Abstract
Many researchers identify influentials in a network by their betweenness centrality. Whereas betweenness centrality can be calculated in small, static, connected networks, its calculation in complex, large, evolving networks frequently causes some problems. Hence, we propose a proxy variable for a node’s betweenness centrality that can be calculated in large, evolving networks. We illustrate our approach using the example of Key Opinion Leader (KOL) identification in an evolving co-authorship network of researchers who have published articles about PCSK9 (a protein that regulates cholesterol levels).
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
Notes
- 1.
- 2.
DBLP is a database of computer science publications; http://dblp.org, accessed on July 22nd 2015.
- 3.
PCSK9 is a protein which regulates LDL cholesterol levels. By blocking PCSK9, cholesterol levels can be brought substantially down. Hence, drugs can be developed that reduce the risk of cardiovascular diseases by blocking PCSK9.
- 4.
http://www.ncbi.nlm.nih.gov/pubmed, accessed on June 4th 2015.
- 5.
http://gephi.org, accessed on July 14th 2015.
- 6.
In the analyses, we left out the years 1994–2002, since no papers about PCSK9 were published then.
- 7.
Although Freeman [13] proposed a standardised measure of betweenness centrality that can theoretically be used for comparing centrality scores between components of different size, we think that it is, for example, not meaningful to compare the maximal betweenness centrality of a node in a component with three actors to that of a node in the main component of a co-authorship network.
- 8.
The main component of a network is also sometimes referred to as the “giant component”.
- 9.
There were no other meaningful big components in the network. For example, the second (third) biggest component in the network comprised 1.23 % (0.69 %) of all authors.
- 10.
These influential people include basic researchers as well as researchers conducting clinical trials. Hence, some context knowledge is helpful for reading the tables.
- 11.
We suppose that node A will have a high betweenness centrality in the final network, although node B and node C are more likely to co-author a paper in the future than two random nodes if both have co-authored a paper with node A. In the literature, this fact has been termed the “forbidden triad” [14].
- 12.
This is true for all years except 2004 and 2005. However, there were only very few publications in these years (14 and 18 respectively, compare Table 1), and the high correlation coefficients between an author’s degree centrality and this author’s betweenness centrality for those two years can be explained by chance. Furthermore, the differences in the correlation coefficients between the number of an author’s unclosed triads and betweennness centrality and author’s degree centrality and betweenness centrality for the years 2004 and 2005 are not very large (0.4428995 vs. 0.5012240 and 0.4435424 vs. 0.4919271).
- 13.
The “Florentine families network” is a very small network (with 16 nodes only).
- 14.
Encouraged by a literature review and interviews with marketing managers from the pharmaceutical industry, we assumed that authors with a high betweenness centrality have a high influence as well. Although we think that this is a reasonable assumption for co-authorship networks, we want to be clear that structural importance and dynamic influence of nodes do not necessarily have to be the same.
References
Aggarwal, C., Subbian, K.: Evolutionary network analysis: a survey. ACM Comput. Surv. 47(1), 10 (2014). doi:10.1145/2601412
Backstrom, L., Huttenlocher, D., Kleinberg, J., Lan, X.: Group formation in large social networks: membership, growth, and evolution. In: Paper presented at the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Philadelphia, PA, USA
Bader, D.A., Kintali, S., Madduri, K., Mihail, M.: Approximating betweenness centrality. In: Algorithms and Models for the Web-Graph, pp. 124–137. Springer, (2007)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999). doi:10.1126/science.286.5439.509
Barabási, A.L., Jeong, H., Neda, Z., Ravasz, E., Schubert, A., Vicsek, T.: Evolution of the social network of scientific collaborations. Physica A 311(3–4), 590–614 (2002)
Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25(2), 163–177 (2001)
Breiger, R.L., Pattison, P.E.: Cumulated social roles—the duality of persons and their algebras. Soc. Netw. 8(3), 215–256 (1986). doi:10.1016/0378-8733(86)90006-7
