A time-stamped graph is an undirected graph
with a real number on each edge. Vertex

influences vertex

if there is a non-decreasing path from

to

. The associated influence
digraph of a time-stamped graph is the directed graph that
records the influences.
Among other results, we determine for what

and

there exists a
time-stamped graph whose
associated influence digraph has

vertices and

arcs.
We also investigate the minimum number of vertices a graph can have so that a
given digraph is an induced subgraph of its associated influence digraph.
A number of other questions are also explored.
AMS Subject Classification: primary: 05C38; secondary: 05C35, 90B10,
91D30, 94C15
Keywords: time-stamped graph, influence, collaboration, Erdos
number