  In a recent paper it was shown that, for chemical reaction networks
possessing a subtle structural property called concordance, dynamical behavior
of a very circumscribed (and largely stable) kind is enforced, so long as the
kinetics lies within the very broad and natural weakly monotonic class. In
particular, multiple equilibria are precluded, as are degenerate positive
equilibria. 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 available
computational means, we show here that, when a nondegenerate network's
Species-Reaction Graph satisfies certain mild conditions, concordance and its
dynamical consequences are ensured. These conditions are weaker than earlier
ones invoked to establish kinetic system injectivity, which, in turn, is just
one ramification of network concordance. Because the Species-Reaction Graph
resembles pathway depictions often drawn by biochemists, results here expand
the possibility of inferring signicant dynamical information directly from
standard biochemical reaction diagrams.
