Vaccination is one of the most impactful healthcare interventions in terms of lives saved at a given cost, leading the anti-vaccination movement to be identified as one of the top 10 threats to global health in 2019 by the World Health Organization. This issue increased in importance during the COVID-19 pandemic where, despite good overall adherence to vaccination, specific communities still showed high rates of refusal. Online social media has been identified as a breeding ground for anti-vaccination discussions. In this work, we study how vaccination discussions are conducted in the discussion forum of Mumsnet, a United Kingdom based website aimed at parents. By representing vaccination discussions as networks of social interactions, we can apply techniques from network analysis to characterize these discussions, namely network comparison, a task aimed at quantifying similarities and differences between networks. Using network comparison based on graphlets -- small connected network subgraphs -- we show how the topological structure vaccination discussions on Mumsnet differs over time, in particular before and after COVID-19. We also perform sentiment analysis on the content of the discussions and show how the sentiment towards vaccinations changes over time. Our results highlight an association between differences in network structure and changes to sentiment, demonstrating how network comparison can be used as a tool to guide and enhance the conclusions from sentiment analysis.

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