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Toxicological responses to stressors are more complex than the simple one-biological-perturbation to one-adverse-outcome model portrayed by individual adverse outcome pathways (AOPs). Consequently, the AOP framework was designed to facilitate de facto development of AOP networks that can aid in the understanding and prediction of pleiotropic and interactive effects more common to environmentally realistic, complex exposure scenarios. The present study introduces nascent concepts related to the qualitative analysis of AOP networks. First, graph theory-based approaches for identifying important topological features are illustrated using 2 example AOP networks derived from existing AOP descriptions. Second, considerations for identifying the most significant path(s) through an AOP network from either a biological or risk assessment perspective are described. Finally, approaches for identifying interactions among AOPs that may result in additive, synergistic, or antagonistic responses (or previously undefined emergent patterns of response) are introduced. Along with a companion article (part I), these concepts set the stage for the development of tools and case studies that will facilitate more rigorous analysis of AOP networks, and the utility of AOP network-based predictions, for use in research and regulatory decision-making. The present study addresses one of the major themes identified through a Society of Environmental Toxicology and Chemistry Horizon Scanning effort focused on advancing the AOP framework. Environ Toxicol Chem 2018;37:1734-1748. (c) 2018 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals, Inc. on behalf of SETAC. This article is a US government work and, as such, is in the public domain in the United States of America.