Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Network structure from rich but noisy data


Driven by growing interest across the sciences, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the Internet and the World Wide Web to biological networks and social networks. The data produced by these experiments are often rich and multimodal, yet at the same time they may contain substantial measurement error1,2,3,4,5,6,7. Accurate analysis and understanding of networked systems requires a way of estimating the true structure of networks from such rich but noisy data8,9,10,11,12,13,14,15. Here we describe a technique that allows us to make optimal estimates of network structure from complex data in arbitrary formats, including cases where there may be measurements of many different types, repeated observations, contradictory observations, annotations or metadata, or missing data. We give example applications to two different social networks, one derived from face-to-face interactions and one from self-reported friendships.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Application of the methods described here to two example networks.


  1. 1.

    Killworth, P. D. & Bernard, H. R. Informant accuracy in social network data. Hum. Organ. 35, 269–286 (1976).

    Article  Google Scholar 

  2. 2.

    Marsden, P. V. Network data and measurement. Annu. Rev. Sociol. 16, 435–463 (1990).

    Article  Google Scholar 

  3. 3.

    Lakhina, A., Byers, J., Crovella, M. & Xie, P. Sampling biases in IP topology measurements. In Proc. 22nd Annual Joint Conf. of the IEEE Computer and Communications Societies (Institute of Electrical and Electronics Engineers, New York, NY, 2003).

  4. 4.

    Clauset, A. & Moore, C. Accuracy and scaling phenomena in Internet mapping. Phys. Rev. Lett. 94, 018701 (2005).

    ADS  Article  Google Scholar 

  5. 5.

    Wodak, S. J., Pu, S., Vlasblom, J. & Séraphin, B. Challenges and rewards of interaction proteomics. Mol. Cell. Proteom. 8, 3–18 (2009).

    Article  Google Scholar 

  6. 6.

    Handcock, M. S. & Gile, K. J. Modeling social networks from sampled data. Ann. Appl. Stat. 4, 5–25 (2010).

    MathSciNet  Article  Google Scholar 

  7. 7.

    Lusher, D., Koskinen, J. & Robins, G. Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications (Cambridge Univ. Press, Cambridge, 2012).

  8. 8.

    Butts, C. T. Network inference, error, and informant (in)accuracy: A Bayesian approach. Soc. Netw. 25, 103–140 (2003).

    Article  Google Scholar 

  9. 9.

    Clauset, A., Moore, C. & Newman, M. E. J. Hierarchical structure and the prediction of missing links in networks. Nature 453, 98–101 (2008).

    ADS  Article  Google Scholar 

  10. 10.

    Guimerà, R. & Sales-Pardo, M. Missing and spurious interactions and the reconstruction of complex networks. Proc. Natl Acad. Sci. USA 106, 22073–22078 (2009).

    ADS  Article  Google Scholar 

  11. 11.

    Namata, G. M., Kok, S. & Getoor, L. Collective graph identification. In Proc. 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (Association of Computing Machinery, New York, 2011).

  12. 12.

    Allen, J. D., Xie, Y., Chen, M., Girard, L. & Xiao, G. Comparing statistical methods for constructing large scale gene networks. PLoS One 7, e29348 (2012).

    ADS  Article  Google Scholar 

  13. 13.

    Han, X., Shen, Z., Wang, W.-X. & Di, Z. Robust reconstruction of complex networks from sparse data. Phys. Rev. Lett. 114, 028701 (2015).

    ADS  Article  Google Scholar 

  14. 14.

    Martin, T., Ball, B. & Newman, M. E. J. Structural inference for uncertain networks. Phys. Rev. E 93, 012306 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    Casiraghi, G., Nanumyan, V., Scholtes, I. & Schweitzer, F. From relational data to graphs: Inferring significant links using generalized hypergeometric ensembles. In Proc. International Conf. on Social Informatics (SocInfo 2017), no. 10540 in Lecture Notes in Computer Science (eds Ciampaglia, G. et al.) 111–120 (Springer, Berlin, 2017).

  16. 16.

    Uetz, P. et al. A comprehensive analysis of protein–protein interactions in Saccharomyces cerevisiae. Nature 403, 623–627 (2000).

    ADS  Article  Google Scholar 

  17. 17.

    Ito, T. et al. A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc. Natl Acad. Sci. USA 98, 4569–4574 (2001).

    ADS  Article  Google Scholar 

  18. 18.

    Giot, L., Bader, J. S. & Brouwer, C. et al. A protein interaction map of Drosophila melanogaster. Science 302, 1727–1736 (2003).

    ADS  Article  Google Scholar 

  19. 19.

    Krogan, N. J. et al. Global landscape of protein complexes in the yeast Saccharomyces cerevisiae. Nature 440, 637–643 (2006).

    ADS  Article  Google Scholar 

  20. 20.

    Rapoport, A. & Horvath, W. J. A study of a large sociogram. Behav. Sci. 6, 279–291 (1961).

    Article  Google Scholar 

  21. 21.

