible, making it difficult to study how the global structures affect the biological functions of a network. New method that can calculate the biologically relevant pathways is desirable for structural analysis of metabolic networks.    Results  Here, we present a new method to determine the bow-tie connectivity structure by calculating possible pathways between any pairs of metabolites in the metabolic network using a flux balance analysis (FBA) approach to ensure that the obtained pathways are biologically relevant. We tested this method with 15 selected high-quality genome-scale metabolic models from BiGG database. The results confirmed the key roles of central metabolites in network connectivity, locating in the core part of the bow-tie structure, the giant strongly connected component (GSC). However, the sizes of GSCs revealed by GBA are significantly larger than those by FBA approach. A great number of metabolites in the GSC from GBA actually cannot be produced from or converted to other metabolites through a mass balanced pathway and thus should not be in GSC but in other subsets of the bow-tie structure. In contrast, the bow-tie structural classification of metabolites obtained by FBA is more biologically relevant and suitable for the study of the structure-function relationships of genome scale metabolic networks.    Conclusions  The FBA based pathway calculation improve the biologically relevant classification of metabolites in the bow-tie connectivity structure of the metabolic network, taking us one step further toward understanding how such system-level structures impact the biological functions of an organism.    Supplementary Information  The online version contains supplementary material available at 10.1186/s12866-021-02357-1.

Global connectivity in genome-scale metabolic networks revealed by comprehensive FBA-based pathway analysis