Abstract
In this paper, a spatial preferential attachment model for complex networks in which there is non-uniform distribution of the nodes in the metric space is studied. In this model, the metric layout represents hidden information about the similarity and community structure of the nodes. It is found that, for density functions that are locally constant, the graph properties can be well approximated by considering the graph as a union of graphs from uniform density spatial models corresponding to the regions of different densities. Moreover, methods from the uniform case can be used to extract information about the metric layout. Specifically, through link and co-citation analysis the density of a node’s region can be estimated and the pairwise distances for certain nodes can be recovered with good accuracy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aiello, W., Bonato, A., Cooper, C., Janssen, J., Prałat, P.: A spatial web graph model with local influence regions. Internet Mathematics 5(1-2), 175–196 (2008)
Bonato, A., Janssen, J., Prałat, P.: Geometric protean graphs. Internet Mathematics 8(1-2), 2–28 (2012)
Bradonjić, M., Hagberg, A., Percus, A.G.: Giant component and connectivity in geographical threshold graphs. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 209–216. Springer, Heidelberg (2007)
Cooper, C., Frieze, A.M., Prałat, P.: Some typical properties of the spatial preferred attachment model. In: Bonato, A., Janssen, J. (eds.) WAW 2012. LNCS, vol. 7323, pp. 29–40. Springer, Heidelberg (2012)
Flaxman, A.D., Frieze, A.M., Vera, J.: A geometric preferential attachment model of networks. In: Leonardi, S. (ed.) WAW 2004. LNCS, vol. 3243, pp. 44–55. Springer, Heidelberg (2004)
Hoff, P., Raftery, A., Handcock, M.: Latent space approaches to social network analysis. Journal of the American Statistical Association 97, 1090–1098 (2001)
Jacob, E., Mörters, P.: Spatial preferential attachment networks: Power laws and clustering coefficients. ArXiv e-prints (October 2012)
Janssen, J., Prałat, P., Wilson, R.: Geometric graph properties of the spatial preferred attachment model. Advances in Applied Mathematics 50(2), 243–267 (2013)
Janssen, J., Hurshman, M., Kalyaniwalla, N.: Model selection for social networks using graphlets. Internet Math. 8(4), 338–363 (2012)
Jeh, G., Widom, J.: SimRank: a measure of structural-context similarity. In: Knowledge Discovery and Data Mining, pp. 538–543 (2002)
Jordan, J.: Geometric preferential attachment in non-uniform metric spaces. ArXiv e-prints (August 2012)
Kobayakawa, M., Kinjo, S., Hoshi, M., Ohmori, T., Yamamoto, A.: Fast computation of similarity based on jaccard coefficient for composition-based image retrieval. In: Muneesawang, P., Wu, F., Kumazawa, I., Roeksabutr, A., Liao, M., Tang, X. (eds.) PCM 2009. LNCS, vol. 5879, pp. 949–955. Springer, Heidelberg (2009)
Small, H.: Co-citation in the scientific literature: A new measure of the relationship between two documents. Journal of the American Society for Information Science 24(4), 265–269 (1973)
Zhang, J.: Growing Random Geometric Graph Models of Super-linear Scaling Law. ArXiv e-prints (December 2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Janssen, J., Prałat, P., Wilson, R. (2013). Asymmetric Distribution of Nodes in the Spatial Preferred Attachment Model. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2013. Lecture Notes in Computer Science, vol 8305. Springer, Cham. https://doi.org/10.1007/978-3-319-03536-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-03536-9_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03535-2
Online ISBN: 978-3-319-03536-9
eBook Packages: Computer ScienceComputer Science (R0)