  Social media has become increasingly important in shaping public vaccination
views, especially since the COVID-19 outbreak. This paper uses bow-tie
structure to analyse a temporal dataset of directed online social networks that
represent the information exchange among anti-vaccination, pro-vaccination, and
neutral Facebook pages. Bow-tie structure decomposes a network into seven
components, with two components "SCC" and "OUT" emphasised in this paper: SCC
is the largest strongly connected component, acting as an "information
magnifier", and OUT contains all nodes with a directed path from a node in SCC,
acting as an "information creator". We consistently observe statistically
significant bow-tie structures with different dominant components for each
vaccination group over time. In particular, the anti-vaccination group has a
large OUT, and the pro-vaccination group has a large SCC. We further
investigate changes in opinions over time, as measured by fan count variations,
using agent-based simulations and machine learning models. Across both methods,
accounting for bow-tie decomposition better reflects information flow
differences among vaccination groups and improves our opinion dynamics
prediction results. The modelling frameworks we consider can be applied to any
multi-stance temporal network and could form a basis for exploring opinion
dynamics using bow-tie structure in a wide range of applications.
