  The rise of social media platforms has facilitated the formation of echo
chambers, which are online spaces where users predominantly encounter
viewpoints that reinforce their existing beliefs while excluding dissenting
perspectives. This phenomenon significantly hinders information dissemination
across communities and fuels societal polarization. Therefore, it is crucial to
develop methods for quantifying echo chambers. In this paper, we present the
Echo Chamber Score (ECS), a novel metric that assesses the cohesion and
separation of user communities by measuring distances between users in the
embedding space. In contrast to existing approaches, ECS is able to function
without labels for user ideologies and makes no assumptions about the structure
of the interaction graph. To facilitate measuring distances between users, we
propose EchoGAE, a self-supervised graph autoencoder-based user embedding model
that leverages users' posts and the interaction graph to embed them in a manner
that reflects their ideological similarity. To assess the effectiveness of ECS,
we use a Twitter dataset consisting of four topics - two polarizing and two
non-polarizing. Our results showcase ECS's effectiveness as a tool for
quantifying echo chambers and shedding light on the dynamics of online
discourse.
