  We live in a world increasingly dominated by networks -- communications,
social, information, biological etc. A central attribute of many of these
networks is that they are dynamic, that is, they exhibit structural changes
over time. While the practice of dynamic networks has proliferated, we lag
behind in the fundamental, mathematical understanding of network dynamism.
Existing research on time-varying graphs ranges from preliminary algorithmic
studies (e.g., Ferreira's work on evolving graphs) to analysis of specific
properties such as flooding time in dynamic random graphs. A popular model for
studying dynamic graphs is a sequence of graphs arranged by increasing
snapshots of time. In this paper, we study the fundamental property of
reachability in a time-varying graph over time and characterize the latency
with respect to two metrics, namely store-or-advance latency and cut-through
latency. Instead of expected value analysis, we concentrate on characterizing
the exact probability distribution of routing latency along a randomly
intermittent path in two popular dynamic random graph models. Using this
analysis, we characterize the loss of accuracy (in a probabilistic setting)
between multiple temporal graph models, ranging from one that preserves all the
temporal ordering information for the purpose of computing temporal graph
properties to one that collapses various snapshots into one graph (an operation
called smashing), with multiple intermediate variants. We also show how some
other traditional graph theoretic properties can be extended to the temporal
domain. Finally, we propose algorithms for controlling the progress of a packet
in single-copy adaptive routing schemes in various dynamic random graphs.
