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The evolution and structure of social networks

Published online by Cambridge University Press:  12 December 2014

WHITMAN RICHARDS  and
NICHOLAS WORMALD
WHITMAN RICHARDS
Affiliation:
CSAIL- 32-364, Mass. Inst. of Technology, Cambridge, MA 02139, USA (e-mail: wrichards@mit.edu)
NICHOLAS WORMALD
Affiliation:
School of Mathematical Sciences, Monash University, Clayton VIC 3149, Australia (e-mail: nicholas.wormald@monash.edu)
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Abstract

As social networks evolve, new nodes are linked to the large-scale organization already in place. We show that the combination of two simple algorithms, one the Barabasi-Albert preferential attachment proposal and the other a neighbor attachment rule, successfully generate networks exhibiting both the local and global characteristics of empirical data on social network structures. Ideally, one might hope that some coarse features of this linking process and the form of the local patterns might enable the prediction of large-scale properties. We show that this is generally not the case. This might help explain the variety of local and global patterns in empirical networks.

Keywords

network evolutionpreferential attachmentsocial networksdegree distributions
Type
Research Article
Information
Network Science , Volume 2 , Issue 3 , December 2014 , pp. 326 - 340
Copyright
Copyright © Cambridge University Press 2014 

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References

Adamic, L. A., & Glance, N. (2005) The political blogosphere and the 2004 US election. Proceedings WWW-2005 Workshop on sthe Webblogging Ecosystem.Google Scholar
Atran, S., Bennett, S., Fatica, A., Magouik, J., Noricks, D., Sageman, M., . . . Wright, D. (2008) John Jay & ARTIS Transnational Terrorism (JJATT) dataset. http://doitapps.jjay.cuny.edu/jjatt/ Google Scholar
Barabasi, A-L. (2002). Linked: The New Science of Networks. NY: Perseus Press.Google Scholar
Barabasi, A-L. and Albert, R. (1999) Emergence of scaling in random networks. Science, 286, 509–511.CrossRefGoogle ScholarPubMed
Bebek, G, P. B., Cooper, C., Friedetzky, T., Nadeau, J., & Sahinalp, S. C. (2006). The degree distribution of the generalized duplication model. Theoretical Computer Science, 369, 239–249.Google Scholar
Blum, A., Chan, T. H. H., & Rwebangira, M. R. (2006). A random-surfer web-graph model. ANALCO, 6, 238–246.Google Scholar
Bollabas, B. (2001). Random Graphs (2nd ed.). Cambridge Univ. Press.Google Scholar
Bourassa, V., & Holt, F. (2003) SWAN: Small-world wide area networks. Proceedings of International Conference on Advances in Infrastructure (SSGRR 2003w paper # 64), L'Aquila, Italy.Google Scholar
Caldarelli, G, Pastor-Satorras, R., & Vespignani, A. (2004) Structure of cycles and local ordering in complex networks. European Physics Journal B, 38, 183–186.Google Scholar
Cohen, W. W. (2009). Enron email dataset. http://www.cs.cmu.edu/~enron/ Google Scholar
Dorogovtsev, S. N., & Mendes, J. F. (2003). Evolution of Networks, Oxford Univ. Press.Google Scholar
Dunbar, R. (1992). Neocortical size as a constraint on group size in primates. Journal Human Evolution, 22, 469–493.Google Scholar
Farczadi, L., & Wormald, N. (2013). On the degree distribution of a growing network model, Mathematical arXiv:1401.0933.Google Scholar
Freeman, L. C. (1978). Centrality in social networks: conceptual clarification. Social Networks, 1, 215–239.Google Scholar
Girvan, M., & Newman, M. E. J. (2002). Community structure in social and biological networks. Proceedings National Academy Science, 99, 7821–7826.Google Scholar
Gnawali, O. D. (2009). Linus kernel email communication neworks from Jan 2001 and 2008. Personal communication.Google Scholar
Granovetter, M. (1973). The strength of weak ties. American Journal Sociology, 78, 1360–1368.CrossRefGoogle Scholar
Kasturirangan, R. (1999). Multiple scales in small world graphs. MIT-CSAIL technical reports: //publications.ai.mit.edu/ai-publications/pdf/AIM-1663.pdf Google Scholar
Knuth, D. E. (1993). The Stanford GraphBase: A Platform for Combinatorial Computing. Addison-Wesley, Reading Ma.Google Scholar
Krebs, V. (2003). Books about US politics dataset (unpublished.) http://www.orgnet.com/ Google Scholar
Kumar, R., Rajagopalan, P. R., Sivakumar, S., Tomkins, A, D.. & Upfal, E., (2000). Stochastic models for the web graph. Proceedings Foundations of Computer Science, 41st Annual Symposium, 57–65.Google Scholar
Leskovec, J., Singh, A., & Kleinberg, J. (2006) Patterns of influence in a recommendation network. Proceedings Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD).Google Scholar
Lusseau, D., Schneider, K., Boisseau, O. J., Haase, P., Slooten, E., & Dawson, S. M. (2003) The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behavioral Ecology and Sociobiology, 54, 396–405.Google Scholar
Macindoe, O. (2010). Investigating the fine grained structure of networks. MS Thesis. Dept. Elec. Engr. and Comp. Sci. http://Google Scholar
Macindoe, O. & Richards, W. (2010) Graph comparison using fine structure analysis. Proceedings IEEE Conference on Society Computing, # 244.Google Scholar
Milo et al. (2002). Network Motifs. Science, 298, 824–827.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. (2006). Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E, 74.Google Scholar
Newman, M. E. J. (2005). A measure of betweenness centrality based on random walk. Social Networks, 27, 39–54.Google Scholar
Page, S.E. (2007). The Difference: how the power of diversity creates better groups, firms, schools, and societies. Princeton Univ. Press.Google Scholar
Palmer, E. M. (1985). Graphical Evolution, Wiley & Sons.Google Scholar
Palla, G. Derenyi, I. Farkes, I. & Viesek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435, 814–818.Google Scholar
Read, R. C. & Wilson, R. J. (1998). An Atlas of Graphs. Oxford Press.Google Scholar
Richards, W. & Macindoe, O. (2010). Decomposing Social networks. Proceedings IEEE Conference on Society Computing, # 205.Google Scholar
Richards, W. & Macindoe, O. (2010). Characteristics of small social networks. MIT Computer science and artificial intelligence Lab Tech report MIT-CSAIL-TR-2010-033.Google Scholar
Richards, W. & Wormald, N. (2009). Representing small group evolution. Proceedings IEEE Conference on Society Computing, # 232.Google Scholar
Schelp, R. H. & Thomason, A. (1998). A remark on the number of complete and empty subgraphs. Combinatorics, Probability and Computing, 7, 217–219.Google Scholar
Stoica, A. & Prieur, C. (2009). Structure of neighborhoods in a large social network. Proceedings IEEE Conference on Society Computing, # 225.Google Scholar
Watts, D. (2002). A simple model of global cascades on random networks, PNAS, 99, 5766–5771.Google Scholar
Watts, D. and Strogatz, S. (1998). Collective dynamics of small world networks, Nature, 393, 440–442.Google Scholar
White, J. G., Southgate, E., Thompson, J. N. and Brenner, S. (1986). The structure of the nervous system of the nematode c.elegans. Philosophical Transactions of the Royal Society, 314, 1–340.Google Scholar
Wolfram, S (2002). A New Kind of Science, pp. 508–515. Wolfram Media, Inc. Google Scholar
Zachary, W. W. (1977) An information flow model for conflict and fission in small groups. Journal Anthropological Research, 33, 452–473.Google Scholar