Time-stamped graphs and their associated influence digraphs. Cheng, E., Grossman, J. W, & Lipman, M. J Discrete Applied Mathematics, 128(2):317–335, June, 2003. 32 citations (Semantic Scholar/DOI) [2025-10-11] 20 citations (Crossref/DOI) [2025-02-07]
Time-stamped graphs and their associated influence digraphs [link]Paper  doi  abstract   bibtex   
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.
@article{cheng_time-stamped_2003,
	title = {Time-stamped graphs and their associated influence digraphs},
	volume = {128},
	issn = {0166-218X},
	url = {https://www.sciencedirect.com/science/article/pii/S0166218X02004973},
	doi = {10.1016/S0166-218X(02)00497-3},
	abstract = {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.},
	number = {2},
	urldate = {2025-02-07},
	journal = {Discrete Applied Mathematics},
	author = {Cheng, Eddie and Grossman, Jerrold W and Lipman, Marc J},
	month = jun,
	year = {2003},
	note = {32 citations (Semantic Scholar/DOI) [2025-10-11]
20 citations (Crossref/DOI) [2025-02-07]},
	pages = {317--335},
}

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