This article presents a simple and easily implementable Bayesian approach
to model and quantify uncertainty in small descriptive social networks. While
statistical methods for analyzing networks have seen burgeoning activity over
the last decade or so, ranging from social sciences to genetics, such methods
usually involve sophisticated stochastic models whose estimation requires
substantial structure and information in the networks. At the other end of the
analytic spectrum, there are purely descriptive methods based upon quantities
and axioms in computational graph theory. In social networks, popular
descriptive measures include, but are not limited to, the so called
Krackhardt’s axioms. Another approach, recently gaining attention, is the
use of PageRank algorithms. While these descriptive approaches provide insight
into networks with limited information, including small networks, there is, as
yet, little research detailing a statistical approach for small networks. This
article aims to contribute at the interface of Bayesian statistical inference
and social network analysis by offering practicing social scientists a
relatively straightforward Bayesian approach to account for uncertainty while
conducting descriptive social network analysis. The emphasis is on computational
feasibility and easy implementation using existing R packages, such as sna and
rjags, that are available from the Comprehensive R Archive Network (https://cran.r-project.org/). We analyze a
network comprising 18 websites from the US and UK to discern transnational
identities, previously analyzed using descriptive graph theory with no
uncertainty quantification, using fully Bayesian model-based inference.