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In a recent paper it was shown that, for chemical reaction networkspossessing a subtle structural property called concordance, dynamical behaviorof a very circumscribed (and largely stable) kind is enforced, so long as thekinetics lies within the very broad and natural weakly monotonic class. Inparticular, multiple equilibria are precluded, as are degenerate positiveequilibria. Moreover, under certain circumstances, also related to concordance,all real eigenvalues associated with a positive equilibrium are negative.Although concordance of a reaction network can be decided by readily availablecomputational means, we show here that, when a nondegenerate network'sSpecies-Reaction Graph satisfies certain mild conditions, concordance and itsdynamical consequences are ensured. These conditions are weaker than earlierones invoked to establish kinetic system injectivity, which, in turn, is justone ramification of network concordance. Because the Species-Reaction Graphresembles pathway depictions often drawn by biochemists, results here expandthe possibility of inferring signicant dynamical information directly fromstandard biochemical reaction diagrams.

Concordant Chemical Reaction Networks and the Species-Reaction Graph