    Resnick, M. D. et al. Protecting adolescents from harm: Findings from the National Longitudinal Study on Adolescent Health. J. Am. Med. Assoc. 278, 823–832 (1997).

    Article  Google Scholar 

  22. 22.

    Bernard, H. R. & Killworth, P. D. Informant accuracy in social network data II. Human. Commun. Res. 4, 3–18 (1977).

    Article  Google Scholar 

  23. 23.

    Liu, Y., Liu, N. J. & Zhao, H. Y. Inferring protein–protein interactions through high-throughput interaction data from diverse organisms. Bioinformatics 21, 3279–3285 (2005).

    Article  Google Scholar 

  24. 24.

    Angulo, M. T., Moreno, J. A., Lippner, G., Barabási, A.-L. & Liu, Y.-Y. Fundamental limitations of network reconstruction from temporal data. J. Royal Soc. Interface 14, 20160966 (2017).

    Article  Google Scholar 

  25. 25.

    Overbeek, R. et al. Wit: Integrated system for high-throughput genome sequence analysis and metabolic reconstruction. Nucleic Acids Res. 28, 123–125 (2000).

    Article  Google Scholar 

  26. 26.

    Forster, J., Famili, I., Fu, P., Palsson, B. O. & Nielsen, J. Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Res. 13, 244–253 (2003).

    Article  Google Scholar 

  27. 27.

    Schafer, J. & Strimmer, K. An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics 21, 754–764 (2005).

    Article  Google Scholar 

  28. 28.

    Margolin, A. A. et al. ARACNE: An algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinformatics 7, S7 (2006).

    Article  Google Scholar 

  29. 29.

    Langfelder, P. & Horvath, S. Wgcna: An R package for weighted correlation network analysis. BMC Bioinformatics 9, 559 (2008).

    Article  Google Scholar 

  30. 30.

    Liben-Nowell, D. & Kleinberg, J. The link-prediction problem for social networks. J. Assoc. Inf. Sci. Technol. 58, 1019–1031 (2007).

    Article  Google Scholar 

  31. 31.

    Huisman, M. Imputation of missing network data: Some simple procedures. J. Social Struct. 10, 1–29 (2009).

    Google Scholar 

  32. 32.

    Kim, M. & Leskovec, J. The network completion problem: Inferring missing nodes and edges in networks. In Proc. 2011 SIAM International Conf. on Data Mining (eds Liu, B. et al.) 47–58 (Society for Industrial and Applied Mathematics: Philadelphia, PA, 2011).

  33. 33.

    Smalheiser, N. R. & Torvik, V. I. Author name disambiguation. Annu. Rev. Inf. Sci. Technol. 43, 287–313 (2009).

    Article  Google Scholar 

  34. 34.

    D’Angelo, C. A., Giuffrida, C. & Abramo, G. A heuristic approach to author name disambiguation in bibliometrics databases for large-scale research assessments. J. Assoc. Inf. Sci. Technol. 62, 257–269 (2011).

    Article  Google Scholar 

  35. 35.

    Ferreira, A. A., Goncalves, M. A. & Laender, A. H. F. A brief survey of automatic methods for author name disambiguation. SIGMOD Rec. 41, 15–26 (2012).

    Article  Google Scholar 

  36. 36.

    Tang, J., Fong, A. C. M., Wang, B. & Zhang, J. A unified probabilistic framework for name disambiguation in digital library. IEEE Trans. Knowl. Data Eng. 24, 975–987 (2012).

    Article  Google Scholar 

  37. 37.

    Brugere, I., Gallagher, B. & Berger-Wolf, T. Y. Network structure inference, a survey: Motivations, methods, and applications. ACM Comput. Surv. 1, 1 (2016).

    Google Scholar 

  38. 38.

    Dempster, A. P., Laird, N. M. & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. J. Royal Stat. Soc. B 39, 185–197 (1977).

    MathSciNet  MATH  Google Scholar 

  39. 39.

    Eagle, N. & Pentland, A. Reality mining: Sensing complex social systems. J. Personal Ubiquitous Comput. 10, 255–268 (2006).

    Article  Google Scholar 

Download references


The author thanks E. Bruch, G. Cantwell, T. Martin, G. Reinert and M. Riolofor useful comments. This work was funded in part by the US National Science Foundation under grants DMS–1407207 and DMS–1710848. This work uses data from Add Health, a programme project designed by J. R. Udry, P. S. Bearman and K. Mullan Harris, and funded by a grant P01–HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. A special acknowledgment is due to R. R. Rindfuss and B. Entwisle for assistance in the original design. Anyone interested in obtaining data files from Add Health should contact Add Health, Carolina Population Center, 123 W. Franklin Street, Chapel Hill, NC 27516-2524 ( No direct support was received from grant P01-HD31921 for this analysis.

Author information




M.E.J.N. designed and conducted the research and wrote the paper.

Corresponding author

Correspondence to M. E. J. Newman.

Ethics declarations

Competing interests

The author declares no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Material

Supplementary notes, supplementary figures 1–3

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Newman, M.E.J. Network structure from rich but noisy data. Nature Phys 14, 542–545 (2018).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing