Contextual Effects in Hashtag Publics: Introducing Exponential Random Graph Modeling (ERGM) for Analyzing Locally Emerging Ad Hoc Publics
Matthias Lechle
Theoretical background: Online social networks like Facebook, Twitter or Instagram have now taken an indispensable role in people’s everyday lives by driving social interaction and participation in the global public sphere. In social media, these publics are organized through networked technology while participation is mediated by “devices” such as hashtags. Especially on Twitter and Instagram, hashtags serve a wide range of purposes, from marking the content up to gathering people around a topic or event. Such hashtag publics are in the spotlight of recent research, exploring hashtag use patterns and hashtag typology in social media (Bruns & Burgess, 2011; Papacharissi & De Fatima Oliveira, 2012; Arvidsson & Caliandro, 2015; Bruns & Burgess, 2015; Burgess, Galloway, & Sauter, 2015; Zappavigna, 2015; Faltesek, 2015; Bruns, Moon, Paul, & Münch, 2016; Wang, Liu, & Gao, 2016). While the importance of hashtag typology and possible interdependencies are already explored, less is known about the hashtag as a mediation device and its role in the formation of publics. Especially contextual information reflected through the hashtag, which might affect the structure of ad hoc publics, have not been investigated sufficiently yet.
Research methodology: This methodological work is about the analysis of hashtag patterns and their ability to facilitate the formation of locally emerging ad hoc publics. Relying on network methodology, a hashtag co-occurrence network model was designed, based on observed Instagram data from the New York Fashion Week. Beside descriptive social network analysis, stochastic network modeling was applied through exponential random graph modeling (ERGM). Based on ERGM, several theoretical assumptions on the structure of a hashtag public were examined and conclusions about the specific role of the hashtag as a mediation device were drawn. This method offers several advantages by addressing explicitly (1) the meaning of the common use of hashtags in posts, (2) the interactions between different types of hashtags and (3) the impact of hashtag popularity and hashtag attraction.
Findings: The final network model confirms the role of the hashtag in aggregating topics in a locally emerging ad hoc public in different ways. First, there is a correlation between the popularity as well as the category of a hashtag and the likelihood of joint use. This means, often used, respectively popular hashtags are more often used together within other popular hashtags in Instagram posts. Second, the model shows a tendency for hashtags of the same category to be used jointly, reflecting an effect for uniform homophily. Third, brand hashtags tend to connect with event and time-related hashtags that support also previous research (Arvidsson & Caliandro, 2015; Gillespie, 2014). Fourth, hashtag transitivity has been identified through the application of higher-order terms in the model. This effect supports the theory, that the joint use of certain hashtags might affect the popularity of such hashtag combinations over several posts within the hashtag public. Finally, the model of a locally emerging public shows significant differences in terms of the structure compared to a global hashtag public, which can be seen as patterns of contextual effects. 
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