Measuring and Modeling the Flow of Information Online and on Networks*

We propose a model for the flow of information in the form of symbolic data. Nodes in a graph representing, e.g., a social network take turns generating words, leading to a symbolic time series associated with each node. Information propagates over the graph via a quoting mechanism, where nodes randomly copy short symbolic sequences from each other. We characterize information flows from these data via information-theoretic estimators, and we derive analytic relationships between model parameters and the values of these estimators. We explore and validate the model with simulations on small network motifs and larger random graphs. Tractable models such as ours that generate symbolic data while controlling the information flow allow us to test and compare measures of information flow applicable to realistic data. In particular, by choosing different network structures, we can develop test scenarios to determine whether or not measures of information flow can distinguish between true and spurious interactions, and how topological network properties relate to information flow.