Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T09:36:27.843Z Has data issue: false hasContentIssue false
  • English
  • Français

Algorithms for generating large-scale clustered random graphs

Published online by Cambridge University Press:  21 November 2014

CHENG WANG ,
OMAR LIZARDO  and
DAVID HACHEN
CHENG WANG
Affiliation:
Department of Population Health and Disease Prevention, University of California, Irvine, A.I.R.Bldg 653, Suite 2040H, 653 East Peltason Drive, Irvine, CA 92697, USA (e-mail: [email protected])
OMAR LIZARDO
Affiliation:
Department of Sociology, University of Notre Dame, 735 Flanner, Notre Dame, IN 46545, USA (e-mail: [email protected], [email protected])
DAVID HACHEN
Affiliation:
Department of Sociology, University of Notre Dame, 735 Flanner, Notre Dame, IN 46545, USA (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Real-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure beyond the dyadic level. As a result we need to generate clustered random graph to compare the local structure at higher network levels. In this paper a generalized version of Gleeson's algorithm G(VS, VT, ES, ET, S, T) is advanced to generate a clustered random graph in large-scale which persists the number of vertices |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network and it works successfully for nine large-scale networks. Our new algorithm also has advantages in randomness evaluation and computation efficiency when compared with the existing algorithms.

Keywords

large-scale networkclustered random graphgenerating algorithm
Type
Research Article
Information
Network Science , Volume 2 , Issue 3 , December 2014 , pp. 403 - 415
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, R., Jeong, H., & Barabási, A.-L. (1999). Diameter of the World-Wide Web. Nature, 401, 130–131.Google Scholar
Bagrow, J. P., Wang, D., & Barabási, A.-L. (2011). Collective response on human populations to large-scale emergencies. PLoS One, 6, 1–8.Google Scholar
Bansal, S., Khandelwal, S., & Meyers, L. A. (2009). Exploring biological network structure with clustered random networks. BMC Bioinformatics, 10, 405–419.Google Scholar
Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509–512.CrossRefGoogle ScholarPubMed
Burt, R. S. (1995). Structural Holes: The Social Structure of Competition. Cambridge, MA: Harvard University Press.Google Scholar
Cartwright, D. & Harary, F. (1956). Structural balance: A generalization of Heider's theory. Psychological Review, 63, 277–293.Google Scholar
Cho, E., Myers, S. A., & Leskovec, J. (2011). Friendship and mobility: User movement in location-based social networks. Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York: ACM, pp. 1082–1090.Google Scholar
Davis, J. A. (1967). Clustering and structural balance in graphs. Human Relations, 30, 181–187.Google Scholar
Davis, J. A. (1979). The Davis /Holland /Leinhardt studies: An overview. In Holland, P. W., & Leinhardt, S. (Eds.), Perspectives on Social Network Research (pp. 51–62). New York: Academic Press.CrossRefGoogle Scholar
de Sola Pool, I., & Kochen, M. (1978/1979). Contacts and influence. Social Networks, 1, 5–51.Google Scholar
Ercsey-Ravasz, M., Lichtenwalter, R. N., Chawla, N. V., & Toroczkai, Z. (2011). Range-limited Centrality Measures in Non-weighted and Weighted Complex Networks, arXiv e-print, 1111.5382.Google Scholar
Erdős, P., & Rényi, A. (1959). On random graphs I. Publicationes Mathematicae, 6, 290–297.CrossRefGoogle Scholar
Ghoshal, G., & Barabási, A.-L. (2011). Ranking stability and super-stable nodes in complex networks. Nature Communications, 2, 1–7.Google Scholar
Gleeson, J. P. (2009). Bond percolation on a class of clustered random networks. Physical Review E, 80, 036107.Google Scholar
Granovetter, M. (1973). The strength of weak ties. American Journal of Sociology, 78, 1360–1380.CrossRefGoogle Scholar
Guo, W., & Kraines, S. B. (2009). A random network generator with finely tunable clustering coefficient for small-world social networks. Proceedings of the 2009 International Conference on Computational Aspects of Social Networks. Washington, DC: IEEE Computer Society, pp. 10–17.Google Scholar
