Influence Digraphs Induced by Time-Stamped Graphs (Extended Abstract)

A time-stamped graph is an undirected graph with a real number on each edge. Vertex u influences vertex v if there is an increasing path from u to v. The induced influence digraph of a time-stamped graph is the directed graph that records the influences. In this paper we study the realizability problem: Given a parameter value, does there exist a time-stamped graph whose induced influence digraph has the given parameter value? In particular, we solve this problem when the parameter is the number of arcs. Moreover, if the candidates for the time-stamped graphs are restricted to trees, then every realizable value can be achieved by a tree homeomorphic to K2 or K1,3. A number of other questions are also explored. The full version of this paper is submitted to a referreed journal.