On the time to identify the nodes in a random graph

Jonathan R. Stewart

Statistics & Probability Letters, 2023, vol. 195, issue C

Abstract: The sampling of networks is an important problem at the frontier of statistical network analysis, and the identification of population members of a network is an important step in the sampling process. In this work, we study the random time τ to identify the nodes in an Erdős-Rényi random graph through egocentric sampling We derive the exact distribution of τ and give an exact formula for computing the mean time Eτ as a function of the size of the network. We explore how Eτ varies with the size of the network, the probability of edges, and network sparsity. We establish the scaling of τ with network size in both sparse and dense random graphs, highlighting special cases that demonstrate sub-linear scaling of τ with the size of the network. All theoretical results are non-asymptotic. Lastly, we discuss possible extensions to classes of random graphs beyond Erdős-Rényi random graphs.

Keywords: Sampling times; Random graphs; Egocentric network sampling; Erdős-Rényi random graph (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109779

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