Social media has greatly proliferated over the last decade and has led to a global trove of interconnected content and data. Network scientists have been studying social networks for nearly half a century, and never has the opportunity for the mapping of social systems have been so accessible. Nor has there ever been such an opportunity for an interested public to understand a real-world context for network theory principles. Along with the billions of users on social media, Brands, Public Figures and Organizations (BPOs) also participate alongside, encouraging user participation and building deeper connections between users and BPOs. The BPOs that have best adapted to this social change have integrated social platforms into their existing business model. This often involves allocating more traditional resources toward social campaigns and objectives. It is common for BPOs to have entire departments dedicated to social media, as well as a collection of various social media applications and consultants at their disposal. BPOs that most efficiently manage their day-to-day social resources have seen the highest Return on Investment (ROI). Understanding how to measure ROI then is critical to produce high-level social strategy and analysis. This feedback look between production, measurement and adaptation is necessary to drive an effective and profitable social strategy.The social networks which have become highly adopted by BPOs include Facebook, Twitter, YouTube and LinkedIn. Each network has particular strengths for developing and producing content, and each has particular limitations. What they all have in common is a underlying measure of connectedness. These social networks have fundamentally changed the online presence of many BPOs. Beyond a website and search engine optimization, the social space provides a two-way interaction and openness between users and BPOs. The social space provides a platform for users to offer feedback on various pieces of digital media, comment on topics, and to share these items with their own network. The combination of these factors allows worthwhile information to spread faster and users to freely engage with BPOs.

Users interact with BPOs for many reasons: to obtain locked content, receive benefits, be entertained, to acquire information, or to genuinely support the BPO. User publicity around this interaction, for example sharing it with their own network, signals things about themselves such as their interests or associations. Beyond users, BPOs publicly interact with each other. This could be to show business associations, affiliate with a particular cause, lure a response from the targeted BPOs, or enhance their own online appearance.

There is no shortage of theories or opinions of how to measure the ROI of social media. Unfortunately, none have appreciated the mathematical complexity, and the alignment with current network theory concepts. It might seem obvious that those in the field of social network analysis on the social media side actually understand the principles of network science. Unfortunately that does not seem to be the case, with the overflow of inconsistent and biased metrics, and more and more data without the proper scope for analysis. This manuscript’s purpose is to introduce the principles of complexity and network science, and to show they can resolve inconsistencies in the current social media measurements. Particularly, this manuscript advocates a nonlinear approach to produce consistent, unbiased and valid estimations for social data. We will distill complex network methods and show how the current methods are mathematically arbitrary and lead to incorrect insight. Our flagship discussion will revolve around the “engagement rate”, one of the most pervasive social media statistics and one that is fundamentally invalid when considering the complex and network effects of the model. We will extend these thoughts even to something as simple as an average, and show how even something as simple as an average is incorrect given the heterogeneous topologies of social networks. We will use econometric analysis to provide quantitative and qualitative network insights, and encourage an agile analyst to pick and choose appropriate methods.

Specifically, in this paper we use the engagement rate as an archetype with the invalid methods that pervade social analysis.