Abstract
We give an overview of the properties and models for complex networks, with particular emphasis on models of on-line social networks.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
L.A. Adamic, O. Buyukkokten, E. Adar, A social network caught in the web, First Monday 8 (2003).
Y. Ahn, S. Han, H. Kwak, S. Moon, H. Jeong, Analysis of topological characteristics of huge on-line social networking services, In: Proceedings of the 16th International Conference on World Wide Web, 2007.
A. Bonato, A Course on the Web Graph, American Mathematical Society Graduate Studies Series in Mathematics, Providence, Rhode Island, 2008.
A. Bonato, N. Hadi, P. Horn, P. Prałat, C. Wang, Models of on-line social networks, Internet Mathematics 6 (2011) 285–313.
A. Bonato, R.J. Nowakowski, The Game of Cops and Robbers on Graphs, American Mathematical Society, Providence, Rhode Island, 2011.
A. Bonato, J. Janssen, and P. Prałat, The geometric protean model for on-line social networks, In: Proceedings of the 7th Workshop on Algorithms and Models for the Web-Graph (WAW2010), Lecture Notes in Computer Science 6516, Springer, 2010, 110–121.
F. Chierichetti, R. Kumar, S. Lattanzi, M. Mitzenmacher, A. Panconesi, P. Raghavan, On compressing social networks, In: Proceedings of the 15th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD’09), 2009.
F.R.K. Chung, Spectral Graph Theory, American Mathematical Society, Providence, Rhode Island, 1997.
F.R.K. Chung, L. Lu, Complex Graphs and Networks, American Mathematical Society, U.S.A., 2004.
E. Estrada, Spectral scaling and good expansion properties in complex networks, Europhys. Lett. 73 (2006) 649–655.
Facebook: statistics. Accessed September 1, 2011. http://www.facebook.com/press/info.php?statistics.
S. Fortunato, A. Flammini, F. Menczer, Scale-free network growth by ranking, Phys. Rev. Lett. 96 218701 (2006).
O. Frank, Transitivity in stochastic graphs and digraphs, Journal of Mathematical Sociology 7 (1980) 199–213.
A. Henry, P. Prałat, Rank-Based Models of Network Structure and the Discovery of Content, In: Proceedings of the 8th Workshop on Algorithms and Models for the Web Graph (WAW 2011), 2011.
J. Janssen, P. Prałat, Protean graphs with a variety of ranking schemes, Theoretical Computer Science 410 (2009), 5491–5504.
A. Java, X. Song, T. Finin, B. Tseng, Why we twitter: understanding microblogging usage and communities, In: Proceedings of the Joint 9th WEBKDD and 1st SNA-KDD Workshop 2007, 2007.
M. Kim, J. Leskovec, Multiplicative attribute graph model of real-world networks, In: Proceedings of the 7th Workshop on Algorithms and Models for the Web Graph (WAW 2010), 2010.
J. Kleinberg, The small-world phenomenon: An algorithmic perspective, In: Proceedings of the 32nd ACM Symposium on Theory of Computing, 2000.
R. Kumar, J. Novak, A. Tomkins, Structure and evolution of on-line social networks, In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006.
H. Kwak, C. Lee, H. Park, S. Moon, What is Twitter, a social network or a news media?, In: Proceedings of the 19th International World Wide Web Conference, 2010.
S. Lattanzi, D. Sivakumar, Affiliation networks, In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, 2009.
J. Leskovec, J. Kleinberg, C. Faloutsos, Graphs over time: densification Laws, shrinking diameters and possible explanations, In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2005.
J. Leskovec, D. Chakrabarti, J. Kleinberg, C. Faloutsos, Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication, In: Proceedings of European Conference on Principles and Practice of Knowledge Discovery in Databases, 2005.
J. Leskovec, D. Chakrabarti, J. Kleinberg, C. Faloutsos, Z. Ghahramani, Kronecker Graphs: An approach to modeling networks, Journal of Machine Learning Research 11 (2010) 985–1042.
D.A. Levin, Y. Peres, E.L. Wilmer, Markov Chains and Mixing Times, American Mathematical Society, 2009.
T. Łuczak, P. Prałat, Protean graphs, Internet Mathematics 3 (2006), 21–40.
M. Mahdian, Y. Xu, Stochastic Kronecker graphs, In: Proceedings of the 5th Workshop on Algorithms and Models for the Web-Graph, 2007
A. Mislove, M. Marcon, K. Gummadi, P. Druschel, B. Bhattacharjee, Measurement and analysis of on-line social networks, In: Proceedings of the 7th ACM SIGCOMM Conference on Internet Measurement, 2007.
M.E.J. Newman, J. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 036122 (2003).
J.P. Scott, Social Network Analysis: A Handbook, Sage Publications Ltd, London, 2000.
Yanhua Tian, Models and Mining of On-line Social Networks, M.Sc. Thesis, Ryerson University, 2011.
Twitaholic. Accessed September 1, 2011. http://twitaholic.com/.
D.J. Watts, S.H. Strogatz, Collective dynamics of ‘small-world’ networks, Nature 393 (1998) 440–442.
H. White, S. Harrison, R. Breiger, Social structure from multiple networks, I: Blockmodels of roles and positions, American Journal of Sociology 81 (1976) 730–780.
Wikipedia: List of social networking websites. Accessed September 1, 2011. http://en.wikipedia.org/wiki/Listofsocialnetworkingwebsites.
YouTube, Advertising and Targeting. Accessed September 1, 2011. http://www.youtube.com/t/advertising_targeting.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bonato, A., Tian, Y. (2012). Complex Networks and Social Networks. In: Kranakis, E. (eds) Advances in Network Analysis and its Applications. Mathematics in Industry, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30904-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-30904-5_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30903-8
Online ISBN: 978-3-642-30904-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)