The analysis of networks of ecological trophic transfers is a useful complement to simulation modeling in the quest for understanding whole-ecosystem dynamics. Trophic networks can be studied in quantitative and systematic fashion at several levels. Indirect relationships between any two individual taxa in an ecosystem, which often differ in either nature or magnitude from their direct influences, can be assayed using techniques from linear algebra. The same mathematics can also be employed to ascertain where along the trophic continuum any individual taxon is operating, or to map the web of connections into a virtual linear chain that summarizes trophodynamic performance by the system. Backtracking algorithms with pruning have been written which identify pathways for the recycle of materials and energy within the system. The pattern of such cycling often reveals modes of control or types of functions exhibited by various groups of taxa. The performance of the system as a whole at processing material and energy can be quantified using information theory. In particular, the complexity of process interactions can be parsed into separate terms that distinguish organized, efficient performance from the capacity for further development and recovery from disturbance. Finally, the sensitivities of the information-theoretic system indices appear to identify the dynamical bottlenecks in ecosystem functioning.