2022/05/30 by Ruben Becker, Becker, Ruben, Arnaud Casteigts +11 · 3 citations
Computer Science · #Opportunistic and Delay-Tolerant Networks
paper · pdf · doi:10.48550/arxiv.2205.14888
A temporal graph is a graph whose edges appear only at certain points in time. Recently, the second and the last three authors proposed a natural temporal analog of the Erdős-Rényi random graph model. The proposed model is obtained by randomly permuting the edges of an Erdős-Rényi random graph and interpreting this permutation as an ordering of presence times. It was shown that the connectivity threshold in the Erdős-Rényi model fans out into multiple phase transitions for several distinct notions of reachability in the temporal setting. In the present paper, we identify a sharp threshold for the emergence of a giant temporally connected component. We show that at p = log n/n the size of the largest temporally connected component increases from o(n) to~n-o(n). This threshold holds for both open and closed connected components, i.e. components that allow, respectively forbid, their connecting paths to use external nodes.