Time-stamped graphs and their associated influence digraphs Original Research Article

A time-stamped graph is an undirected graph with a real number on each edge. Vertex u influences vertex v if there is a non-decreasing path from u to v. The associated influence digraph of a time-stamped graph is the directed graph that records the influences. Among other results, we determine for what n and t there exists a time-stamped graph whose associated influence digraph has n vertices and t 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.