  The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.
