How likely is a random graph shift-enabled?
Discrete Mathematics
2021-09-02 v1 Signal Processing
Abstract
The shift-enabled property of an underlying graph is essential in designing distributed filters. This article discusses when a random graph is shift-enabled. In particular, popular graph models ER, WS, BA random graph are used, weighted and unweighted, as well as signed graphs. Our results show that the considered unweighted connected random graphs are shift-enabled with high probability when the number of edges is moderately high. However, very dense graphs, as well as fully connected graphs, are not shift-enabled. Interestingly, this behaviour is not observed for weighted connected graphs, which are always shift-enabled unless the number of edges in the graph is very low.
Cite
@article{arxiv.2109.00339,
title = {How likely is a random graph shift-enabled?},
author = {Liyan Chen and Samuel Cheng and Vladimir Stankovic and Lina Stankovic},
journal= {arXiv preprint arXiv:2109.00339},
year = {2021}
}
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9 pages