8. Modeling and Prediction for Processes on Network Graphs

Throughout this book so far, we have seen numerous examples of network graphs that provide representations—useful for various purposes—of the interaction among elements in a system under study. Often, however, it is some quantity (or attribute) associated with each of the elements that ultimately is of most interest. In such settings it frequently is not unreasonable to expect that this quantity be influenced in an important manner by the interactions among the elements. For example, the behaviors and beliefs of people can be strongly influenced by their social interactions; proteins that are more similar to each other, with respect to their DNA sequence information, often are responsible for the same or related functional roles in a cell; computers more easily accessible to a computer infected with a virus may in turn themselves become more quickly infected; and the relative concentration of species in an environment (e.g., animal species in a forest or chemical species in a vat) can vary over time as a result of the nature of the relationships among species.