Abstract
Many online social networks such as Twitter, Google+, Flickr and Youtube are directed in nature, and have been shown to exhibit a nontrivial amount of reciprocity. Reciprocity is defined as the ratio of the number of reciprocal edges to the total number of edges in the network, and has been well studied in the literature. However, little attention is given to understand the connectivity or network form by the reciprocal edges themselves (reciprocal network), its structural properties, and how it evolves over time. In this paper, we bridge this gap by presenting a comprehensive measurement-based characterization of the connectivity among reciprocal edges in Google+ and their evolution over time, with the goal to gain insight into the structural properties of the reciprocal network. Our analysis shows that the reciprocal network of Google+ reveals some important user behavior patterns, which reflect how the social network was being adopted over time.
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 subscriptionsNotes
- 1.
In this paper we use the terms “user” and “node” interchangeable.
- 2.
G+ assigns each user a 21-digit integer ID, where the highest order digit is always 1 (e.g., 100000000006155622736).
- 3.
It contains more than 90 % of the nodes with at least one reciprocal edge in G+. Hence, our analysis of the dataset is eventually approximate.
- 4.
We follow the terminology in [22] in order to compare with previous results.
- 5.
Similar results are obtained using the other subgraphs (\(H^{i=3,...,12}\)).
- 6.
We will analyse the community structure in a reciprocal network as future work.
- 7.
The authors in [9] stated similar conclusion.
References
Gong, N.Z., Xu, W.: Reciprocal versus parasocial relationships in online social networks. Soc. Netw. Anal. Min. 4(1), 184–197 (2014)
Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: IMC 2007, pp. 29–42. ACM (2007)
Kwak, H., Lee, C., Park, H., Moon, S.: What is twitter, a social network or a news media? In: WWW 2010, pp. 591–600. ACM (2010)
Magno, G., Comarela, G., Saez-Trumper, D., Cha, M., Almeida, V.: New kid on the block: exploring the Google+ social graph. In: IMC 2012, pp. 159–170. ACM (2012)
Garlaschelli, D., Loffredo, M.I.: Patterns of link reciprocity in directed networks. Phys. Rev. Lett. 93, 268–701 (2004)
Jiang, B., Zhang, Z.-L., Towsley, D.: Reciprocity in social networks with capacity constraints. In: KDD 2015, pp. 457–466. ACM (2015)
Hai, P.H., Shin, H.: Effective clustering of dense and concentrated online communities. In: Asia-Pacific Web Conference (APWEB) 2010, pp. 133–139. IEEE (2010)
Gong, N.Z., Xu, W., Huang, L., Mittal, P., Stefanov, E., Sekar, Song, D.: Evolution of the social-attribute networks: measurements, modeling, and implications using Google+. In: IMC 2015, pp. 131–144. ACM (2015)
Gonzalez, R., Cuevas, R., Motamedi, R., Rejaie, R., Cuevas, A.: Google+ or Google\(-?\) dissecting the evolution of the new OSN in its first year. In: WWW 2013, pp. 483–494. ACM (2013)
Wolfe, A.: Social network analysis: methods and applications. Am. Ethnologist 24(1), 219–220 (1997)
Jamali, M., Haffari, G., Ester, M.: Modeling the temporal dynamics of social rating networks using bidirectional effects of social relations and rating patterns. In: WWW 2011, pp. 527–536. ACM (2011)
Li, Y., Zhang, Z.-L., Bao, J.: Mutual or unrequited love: identifying stable clusters in social networks with uni- and bi-directional links. In: Bonato, A., Janssen, J. (eds.) WAW 2012. LNCS, vol. 7323, pp. 113–125. Springer, Heidelberg (2012)
Schiberg, D., Schneider, F., Schiberg, H., Schmid, S., Uhlig, S., Feldmann, A.: Tracing the birth of an OSN: social graph and profile analysis in Google+. In: WebSci 2012, pp. 265–274. ACM (2012)
Google+ Platform. http://www.google.com/intl/en/+/learnmore/
Google+. http://en.wikipedia.org/wiki/Google+
Kwak, H., Chun, H., Moon, S.: Fragile online relationship: a first look at unfollow dynamics in twitter. In: CHI 2011, pp. 1091–1100. ACM (2011)
Google+ New Feature. http://googledrive.blogspot.com/2012/10/share-your-stuff-from-google-drive-to.html
Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-Law Distributions in Empirical Data. SIAM Rev. 51, 661–703 (2009)
Fitting Power Law Distribution. http://tuvalu.santafe.edu/aaronc/powerlaws/
Backstrom, L., Boldi, P., Rosa, M., Ugander, J., Vigna, S.: Four degrees of separation. In: WebSci 2012, pp. 33–42. ACM (2012)
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: KDD 2005, pp. 177–187. ACM (2005)
Kumar, R., Novak, J., Tomkins, A.: Structure and evolution of online social networks. In: KDD 2006, pp. 611–617. ACM (2006)
Kossinets, G., Watts, D.J.: Empirical analysis of an evolving social network. Sci. 311, 88–90 (2006)
Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., Ghahramani, Z.: Kronecker graphs: an approach to modeling networks. J. Mach. Learn. Res. 11, 985–1042 (2010)
Google Strips Down Google Plus. http://blogs.wsj.com/digits/2015/11/17/google-strips-down-google-plus/
Acknowledgments
This research was supported in part by a Raytheon/NSF subcontract 9500012169/CNS-1346688, DTRA grants HDTRA1- 09-1-0050 and HDTRA1-14-1-0040, DoD ARO MURI Award W911NF-12-1-0385, and NSF grants CNS-1117536, CRI-1305237 and CNS-1411636. We thank the authors of [9] for the datasets and the workshop reviewers for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Dumba, B., Golnari, G., Zhang, ZL. (2016). Analysis of a Reciprocal Network Using Google+: Structural Properties and Evolution. In: Nguyen, H., Snasel, V. (eds) Computational Social Networks. CSoNet 2016. Lecture Notes in Computer Science(), vol 9795. Springer, Cham. https://doi.org/10.1007/978-3-319-42345-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-42345-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42344-9
Online ISBN: 978-3-319-42345-6
eBook Packages: Computer ScienceComputer Science (R0)