In the 1998 technical note Computing on data streams by Monika Rauch Henzinger , Prabhakar Raghavan , Sridar Rajagopalan (found here: http://www.eecs.harvard.edu/~michaelm/E210/datastreams.pdf)They define a directed multigraph with node set V1 union V2 union union Vk, all of whose edges are directed from a node in Vi to a nodein Vi+1.I cannot see how this allows for disconnected components?  Can anyone clarify this?
Computing on data streams clarification
data streams;streaming
The definition says that every edge that exists has to go from some $V_i$ to $V_{i+1}$.  It doesn't say that every possible edge from $V_i$ to $V_{i+1}$ has to be there.  For example, $V_1=\{a,b\}$, $V_2=\{c,d\}$ with edges $ac$ and $bd$ gives a disconnected graph.