Heider, F. (1946). Attitudes and cognitive organization. Journal of Psychology, 21, 107–112.Google Scholar
Hidalgo, C. A. & Rodriguez-Sickert, C. (2008). The Dynamics of a mobile phone network. Physica A, 387, 3017–3024.Google Scholar
Krackhardt, D. (1998). Simmelian ties: Super strong and sticky. In Kramer, R. M. & Neale, M. A. (Eds.), Power and Influence in Organizations (pp. 21–38). Thousand Oaks, CA: Sage.Google Scholar
Krackhardt, D., & Handcock, M. S. (2006). Heider vs. Simmel: Emergent features in dynamic structures. In Airoldi, E. M., & Blei, D. M. (Eds.), Statistical Network Analysis: Models, Issues and New Directions (ICML 2006) (pp. 14–27). Berlin: Springer.Google Scholar
Leskovec, J., Huttenlocher, D., & Kleinberg, J. (2010). Signed networks in social media. CHI ‘10 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems. New York: ACM, pp. 1361–1370.Google Scholar
Leskovec, J., Kleinberg, J., & Faloutsos, C. (2005). Graphs over time: Densification laws, shrinking diameters and possible explanations. In KDD ‘05 Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining. New York. ACM, pp. 177–187.Google Scholar
Leskovec, J., Lang, K., Dasgupta, A., & Mahoney, M. (2009). Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Mathematics, 6, 29–123.Google Scholar
Lichtenwalter, R. N., Lussier, J. T., & Chawla, N. V. (2010). New perspectives and methods in link prediction. Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). New York: ACM, pp. 243–252.CrossRefGoogle Scholar
Liu, Y.-Y., Slotine, J.-J., & Barabási, A.-L. (2011). Controllability of complex networks. Nature, 473, 167–173.Google Scholar
McAuley, J., & Leskovec, J. (2012). Image labeling on a network: Using social-network metadata for image classification. ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV, Berlin, Heidelberg: Springer-Verlag, pp. 828–841.Google Scholar
Miller, J. C. (2009). Percolation and epidemics in random clustered networks. Physical Review E, 80, 020901(R).Google Scholar
Molloy, M., & Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures & Algorithm, 6, 161–179.Google Scholar
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45, 167–256.Google Scholar
Newman, M. E. J. (2009). Random graphs with clustering. Physical Review Letters, 103, 05870.Google Scholar
Onnela, J. P., Arbesman, S., Gonzalez, M. C., Barabási, A.-L., & Christakis, N. A. (2011). Geographic constraints on social network groups. PLoS One, 6, 1–7.Google Scholar
Opsahl, T., & Panzarasa, P. (2009). Clustering in weighted networks. Social Networks, 31, 155–163.CrossRefGoogle Scholar
Raeder, T., Lizardo, O., Hachen, D., & Chawla, N. V. (2011). Predictors of short-term decay of cell phone contacts in a large-scale communication network. Social Networks, 33, 245–257.Google Scholar
Serrano, M. Á., & Boguñá, M. (2005). Tuning clustering in random networks with arbitrary degree distributions. Physical Review E, 72, 036133.Google Scholar
Serrano, M. Á., & Boguñá, M. (2006a). Clustering in complex networks. I. General formalism. Physical Review E, 74, 056114.Google Scholar
Serrano, M. Á., & Boguñá, M. (2006b). Clustering in complex networks. II. Percolation properties. Physical Review E, 74, 056115.Google Scholar
Simmel, G. (1908/1950). The Sociology of Georg Simmel. New York: Free Press.Google Scholar
Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry, 32, 425–443.Google Scholar
Wang, C., Lizardo, O, Hachen, D., Strathman, A., Toroczkai, Z., & Chawla, N. V. (2013). A dyadic reciprocity index for repeated interaction networks. Network Science, 1, 31–48.Google Scholar
Wang, D., Pedreschi, D., Song, C, Giannotti, F., & Barabási, A.-L. (2011). Human mobility, social ties, and link prediction. ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), New York: ACM, pp. 1100–1108.Google Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of “Small-world” networks. Nature, 393, 440–442.Google Scholar
Yang, J., & Leskovec, J. (2012). Defining and evaluating network communities based on ground-truth. MDS ‘12 Proceedings of the ACM SIGKDD Workshop on Mining Data Semantics, Article No. 3. New York: ACM.Google Scholar