  All networks can be analyzed at multiple scales. A higher scale of a network
is made up of macro-nodes: subgraphs that have been grouped into individual
nodes. Recasting a network at higher scales can have useful effects, such as
decreasing the uncertainty in the movement of random walkers across the network
while also decreasing the size of the network. However, the task of finding
such a macroscale representation is computationally difficult, as the set of
all possible scales of a network grows exponentially with the number of nodes.
Here we compare various methods for finding the most informative scale of
preferential attachment networks, discovering that an approach based on
spectral analysis outperforms greedy and gradient descent-based methods. We
then use this procedure to show how several structural properties of these
networks vary across scales. We describe how meso- and macroscale
representations of networks can have significant benefits over their underlying
microscale in terms of information transmission, which include properties such
as increase in determinism, a decrease in degeneracy, a lower entropy rate of
random walkers on the network, an increase in global network efficiency, and
higher values for a variety of centrality measures than the microscale.
