This paper aims to answer the ‘So What?’ question in regard to the use of mathematical and computational methods for the analysis of social media (SM) as a locus of social influence understood broadly as a process of the spread/exchange of information, ideologies, and opinions. Focusing on the issue of time as both a factor affecting the results of influence and a specific kind of data on SM, this paper draws upon two streams of research aiming to exploit mathematics and computational methods for the analysis of mediated interaction. One is concerned with studies of computer-mediated communication (CMC) vs face-to-face communication; the other with studies of the spread of information in SM.

The use of social media and the consequent generation of large quantities of digitised data enabled a wide application of computational methods for the analysis of information flows in online networks. This also contributed to the proliferation of mathematical approaches that represent SM-mediated processes as structures by exploiting aggregated data sets and large-scale statistical analysis. The structure-oriented view on SM-mediated spread of information, ideas, and opinions, however, provides a very limited opportunity for understanding the phenomenon of influence as a process of change that is inherently time-dependent and is manifested at the individual level rather than the societal level. This paper argues that an analysis of SM as a medium (locus and/or tool) of influence requires shifting the focus from structure to interaction, and from the source and content of the means of influence to the actual effects manifested by certain kinds of observable response, both online (e.g. retweets and mentions) and offline (e.g. social actions).
As studies in CMC have shown, mathematical analysis of the temporal patterns of interaction can provide some useful insights on the process of influence. However, the SM-mediated interaction differs significantly from CMC. This paper discusses how social scientific constructs of SM as an object of research can help identify mathematical approaches and computational methods most adequate / useful for the analysis of SM-mediated influence.