Assortativity in complex networks

Journal of Complex Networks

Volumn 3, Issue 4, 2014, Pages 507-542

  Noldus, Rogier ^a   Mieghem, Piet Van ^b  

^a Ericsson Telecommunications   (Germany)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Assortativity; Degree; Degree correlation; Graph; Graph spectrum; Network; Robustness

Indexed keywords

COMPLEX NETWORKS; GRAPH THEORY; NETWORKS (CIRCUITS); ROBUSTNESS (CONTROL SYSTEMS); SURVEYS;

ASSORTATIVITY; DEGREE; DEGREE CORRELATION; GRAPH; GRAPH SPECTRA;

DIRECTED GRAPHS;

EID: 84949804360     PISSN: 20511310     EISSN: 20511329     Source Type: Journal    
DOI: 10.1093/comnet/cnv005     Document Type: Article

References (64)

1. Newman, M. (2002) Assortative mixing in networks. Phys. Rev. Lett., 89, 208701.
2. Quayle, A., Siddiqui, A., Jones, A. (2006) Modeling network growth with assortative mixing. Eur. Phys. J. B 50, 617-630.
3. Nagoshi, C., Johnson, R., Danko, G. (1990) Assortative mating for cultural identification as indicated by language use. Behav. Genet., 20, 23-31.
4. Van Mieghem, P. (2014) Performance Analysis of Complex Networks and Systems. Cambridge: Cambridge University Press.
5. Newman, M. (2003) Mixing patterns in networks. Phys. Rev. E, 67, 026126.
6. Newman, M. (2003) The structure and function of complex networks. SIAM Rev., 45, 167-256.
7. D'Agostino, G., Scala, A., Zlatic, V., Caldarelli, G. (2012) Assortativity effects on diffusion-like processes in scale-free networks. Eur. Phys. Lett., 97, 68006.
8. Chang, H., Su, B., Zhou, Y.&He, D. (2007) Assortativity and act degree distribution of some collaboration networks. Phys. A: Stat. Mech. Appl., 383, 687-702.
9. Estrada, E. (2011) Combinatorial study of degree assortativity in networks. Phys. Rev. E, 84, 047101.
10. Holme, P., Zhao, J. (2007) Exploring the assortativity-clustering space of a network's degree sequence. Phys. Rev. E, 75, 046111.
11. Konig, M., Tessone, C., Zenou, Y. (2008) From Assortative to Dissortative Networks: The Role of Capacity. CCSS Working Paper Series.
12. Leung, C., Chau, H. (2007)Weighted assortative and disassortative networksModel. Phys. A: Stat. Mech. Appl., 378, 591-602.
13. Litvak, N., van der Hofstad, R. (2013) Uncovering disassortativity in large scale-free networks. Phys. Rev. E, 87, 1-11.
14. Liu, D., Trajanovski, S., Van Mieghem, P. (2013) Random line graphs and a linear law for assortativity. Phys. Rev. E, 87, 012816, 1-10.
15. Manka-Krason, A., Kulakowski, K. (2010) Assortativity in random line graphs. Acta Phys. Pol. B, 3, 259-268.
16. Nguyen, D., Tran, D. (2010) On generating power-law networks with assortative mixing. International Conference on Communications and Electronics, Nha Trang, pp. 30-35.
17. Piraveenan,M., Prokopenko,M., Zomaya, A. (2011) On congruity of nodes and assortative information content in complex networks. School of information technologies, Sydney University, Technical Report 668.
18. Piraveenan, M., Prokopenko, M., Zomaya, A. (2008) Local assortativeness in scale-free networks. Europhys. Lett., 84, 28002.
19. Piraveenan, M., Prokopenko, M., Zomaya, A. (2008) Assortativeness and information in scale-free networks. Eur. Phys. J. B, 67, 291-300.
20. Piraveenan,M., Prokopenko,M., Zomaya, A. (2009) AssortativeMixing in Directed Networks. School of information technologies, Sydney University, Technical Report 637.
21. Piraveenan, M. (2010) Topological analysis of complex networks using assortativity. PhD thesis.
22. Piraveenan, M., Prokopenko, M., Zomaya, A. (2010) Assortative mixing in directed biological networks. IEEE/ACM Trans. Comput. Biol. Bioinf., 9, 66-78.
23. Piraveenan, M., Prokopenko, M., Zomaya, A. (2006) Information-cloning of scale-free networks. Proceedings of the 9th European conference on Advances in artificial life, Lisbon, pp. 925-935.
24. Van Mieghem, P., Ge, X., Schumm, P., Trajanovski, S., Wang, H. (2010) Spectral graph analysis of modularity and assortativity. Phys. Rev. E, 82, 056113.
25. Van Mieghem, P., Wang, H., Ge, X., Tang, S., Kuipers, F. (2010) Influence of assortativity and degreepreserving rewiring on the spectra of networks. Eur. Phys. J. B, 76, 643-652.
26. Wang, H.,Winterbach,W., VanMieghem, P. (2011) Assortativity of complementary graphs. Eur. Phys. J. B, 83, 203-214.
27. Winterbach,W., Ridder, D.,Wang, H., Reinders,M., Van Mieghem, P. (2012) Do greedy assortativity optimization algorithms produce good results? Eur. Phys. J. B, 85, article 151.
28. Xia,Y., Tse, C., Lau, F. (2012) Effect of assortativity on traffic performance in scale-free networks. IEEE Int. Symp. on Circuits Syst., 906-909. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6272190&sortType%3Dasc_p_Sequence%26filter%3DAND(p_IS_Number%3A6270389)%26pageNumber%3D10.
29. Xu, X., Zhang, J., Sun, J., Small, M. (2009) Revising the simple measures of assortativity in complex networks. Phys. Rev. E, 80, 056106.
