  We present a novel set of methods for analyzing coverage properties in
dynamic sensor networks. The dynamic sensor network under consideration is
studied through a series of snapshots, and is represented by a sequence of
simplicial complexes, built from the communication graph at each time point. A
method from computational topology called zigzag persistent homology takes this
sequence of simplicial complexes as input, and returns a `barcode' containing
the birth and death times of homological features in this sequence. We derive
useful statistics from this output for analyzing time-varying coverage
properties. Further, we propose a method which returns specific representative
cycles for these homological features, at each point along the birth-death
intervals. These representative cycles are then used to track coverage holes in
the network, and obtain size estimates for individual holes at each time point.
A weighted barcode, incorporating the size information, is then used as a
visual and quantitative descriptor of the dynamic network coverage.
