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Detecting Nestedness in Graphs

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Complex Networks & Their Applications V (COMPLEX NETWORKS 2016 2016)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 693))

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Many real-world networks have a nested structure. Examples range from biological ecosystems (e.g. mutualistic networks), industry systems (e.g. New York garment industry) to inter-bank networks (e.g. Fedwire bank network). A nested network has a graph topology such that a vertex’s neighborhood contains the neighborhood of vertices of lower degree. Thus –upon node reordering– the adjacency matrix is stepwise, and it can be found in both bipartite and non-bipartite networks. Despite the strict mathematical characterization and their common occurrence, it is not easy to detect nested graphs unequivocally. Among others, there exist three methods for detection and quantification of nestedness that are widely used: BINMATNEST, NODF, and FCM. However, these methods fail in detecting nestedness for graphs with low (NODF) and high (NODF, BINMATNEST) density or are developed for bipartite networks (FCM). Another common shortcoming of these approaches is the underlying asumption that all vertices belong to a nested component. However, many real-world networks have solely a sub-component (i.e. not all vertices) that is nested. Thus, unveiling which vertices pertain to the nested component is an important research question, unaddressed by the methods available so far. In this contribution, we study in detail the algorithm Nestedness detection based on Local Neighborhood (NESTLON) [7]. This algorithm detects nestedness on a broad range of nested graphs independently of their density and resorts solely on local information. Further, by means of a benchmarking model we are able to tune the degree of nestedness in a controlled manner and study its efficiency. Our results show that NESTLON outperforms both BINMATNEST and NODF.

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  1. Almeida-Neto, M., Guimarães, P., Guimarães, P.R., Ulrich, W.: A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement. Oikos 117(March), 1227–1239 (2008). DOI 10.1111/j.2008.0030-1299.16644.x

  2. Atmar, W., Patterson, B.D.: The Measure of Order and Disorder in the Distribution of Species in Fragmented Habitat. International Association for Ecology 96(3), 373–382 (1993)

    Google Scholar 

  3. Bardoscia, M., Luca, G., Livan, G., Marsili, M., Tessone, C.J.: The Social Climbing Game. Journal of Statistical Physics 151(3-4), 440–457 (2013). DOI 10.1007/s10955-013-0693-0

  4. Bascompte, J., Jordano, P., Melián, C.J., Olesen, J.M.: The nested assembly of plant-animal mutualistic networks. Proceedings of the National Academy of Sciences of the United States of America 100(16), 9383–9387 (2003). DOI 10.1073/pnas.1633576100

  5. Brualdi, R., Hoffmann, A.: On the Spectral Radius of (0,1)-Matrices. Linear Algebra and its Applications 146, 133–146 (1985)

    Google Scholar 

  6. Flores, C.O., Valverde, S., Weitz, J.S.: Multi-scale structure and geographic drivers of crossinfection within marine bacteria and phages. The ISME Journal 7(3), 520–532 (2012). DOI 10.1038/ismej.2012.135. URL

  7. Grimm, A., Tessone, C.J.: Detecting the nested components of generic graphs (2017). In preparation

    Google Scholar 

  8. König, M.D., Tessone, C.J.: Network evolution based on centrality. Physical Review E 84(5), 056,108 (2011). DOI 10.1103/PhysRevE.84.056108

  9. König, M.D., Tessone, C.J., Zenou, Y.: Nestedness in networks: A theoretical model and some applications. Theoretical Economics 9(3), 695–752 (2014). DOI 10.3982/TE1348

  10. Mahadev, N., Peled, U.: Threshold Graphs and Related Topics. North-Holland, Amsterdam (1995)

    Google Scholar 

  11. Rodríguez-Gironés, M.A., Santamaría, L.: A new algorithm to calculate the nestedness temperature of presence-absence matrices. Journal of Biogeography 33(5), 924–935 (2006). DOI 10.1111/j.1365-2699.2006.01444.x

  12. Saavedra, S., Stouffer, D.B., Uzzi, B., Bascompte, J.: Strong contributors to network persistence are the most vulnerable to extinction. Nature 478(7368), 233–235 (2011). DOI 10.1038/nature10433

  13. Soramäki, K., Bech, M.L., Arnold, J., Glass, R.J., Beyeler, W.E.: The topology of interbank payment flows. Physica A: Statistical Mechanics and its Applications 379(1), 317–333 (2007). DOI 10.1016/j.physa.2006.11.093. URL

  14. Tacchella, A., Cristelli, M., Caldarelli, G., Gabrielli, A., Pietronero, L.: A New Metrics for Countries’ Fitness and Products’ Complexity. Scientific Reports 2, 1–4 (2012). DOI 10.1038/srep00723

  15. Uzzi, B.: The Sources and Consequences of Embeddedness for the Economic Performance of Organizations: The network Effect (1996)

    Google Scholar 

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Correspondence to Alexander Grimm or Claudio J. Tessone .

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Grimm, A., Tessone, C.J. (2017). Detecting Nestedness in Graphs. In: Cherifi, H., Gaito, S., Quattrociocchi, W., Sala, A. (eds) Complex Networks & Their Applications V. COMPLEX NETWORKS 2016 2016. Studies in Computational Intelligence, vol 693. Springer, Cham.

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  • Print ISBN: 978-3-319-50900-6

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