The process of extricating relationships and interchanges via visual mapping refers to Social Network Analysis (SNA). Through social network and graph theory lenses, this study explore Twitter data shortly after the announcement of the National Health Insurance (NHI) Bill to the South African parliament. An instrumental, single case study design and SNA secured contextual and timely Twitter interchanges of 4 112 tweets of the hashtag “NHI”. Given the growing call for the comprehension of social media network interactions in different contexts, this paper use the underutilized tool for social media analytics, ‘Network Overview, Discovery and Exploration for Excel Pro’ (NodeXL Pro) to extract and visually present knowledge from pairwise relations between actors in the #NHI social media network. The findings explain the data dispersion and network structure of the #NHI case. The results clearly identifies the influencers – mostly the South African government, specific Twitter users and gatekeepers in the announcement of a highly controversial healthcare bill that will affect all South African citizens. The paper contributes theoretically by adding graph theory to the social media research field and to a less studied social media research cluster, namely social media during critical events. The practical contribution of the study is the use of NodeXL Pro, a unique SNA tool for advanced social media crawling, SNA and advanced network metric analysis.