  The shift-enabled property of an underlying graph is essential in designing
distributed filters. This article discusses when a random graph is
shift-enabled. In particular, popular graph models ER, WS, BA random graph are
used, weighted and unweighted, as well as signed graphs. Our results show that
the considered unweighted connected random graphs are shift-enabled with high
probability when the number of edges is moderately high. However, very dense
graphs, as well as fully connected graphs, are not shift-enabled.
Interestingly, this behaviour is not observed for weighted connected graphs,
which are always shift-enabled unless the number of edges in the graph is very
low.
