[Characterization of access to normal childbirth care in Bahia State, Brazil, based on graph theory]

Origin-destination flow is a phenomenon that can be modeled as a network. Graph theory is a mathematical tool to characterize a network and thus allows studying the topological properties and temporal and spatial development of a set of related elements. The article aims to estimate the topological evolution of an inter-municipal network of normal deliveries. We selected the admissions for normal deliveries in the Hospital Information System of the Brazilian Unified National Health System, from 2008 to 2014, for women residing in Bahia State, Brazil. The following indices were applied: entry degree (from how many municipalities the women came for childbirth), exit degree (to how many municipalities they left), entry flow (how many women came), exit flow (how many women left), and the mean size of the exit edge (distance traveled). Analyses between macro-regions used the following indicators: proportion of normal deliveries performed outside the municipality of residence and mean size of the exit edge. The results indicate an increase in deliveries performed outside the municipality of residence, in addition to the persistence of concentration of deliveries in the hub municipalities in the Health Regions, and an increase in the distance between the municipality of residence and the municipality where the delivery took place. The organization of networks for normal childbirth poses an on-going challenge. It is important to analyze the flow of women for childbirth care in order to support the establishment of inter-municipal references to guarantee safe labor and childbirth. In conclusion, it is necessary to develop a regionalized network to meet the demand by pregnant women in the territory with universal and equitable coverage.