Degree-Degree Dependencies in Directed Networks with Heavy-Tailed Degrees

REFERENCES

• R. Albert and A.-L. Barabási. “Statistical Mechanics of Complex Networks.” Reviews of Modern Physics 74:1(2002), 47.
   Web of Science ®Google Scholar
• M. Boguná and R. Pastor-Satorras. “Epidemic Spreading in Correlated Complex Networks.” Physical Review E 66:4(2002), 047104.
   Google Scholar
• P. Boldi and S. Vigna. “The Webgraph Framework I: Compression Techniques.” In Proceedings of the 13th International Conference on the World Wide Web, pp. 595–602. ACM, 2004.
   Google Scholar
• P. Boldi and S. Vigna. “The Webgraph Framework II: Codes For The World-Wide Web.” In Proceedings of the Data Compression Conference, 2004, p. 528. IEEE, 2004.
   Google Scholar
• M. Brede and S. Sinha. “Assortative Mixing by Degree Makes a Network More Unstable.” arXiv preprint cond-mat/0507710, 2005.
   Google Scholar
• N. Chen and M. Olvera-Cravioto. “Directed Random Graphs with Given Degree Distributions.” Stochastic Systems 3:1(2013), 147–186.
   Google Scholar
• D. B. H. Cline. “Convolution Tails, Product Tails and Domains of Attraction.” Probability Theory and Related Fields 72:4(1986), 529–557.
   Web of Science ®Google Scholar
• S. de Franciscis, S. Johnson, and J. J. Torres. “Enhancing Neural Network Performance via Assortativity.” Physical Review E 83:3(2011), 036114.
   Google Scholar
• J. G. Foster, D. V. Foster, P. Grassberger, and M. Paczuski. “Edge Direction and the Structure of Networks.” In Proceedings of the National Academy of Sciences 107:24(2010), 10815–10820.
   PubMed Web of Science ®Google Scholar
• A. Kaltenbrunner, G. Gonzalez, R. R. De Querol, and Y. Volkovich. “Comparative Analysis of Articulated and Behavioural Social Networks in a Social News Sharing Website.” New Review of Hypermedia and Multimedia 17:3(2011), 243–266.
   Web of Science ®Google Scholar
• M. G. Kendall. “A New Measure of Rank Correlation.” Biometrika 30:1–2(1938), 81–93.
   Google Scholar
• D. Laniado, R. Tasso, Y. Volkovich, and A. Kaltenbrunner. “When the Wikipedians Talk: Network and Tree Structure of Wikipedia Discussion Pages.” In International Conference on Weblogs and Social Media. AAAI, 2011.
   Google Scholar
• N. Litvak and R. van der Hofstad. “Degree-Degree Correlations in Random Graphs with Heavy-Tailed Degrees.” arXiv preprint arXiv:1202.3071, 2012. To appear in Internet Mathematics.
   Google Scholar
• N. Litvak and R. van der Hofstad. “Uncovering Disassortativity in Large Scale Free Networks.” Physical Review E 87:2(2013), 022801.
   Google Scholar
• X. F. Liu and C. K. Tse. “Impact of Degree Mixing Pattern on Consensus Formation in Social Networks.” Physica A: Statistical Mechanics and its Applications 407(2014), 1–6.
   Web of Science ®Google Scholar
• M. E. J. Newman. “Assortative Mixing in Networks.” Physical Review Letters 89:20(2002), 208701.
   PubMed Web of Science ®Google Scholar
• M. E. J. Newman. “Mixing Patterns in Networks.” Physical Review E 67:2(2003), 026126.
   Web of Science ®Google Scholar
• M. E. J. Newman. “The Structure and Function of Complex Networks.” SIAM Review 45:2(2003), 167–256.
   Web of Science ®Google Scholar
• M. Piraveenan, M. Prokopenko, and A. Y. Zomaya. “Assortativeness and Information in Scale-Free Networks.” The European Physical Journal B 67:3(2009), 291–300.
   Web of Science ®Google Scholar
• M. Piraveenan, M. Prokopenko, and A. Zomaya. “Assortative Mixing in Directed Biological Networks.” IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 9:1(2012), 66–78.
   Web of Science ®Google Scholar
• S. I. Resnick. Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer, 2007.
   Google Scholar
• C. Spearman. “The Proof and Measurement of Association Between Two Things.” The American Journal of Psychology 15:1(1904), 72–101.
   Google Scholar
• A. Srivastava, B. Mitra, N. Ganguly, and F. Peruani. “Correlations in Complex Networks Under Attack.” Physical Review E 86:3(2012), 036106.
   Google Scholar
• A. Srivastava, B. Mitra, F. Peruani, and N. Ganguly. “Attacks on Correlated Peer-To-Peer Networks: An Analytical Study.” In IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), 2011, pp. 1076–1081. IEEE, 2011.
   Google Scholar
• P. van der Hoorn and N. Litvak. “Convergence of Rank Based Degree-Degree Correlations in Random Directed Networks.” arXiv preprint arXiv:1407.7662, 2014.
   Google Scholar
• A.Vázquez and Y. Moreno. “Resilience to Damage of Graphs with Degree Correlations.” Physical Review E 67(2003), 015101.
   Google Scholar
• S. Vigna. “A Weighted Correlation Index for Rankings with Ties.” arXiv preprint arXiv:1404.3325, 2014.
   Google Scholar