Discovering Influence in Communication Networks Using Dynamic Graph Analysis

The rise of Internet-based social networks has shifted many decision-impacting discussions online. Increasingly, people weigh new ideas, choose products, pick technologies, find entertainment and socialize virtually by engaging in online discourse. The participants depend on who people find online, who they get to know and trust, and who they consider as authorities on subjects of interest. This paper presents techniques to track who has influence in such a network and how they got there. Many definitions of influence are possible; here we focus specifically on the social interaction and its dynamics, using Twitter as the reference network and data source. We build a replier graph from each user $A$'s messages mentioning another user $B$ (which may be either ``for'' or ``about'' $B$), and study how this graph evolves. (In a tweet from $A$ mentioning \verb|@B|, $A$ is the replier mentioning $B$.) For every day in the study, we compute a pagerank-type score and a \emph{drank}, a dynamic function of the pagerank, for all users, together with a series of features such as the number of mentions a user gives or receives. The daily-versioned features enable exploratory data analysis of the conversational dynamics by looking at the relative decline or growth in specific features for every user every day, separately or relative to others. For instance, we find the longest periods of growth in the number of times a user $A$ is mentioned by other users on a day $d$, $m=|M(A,d)|$, over a contiguous period of days, and also compute its acceleration over that period, $dm/dt$. Those accelerating the most, or sustaining the longest growth, or both, are worth closer modeling. Our metrics are applicable to any evolving directed graphs and allow us to find people of growing influence in social networks based purely on the structure and dynamics of their conversations. These are the first dynamic metrics for social networks which take into the account both global and local influence (pagerank and repliers), and can be applied to other communication networks as well. Most interestingly, using them, we uncover a high-intensity ecosystem with its own ``mind economy,'' adapting to maximize the participants' rankings and promote their shared message.