• Corpus ID: 245502185

# Modularity and edge sampling

@article{McDiarmid2021ModularityAE,
title={Modularity and edge sampling},
author={Colin McDiarmid and Fiona Skerman},
journal={ArXiv},
year={2021},
volume={abs/2112.13190}
}
• Published 25 December 2021
• Mathematics
• ArXiv
Suppose that there is an unknown underlying graph G on a large vertex set, and we can test only a proportion of the possible edges to check whether they are present in G. If G has high modularity, is the observed graph G′ likely to have high modularity? We see that this is indeed the case under a mild condition, in a natural model where we test edges at random. We find that q∗(G′) ≥ q∗(G) − ε with probability at least 1 − ε, as long as the expected number edges in G′ is large enough. Similarly…

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