Abstract Background The set of extreme pathways (ExPa), {p i }, defines the convex basis vectors used for the mathematical characterization of the null space of the stoichiometric matrix for biochemical reaction networks. ExPa analysis has been used for a number of studies to determine properties of metabolic networks as well as to obtain insight into their physiological and functional states in silico. However, the number of ExPas, p = |{p i }|, grows with the size and complexity of the network being studied, and this poses a computational challenge. For this study, we investigated the relationship between the number of extreme pathways and simple network properties. Results We established an estimating function for the number of ExPas using these easily obtainable network measurements. In particular, it was found that log [p] had an exponential relationship with log [ ∑ i = 1 R d − i d + i c i ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacyGGSbaBcqGGVbWBcqGGNbWzdaWadaqaamaaqadabaGaemizaq2aaSbaaSqaaiabgkHiTmaaBaaameaacqWGPbqAaeqaaaWcbeaakiabdsgaKnaaBaaaleaacqGHRaWkdaWgaaadbaGaemyAaKgabeaaaSqabaGccqWGJbWydaWgaaWcbaGaemyAaKgabeaaaeaacqWGPbqAcqGH9aqpcqaIXaqmaeaacqWGsbGua0GaeyyeIuoaaOGaay5waiaaw2faaaaa@4414@ , where R = |R eff | is the number of active reactions in a network, d − i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGKbazdaWgaaWcbaGaeyOeI0YaaSbaaWqaaiabdMgaPbqabaaaleqaaaaa@30A9@ and d + i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGKbazdaWgaaWcbaGaey4kaSYaaSbaaWqaaiabdMgaPbqabaaaleqaaaaa@309E@ the incoming and outgoing degrees of the reactions r i ∈ R eff , and c i the clustering coefficient for each active reaction. Conclusion This relationship typically gave an estimate of the number of extreme pathways to within a factor of 10 of the true number. Such a function providing an estimate for the total number of ExPas for a given system will enable researchers to decide whether ExPas analysis is an appropriate investigative tool.