  In the study of networked systems such as biological, technological, and
social networks the available data are often uncertain. Rather than knowing the
structure of a network exactly, we know the connections between nodes only with
a certain probability. In this paper we develop methods for the analysis of
such uncertain data, focusing particularly on the problem of community
detection. We give a principled maximum-likelihood method for inferring
community structure and demonstrate how the results can be used to make
improved estimates of the true structure of the network. Using
computer-generated benchmark networks we demonstrate that our methods are able
to reconstruct known communities more accurately than previous approaches based
on data thresholding. We also give an example application to the detection of
communities in a protein-protein interaction network.
