Abstract
The distribution of shortest path lenghts is a useful characterisation of the connectivity in a network. The small-world experiment is a classical way to study the shortest path distribution in real-world social networks that cannot be directly observed. However, the data observed in these experiments are distorted by two factors: attrition and routing (in)efficiency. This leads to inaccuracies in the estimates of shortest path lenghts. In this paper we propose a model to analyse small-world experiments that corrects for both of the aforementioned sources of bias. Under suitable circumstances the model gives accurate estimates of the true underlying shortest path distribution without directly observing the network. It can also quantify the routing efficiency of the underlying population. We study the model by using simulations, and apply it to real data from previous small-world experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S.: Four degrees of separation. In: WebSci., pp. 33–42 (2012)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Bauckhage, C., Kersting, K., Rastegarpanah, B.: The Weibull as a model of shortest path distributions in random networks. In: MLG (2013)
Bonchi, F., De Francisci Morales, G., Gionis, A., Ukkonen, A.: Activity preserving graph simplification. Data Min. Knowl. Discov. 27(3), 321–343 (2013)
Dodds, P.S., Muhamad, R., Watts, D.J.: An experimental study of search in global social networks. Science 301(5634), 827–829 (2003)
Erdős, P., Rényi, A.: On random graphs. Publicationes Mathematicae Debrecen 6, 290–297 (1959)
Goel, S., Muhamad, R., Watts, D.J.: Social search in ”small-world” experiments. In: WWW, pp. 701–710 (2009)
Gomez-Rodriguez, M., Leskovec, J., Krause, A.: Inferring networks of diffusion and influence. Transactions on Knowledge Discovery from Data 5(4), 21 (2012)
Gomez-Rodriguez, M., Schölkopf, B.: Submodular inference of diffusion networks from multiple trees. In: ICML (2012)
Killworth, P.D., McCarty, C., Bernard, H.R., House, M.: The accuracy of small world chains in social networks. Social Networks 28(1), 85–96 (2006)
Kleinberg, J.M.: Navigation in a small world. Nature 406(6798), 845 (2000)
Korte, C., Milgram, S.: Acquaintance links between white and negro populations: Application of the small world method. Journal of Personality and Social Psychology 15(2), 101–108 (1970)
Liben-Nowell, D., Novak, J., Kumar, R., Raghavan, P., Tomkins, A.: Geographic routing in social networks. Proceedings of the National Academy of Sciences 102(33), 11623–11628 (2005)
Mathioudakis, M., Bonchi, F., Castillo, C., Gionis, A., Ukkonen, A.: Sparsification of influence networks. In: KDD, pp. 529–537 (2011)
Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry 32(4), 425–443 (1969)
Watts, D.J., Dodds, P.S., Newman, M.E.J.: Identity and search in social networks. Science 296(5571), 1302–1305 (2002)
Zachary, W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33(4), 452–473 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ukkonen, A. (2014). Indirect Estimation of Shortest Path Distributions with Small-World Experiments. In: Blockeel, H., van Leeuwen, M., Vinciotti, V. (eds) Advances in Intelligent Data Analysis XIII. IDA 2014. Lecture Notes in Computer Science, vol 8819. Springer, Cham. https://doi.org/10.1007/978-3-319-12571-8_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-12571-8_29
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12570-1
Online ISBN: 978-3-319-12571-8
eBook Packages: Computer ScienceComputer Science (R0)