With the development of new sequencing technologies of modern molecular biology, it is increasingly common to collect time-series data on the abundance of molecular species encoded within the genomes. This presentation shall illustrate how such data may be used to infer the parameters as well as the structure of the biochemical network under mass-action kinetics. Given certain constraints on the geometry of the stoichiometric space, we use algebraic methods as an alternative to conventional hierarchical graphical models, to carry out network structure inference by identifying reaction rate constants which are significantly different from zero.