Measuring the Generalized Friendship Paradox in Networks with Quality-Dependent Connectivity
- 791 Downloads
The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment-like network growth mechanism governed by both node degrees and ‘qualities’. We introduce measures to quantify paradoxes, and contrast the results obtained in our model to those obtained for an uncorrelated network, where the degrees and qualities of adjacent nodes are uncorrelated. We shed light on the effect of the distribution of node qualities on the friendship paradox. We consider both the mean and the median to measure paradoxes, and compare the results obtained by using these two statistics.
KeywordsNode Degree Quality Distribution Decay Factor Median Version Critical Degree
Unable to display preview. Download preview PDF.
- 3.Hodas, N.O., Kooti, F., Lerman, K.: Friendship Paradox Redux: Your Friends Are More Interesting Than You. In: Proc. 7th Int. Conf. on Weblogs and Social Media, ICWSM 2013, pp. 1–8. ACM, New York (2013)Google Scholar
- 4.Ugandre, J., Karrer, B., Backstorm, L., Marlow, C.: The Anatomy of the Facebook Social Graph. arXiv preprint arxiv:1111.4503 (2011)Google Scholar
- 5.Eom, Y.H., Jo, H.H.: Generalized Friendship Paradox in Complex Networks: The Case of Scientific Collaboration. Nature Scientific Reports 4 (2014)Google Scholar
- 6.Jo, H.H., Eom, Y.H.: Generalized Friendship Paradox in Networks with Tunable Degree-attribute Correlation. Physical Review E 90(2) (2014)Google Scholar
- 7.Kooti, F., Hoda, N.O., Lerman, K.: Network Weirdness: Exploring the Origins of Network Paradoxes. In: Proc. 8th Int. Conf. on Weblogs and Social Media, ICWSM 2014, pp. 266–274 (2014)Google Scholar
- 10.Kryvasheyeu, Y., Chen, H., Moro, E., Van Hentenryck, P., Cebrian, M.: Performance of Social Network Sensors During Hurricane Sandy. arXiv preprint arXiv:1402.2482 (2014)Google Scholar
- 12.Fotouhi, B., Momeni, N., Rabbat, M.G.: Generalized Friendship Paradox: An Analytical Approach. Appearing in Proc. 6th Int. Conf. on Social Informatics (workshops), SocInfo 2014, arXiv preprint arXiv:1410.0586 (2014)Google Scholar