  Stance detection is an important task, supporting many downstream tasks such
as discourse parsing and modeling the propagation of fake news, rumors, and
science denial. In this paper, we propose a novel framework for stance
detection. Our framework is unsupervised and domain-independent. Given a claim
and a multi-participant discussion - we construct the interaction network from
which we derive topological embedding for each speaker. These speaker embedding
enjoy the following property: speakers with the same stance tend to be
represented by similar vectors, while antipodal vectors represent speakers with
opposing stances. These embedding are then used to divide the speakers into
stance-partitions. We evaluate our method on three different datasets from
different platforms. Our method outperforms or is comparable with supervised
models while providing confidence levels for its output. Furthermore, we
demonstrate how the structural embedding relate to the valence expressed by the
speakers. Finally, we discuss some limitations inherent to the framework.