Butts, C.T.: Social network analysis with sna. J. Stat. Softw. 24(6), 1–51 (2008)
Czárdi, G., Nepusz, T.: The igraph software package for complex network research. InterJournal, Complex Syst. 1695 (2006)
Ediger, D., Jiang, K., Riedy, J., Bader, D., Corley, C., Farber, R., Reynolds, W.N.: Massive social network analysis: mining twitter for social good. In: Paper presented at the 39th International Conference on Parallel Processing (ICPP) San Diego, CA
Franceschet, M.: Collaboration in computer science: a network science approach. J. Am. Soc. Inform. Sci. Technol. 62(10), 1992–2012 (2011). doi:10.1002/asi.21614
Freeman, L.C.: Set of measures of centrality based on betweenness. Sociometry 40(1), 35–41 (1977). doi:10.2307/3033543
Freeman, L.C.: Centrality in social networks conceptual clarification. Soc. Netw. 1(3), 215–239 (1979). doi:10.1016/0378-8733(78)90021-7
Granovetter, M.S.: The strength of weak ties. Am. J. Sociol. 78(6), 1360–1380 (1973). doi:10.1086/225469
Jeong, H., Mason, S.P., Barabási, A.L., Oltvai, Z.N.: Lethality and centrality in protein networks. Nature 411(6833), 41–42 (2001). doi:10.1038/35075138
Knuth, D.E.: The Stanford GraphBase: A Platform for Combinatorial Computing. Addison-Wesley Reading (1993)
Liu, P., Xia, H.: Structure and evolution of co-authorship network in an interdisciplinary research field. Scientometrics 103(1), 101–134 (2015). doi:10.1007/s11192-014-1525-y
McLaughlin, A., Bader, D.A.: Scalable and high performance betweenness centrality on the GPU. In: Paper presented at the International Conference for High Performance Computing, Networking, Storage and Analysis, New Orleans, Louisana
Morstatter, F., Pfeffer, J., Liu, H., Carley, K.M.: Is the sample good enough? comparing data from Twitter’s streaming API with Twitter’s firehose. In: Paper presented at the International AAAI Conference on Web and Social Media, Cambridge, Massachusetts
Newman, M.E.: Scientific collaboration networks—I. Network construction and fundamental results. Phys. Rev. E 64, 016131 (2001)
Newman, M.E.: Scientific collaboration networks—II. Shortest paths, weighted networks, and centrality. Phys. Rev. E 64, 016132 (2001)
Newman, M.E.J.: The structure of scientific collaboration networks. Proc. Nat. Acad. Sci. USA 98(2), 404–409 (2001). doi:10.1073/pnas.021544898
Newman, M.E.J.: Coauthorship networks and patterns of scientific collaboration. Proc. Nat. Acad. Sci. 101(suppl 1), 5200–5205 (2004). doi:10.1073/pnas.0307545100
Shi, X., Bonner, M., Adamic, L.A., Gilbert, A.C.: The very small world of the well-connected. In: Paper presented at the Nineteenth ACM Conference on Hypertext and Hypermedia, Pittsburgh, PA, USA
Spearman, C.: The proof and measurement of association between 2 Things (Reprinted from Amer. J. Psychol. vol. 15, pp. 72–101, 1904). Am. J. Psychol 100(3–4), 441–471 (1987)
Tomassini, M., Luthi, L.: Empirical analysis of the evolution of a scientific collaboration network. Physica A 385(2), 750–764 (2007)
Vidgen, R., Henneberg, S., Naude, P.: What sort of community is the European Conference on information systems? a social network analysis 1993–2005. Eur. J. Inf. Syst. 16(1), 5–19 (2007)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998). doi:10.1038/30918
Yan, E., Ding, Y.: Applying centrality measures to impact analysis: a coauthorship network analysis. J. Am. Soc. Inform. Sci. Technol. 60(10), 2107–2118 (2009). doi:10.1002/asi.21128
Yang, J., Chen, Y.: Fast computing betweenness centrality with virtual nodes on large sparse networks. PLoS ONE 6(7), e22557 (2011). doi:10.1371/journal.pone.0022557
Yang, Y., Dong, Y., Chawla, N.V.: Predicting node degree centrality with the node prominence profile. Sci. Rep. 4(7236) (2014). doi:10.1038/srep07236
Acknowledgments
This work was supported by a fellowship within the FITweltweit programme of the German Academic Exchange Service (DAAD).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Putzke, J., Takeda, H. (2016). Identifying Key Opinion Leaders in Evolving Co-authorship Networks—A Descriptive Study of a Proxy Variable for Betweenness Centrality. In: Cherifi, H., Gonçalves, B., Menezes, R., Sinatra, R. (eds) Complex Networks VII. Studies in Computational Intelligence, vol 644. Springer, Cham. https://doi.org/10.1007/978-3-319-30569-1_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-30569-1_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30568-4
Online ISBN: 978-3-319-30569-1
eBook Packages: EngineeringEngineering (R0)