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Node Ordering for Rescalable Network Summarization (or, the Apparent Magic of Word Frequency and Age of Acquisition in the Lexicon)

Part of the Studies in Computational Intelligence book series (SCI,volume 812)

Abstract

How can we “scale down” an n-node network G to a smaller network \(G'\), with \(k \ll n\) nodes, so that \(G'\) (approximately) maintains the important structural properties of G? There is a voluminous literature on many versions of this problem if k is given in advance, but one’s tolerance for approximation (and the resulting value of k) will vary. Here, then, we formulate a “rescalable” version of this approximation task for complex networks. Specifically, we propose a node ordering version of graph summarization: permute the nodes of G so that the subgraph induced by the first k nodes is a good size-k approximation of G, averaged over the full range of possible sizes k. We consider as a case study the phonological network of English words, and discover two natural word orders (word frequency and age of acquisition) that do a surprisingly good job of rescalably summarizing the lexicon.

Keywords

  • Network summarization
  • Node ordering
  • Phonological networks

This work grew out of portions of a research project that was carried out by the authors of this work in collaboration with Aman Panda and Duo Tao. We gratefully acknowledge their contributions. This work was supported in part by Carleton College. Comments are welcome.

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Correspondence to David Liben-Nowell .

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Brown, V. et al. (2019). Node Ordering for Rescalable Network Summarization (or, the Apparent Magic of Word Frequency and Age of Acquisition in the Lexicon). In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 812. Springer, Cham. https://doi.org/10.1007/978-3-030-05411-3_6

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