  In this paper, we investigate the controllability of a linear time-invariant
network following a Laplacian dynamics defined on a threshold graph. In this
direction, an algorithm for deriving the modal matrix associated with the
Laplacian matrix for this class of graphs is presented. Then, based on the
Popov-Belevitch-Hautus criteria, a procedure for the selection of control nodes
is proposed. The procedure involves partitioning the nodes of the graph into
cells with the same degree; one node from each cell is then selected. We show
that the remaining nodes can be chosen as the control nodes rendering the
network controllable. Finally, we consider a wider class of graphs, namely
cographs, and examine their controllability properties.
