An activity-based information-theoretic annotation of social graphs

The explosion in social media adoption has opened up new opportunities to understand human interaction and information flow at an unprecedented scale. Influence between people represented as nodes of a social graph is best characterized in terms of the direction, the volume and the delay associated with the information flow. In this work we investigate the relatively new information-theoretic measure called transfer entropy as a measure of directed causal influence in online social interactions. The classical definition of transfer entropy is extended to a form applicable to activity on social graphs characterized by causal influence through delayed responses. For fixed but arbitrary interaction delays, we show that the swept delayed transfer entropy (DTE) profile peaks at the true delay. By extending the results to discrete and continuous distributions of interaction delays, the efficacy of DTE in recovering the interaction delay distributions between two causally related signals is demonstrated. An information theoretic annotation of social graphs that captures the volume and velocity of information transfer is presented based on the swept DTE.