Abstract
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of organization in the network. Here, we give a precise definition of hierarchical structure, give a generic model for generating arbitrary hierarchical structure in a random graph, and describe a statistically principled way to learn the set of hierarchical features that most plausibly explain a particular real-world network. By applying this approach to two example networks, we demonstrate its advantages for the interpretation of network data, the annotation of graphs with edge, vertex and community properties, and the generation of generic null models for further hypothesis testing.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Markov Chain Monte Carlo
- Random Graph
- Community Detection
- Hierarchical Organization
- Bayesian Model Average
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Kleinberg, J.: The small-world phenomenon: an algorithmic perspective. In: 32nd ACM Symposium on Theory of Computing (2000)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002)
Söderberg, B.: General formalism for inhomogeneous random graphs. Phys. Rev. E 66, 066121 (2002)
Wasserman, S., Robins, G.L.: An introduction to random graphs, dependence graphs, and p *. In: Carrington, P., Scott, J., Wasserman, S. (eds.) Models and Methods in Social Network Analysis, Cambridge University Press, Cambridge (2005)
Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, Cambridge (1994)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, New York (2001)
Casella, G., Berger, R.L.: Statistical Inference. Duxbury Press, Belmont (1990)
Newman, M.E.J., Barkema, G.T.: Monte Carlo Methods in Statistical Physics. Clarendon Press, Oxford (1999)
Zachary, W.W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452–473 (1977)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002)
Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. Proc. Natl. Acad. Sci. USA 101, 2658–2663 (2004)
Newman, M.E.J.: Detecting community structure in networks. Eur. Phys. J. B 38, 321–330 (2004)
Bryant, D.: A classification of consensus methods for phylogenies. In: Janowitz, M., Lapointe, F.J., McMorris, F.R., Mirkin, B., Roberts, F. (eds.) BioConsensus, pp. 163–184. DIMACS (2003)
Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., Barabási, A.L.: Hierarchical organization of modularity in metabolic networks. Science 30, 1551–1555 (2002)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70, 066111 (2004)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. ACM Machine Learning 56, 89–113 (2004)
Hastings, M.B.: Community detection as an inference problem. Preprint cond-mat/0604429 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clauset, A., Moore, C., Newman, M.E.J. (2007). Structural Inference of Hierarchies in Networks. In: Airoldi, E., Blei, D.M., Fienberg, S.E., Goldenberg, A., Xing, E.P., Zheng, A.X. (eds) Statistical Network Analysis: Models, Issues, and New Directions. ICML 2006. Lecture Notes in Computer Science, vol 4503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73133-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-73133-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73132-0
Online ISBN: 978-3-540-73133-7
eBook Packages: Computer ScienceComputer Science (R0)