  There is increasing appetite for analysing populations of network data due to
the fast-growing body of applications demanding such methods. While methods
exist to provide readily interpretable summaries of heterogeneous network
populations, these are often descriptive or ad hoc, lacking any formal
justification. In contrast, principled analysis methods often provide results
difficult to relate back to the applied problem of interest. Motivated by two
complementary applied examples, we develop a Bayesian framework to
appropriately model complex heterogeneous network populations, whilst also
allowing analysts to gain insights from the data, and make inferences most
relevant to their needs. The first application involves a study in Computer
Science measuring human movements across a University. The second analyses data
from Neuroscience investigating relationships between different regions of the
brain. While both applications entail analysis of a heterogeneous population of
networks, network sizes vary considerably. We focus on the problem of
clustering the elements of a network population, where each cluster is
characterised by a network representative. We take advantage of the Bayesian
machinery to simultaneously infer the cluster membership, the representatives,
and the community structure of the representatives, thus allowing intuitive
inferences to be made. The implementation of our method on the human movement
study reveals interesting movement patterns of individuals in clusters, readily
characterised by their network representative. For the brain networks
application, our model reveals a cluster of individuals with different network
properties of particular interest in Neuroscience. The performance of our
method is additionally validated in extensive simulation studies.
