  We investigate the impact of noise and topology on opinion diversity in
social networks. We do so by extending well-established models of opinion
dynamics to a stochastic setting where agents are subject both to assimilative
forces by their local social interactions, as well as to idiosyncratic factors
preventing their population from reaching consensus. We model the latter to
account for both scenarios where noise is entirely exogenous to peer influence
and cases where it is instead endogenous, arising from the agents' desire to
maintain some uniqueness in their opinions. We derive a general analytical
expression for opinion diversity, which holds for any network and depends on
the network's topology through its spectral properties alone. Using this
expression, we find that opinion diversity decreases as communities and
clusters are broken down. We test our predictions against data describing
empirical influence networks between major news outlets and find that
incorporating our measure in linear models for the sentiment expressed by such
sources on a variety of topics yields a notable improvement in terms of
explanatory power.