30. Xulvi-Brunet, R., Sokolov, I. (2005) Changing correlations in networks: assortativity and dissortativity. Acta Phys. Pol. B, 36, 1431-1455.
31. Zhou, J., Xu, X., Zhang, J., Sun, J., Small, M., Lu, J. (2008) Generating an assortative network with a given degree distribution. Int. J. Bifurcation Chaos, 18, 3495-3502.
32. Zhou, D., Stanley, H., D'Agostino, G., Scala, A. Assortativity decreases the robustness of interdependent networks. Phys. Rev. E, 86, 066103, 1-7.
33. Foster, J., Foster, D., Grassberger, P., Paczuski, M. (2010) Edge direction and the structure of networks. Proc. Natl Acad. Sci. USA, 107, 10815-10820.
34. Van Mieghem, P. (2010) Graph Spectra for Complex Networks. Cambridge: Cambridge University Press.
35. Erdos, P., Rényi, A. (1959) On random graphs. Publicationes Mathematicae, 6, 290-297.
36. Erdos, P., Rényi A. (1960) On the evolution of random graphs. Publ. Math. Inst. the Hung. Acad. Sci., 5, 17-61.
37. Barabási, A., Albert, R. (1999) Emergence of scaling in random networks. Science, 286, 509-512.
38. Watts, D., Strogatz, S. (1998) Collective dynamics of 'small-world' networks. Nature, 393, 440-442.
39. Callaway, D., Hopcroft, J., Kleinberg, J., Newman, M., Strogatz, S. (2001) Are randomly grown graphs really random. Phys. Rev. E, 64, 041902.
40. Catanzaro, M., Caldarelli, G., Pietronero, L. (2004) Assortative model for social networks. Phys. Rev. E, 70, 037101.
41. Grossman, J., Ion, P. (1995) On a portion of the well-known collaboration graph. Conf. Comb. Graph Theory Comput., 108, 129-131.
42. Pastor-Satorras, R., Vázquez, A., Vespignani, A. (2001) Dynamical and correlation properties of the internet. Phys. Rev. Lett., 87, 258701, 1-4.
43. Chen, N., Olvera-Cravioto, M. (2013) Directed random graphs with given degree distributions. Stoch. Syst., 3, 147-186.
44. Sole, R., Valverde, S. (2004) Information theory of complex networks?: on evolution and architectural constraints. Complex Netw., Lect. Notes Phys., 650, 189-207.
45. Wang, H., Douw, L., Hernández, J., Reijneveld, J., Stam, C., Van Mieghem, P. (2010) Effect of tumor resection on the characteristics of functional brain networks. Phys. Rev. E, 82, 021924.
46. Spearman, C. Refer to http://udel.edu/~mcdonald/statspearman.html for explanation of Spearman's rho.
47. Martin-Hernandez, J., Li, Z., Van Mieghem, P. (2014) Weighted betweenness and algebraic connectivity. J. Complex Netw., 2, 272-287.
48. Noldus, R., VanMieghem, P. (2013) Effect of degree-preserving, assortative rewiring on OSPF router configuration. 25th International Teletraffic Congress (ITC), Shanghai, 10-12 September 2013.
49. Maslov, S., Sneppen, K. (2002) Specificity and stability in topology of protein networks. Science 296, 910-913.
50. Youssef, M., Khorramzadeh, Y., Eubank, S. (2013) Network reliability: the effect of local network structure on diffusive processes. Phys. Rev. E, 88, 052810(10).
51. Li, L., Alderson, D., Willinger, W., Doyle, J. (2004) A first-principles approach to understanding the internet's router-level topology. ACM SIGCOMM Comput. Commun. Rev., 34, 3-14.
52. Gutman, I., Trinajstic, N. (1972) Graph theory and molecular orbitals, Total p electron energy of alternant hydrocarbons. Chem. Phys. Lett., 17, 535-538.
53. Makowiec, D. (2005) Evolving network-simulation study. From regular lattice to scale free network. Eur. Phys. J. B -Condens. Matter Complex Syst., 48, 547-555.
54. Dorogovtsev, N., Mendes, J. (2002) Evolution of networks. Adv. Phys., 51, 1079-1187.
55. Li, C., Wang, H., Van Mieghem, P. (2013) Epidemic threshold in directed networks. Phys. Rev. E, 88, 062802, 1-11.
56. Myers, C. (2003) Software systems as complex networks: structure, function, and evolvability of software collaboration graphs. Phys. Rev. E 68, 046116.
57. Fiedler, M. (1973) Algebraic connectivity of graphs. Czech. Math. J., 23, 298-305.
58. Cvetkoviæ, D., Doob, M., Sachs, H. (1980) Spectra of Graphs: Theory and Application. New York: Academic Press.
59. Mohar, B. (1991) The Laplacian spectrum of graphs. Graph theory, combinatorics and applications", Wiley, 2, 871-898.
60. Klein, D., Randiæ, M. (1993) Resistance distance. J. Math. Chem., 12, 81-95.
61. Ellens,W., Spieksma, F., VanMieghem, P., Jamakovic, A., Kooij, R. (2011) Effective graph resistance. Linear Algebra Appl.,435, 2491-2506.
62. Trajanovski, S., Martín-Hernández, J., Winterbach, W., Van Mieghem, P. (2013) Robustness envelopes of networks. J. Complex Netw., 1, 44-62.
63. Liu, D., Trajanovski, S., Van Mieghem, P. (2014) ILIGRA: an efficient inverse line graph algorithm. J. Math. Model. Algorithms Oper. Res. (to appear).
64. Zhang, G., Cheng, S., Zhang, G. (2011) A universal assortativity measure for network analysis. Phys. Rev. E. http://arxiv.org/abs/1212.6456.