Scale-free networks with exponent one

Physical Review E

Volumn 94, Issue 2, 2016, Pages

  Timar G ^a   Dorogovtsev, S N ^a,b   Mendes, J F F ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

^b IOFFE INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSED MATTER PHYSICS;

DEGREE DISTRIBUTIONS; DEGREE-DEGREE CORRELATIONS; EMPIRICAL DATA; FINITE SIZE EFFECT; NETWORK STRUCTURES; REAL NETWORKS; REAL-WORLD NETWORKS; SIMILAR DEGREE;

PHYSICS;

EID: 84982705770     PISSN: 24700045     EISSN: 24700053     Source Type: Journal    
DOI: 10.1103/PhysRevE.94.022302     Document Type: Article

References (38)

1. M. E. J. Newman, Scientific collaboration networks. I. Network construction and fundamental results, Phys. Rev. E 64, 016131 (2001). 1063-651X 10.1103/PhysRevE.64.016131
2. F. Liljeros, C. R. Edling, L. A. N. Amaral, H. E. Stanley, and Y. Åberg, The web of human sexual contacts, Nature (London) 411, 907 (2001). NATUAS 0028-0836 10.1038/35082140
3. R. Albert, Scale-free networks in cell biology, J. Cell Sci. 118, 4947 (2005). JNCSAI 0021-9533 10.1242/jcs.02714
4. V. M. Eguiluz, D. R. Chialvo, G. A. Cecchi, M. Baliki, and A. V. Apkarian, Scale-Free Brain Functional Networks, Phys. Rev. Lett. 94, 018102 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.018102
5. M. Faloutsos, P. Faloutsos, and C. Faloutsos, On power-law relationships of the internet topology, in Proceedings of the ACM SIGCOMM Computer Communication Review (ACM, New York, 1999), Vol. 29, p. 251.
6. R. Albert, H. Jeong, and A.-L. Barabási, Internet: Diameter of the world-wide web, Nature (London) 401, 130 (1999). NATUAS 0028-0836 10.1038/43601
7. A.-L. Barabási, R. Albert, and H. Jeong, Scale-free characteristics of random networks: The topology of the World-Wide Web, Physica A 281, 69 (2000). PHYADX 0378-4371 10.1016/S0378-4371(00)00018-2
8. A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999). SCIEAS 0036-8075 10.1126/science.286.5439.509
9. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Structure of Growing Networks with Preferential Linking, Phys. Rev. Lett. 85, 4633 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.4633
10. P. L. Krapivsky, S. Redner, and F. Leyvraz, Connectivity of Growing Random Networks, Phys. Rev. Lett. 85, 4629 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.4629
11. R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.47
12. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of networks, Adv. Phys. 51, 1079 (2002). ADPHAH 0001-8732 10.1080/00018730110112519
13. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
14. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Principles of statistical mechanics of uncorrelated random networks, Nucl. Phys. B 666, 396 (2003). NUPBBO 0550-3213 10.1016/S0550-3213(03)00504-2
15. L. A. Adamic and B. A. Huberman, Power-law distribution of the World Wide Web, Science 287, 2115 (2000). SCIEAS 0036-8075 10.1126/science.287.5461.2115a
16. M. Levy and S. Solomon, Power laws are logarithmic Boltzmann laws, Int. J. Mod. Phys. C 7, 595 (1996). IJMPEO 0129-1831 10.1142/S0129183196000491
17. D. Sornette, Multiplicative processes and power laws, Phys. Rev. E 57, 4811 (1998). 1063-651X 10.1103/PhysRevE.57.4811
18. M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions, Internet Math. 1, 226 (2004). 1542-7951 10.1080/15427951.2004.10129088
19. G. Bianconi and A.-L. Barabási, Competition and multiscaling in evolving networks, Europhys. Lett. 54, 436 (2001). EULEEJ 0295-5075 10.1209/epl/i2001-00260-6
20. G. Bianconi and A.-L. Barabási, Bose-Einstein Condensation in Complex Networks, Phys. Rev. Lett. 86, 5632 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.5632
21. G. Caldarelli, A. Capocci, P. De Los Rios, and M. A. Munoz, Scale-free Networks from Varying Vertex Intrinsic Fitness, Phys. Rev. Lett. 89, 258702 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.258702
22. B. J. Kim, A. Trusina, P. Minnhagen, and K. Sneppen, Self organized scale-free networks from merging and regeneration, Eur. Phys. J. B 43, 369 (2005). EPJBFY 1434-6028 10.1140/epjb/e2005-00065-y
23. M. J. Alava and S. N. Dorogovtsev, Complex networks created by aggregation, Phys. Rev. E 71, 036107 (2005). PLEEE8 1539-3755 10.1103/PhysRevE.71.036107
24. H. Seyed-allaei, G. Bianconi, and M. Marsili, Scale-free networks with an exponent less than two, Phys. Rev. E 73, 046113 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.73.046113
25. S. Valverde, R. Ferrer Cancho, and R. V. Solé, Scale-free networks from optimal design, Europhys. Lett. 60, 512 (2002). EULEEJ 0295-5075 10.1209/epl/i2002-00248-2
26. R. M. D'Souza, P. L. Krapivsky, and C. Moore, The power of choice in growing trees, Eur. Phys. J. B 59, 535 (2007). EPJBFY 1434-6028 10.1140/epjb/e2007-00310-5
27. Z. Burda, J. D. Correia, and A. Krzywicki, Statistical ensemble of scale-free random graphs, Phys. Rev. E 64, 046118 (2001). 1063-651X 10.1103/PhysRevE.64.046118
28. Z. Burda and A. Krzywicki, Uncorrelated random networks, Phys. Rev. E 67, 046118 (2003). 1063-651X 10.1103/PhysRevE.67.046118
29. D. Krioukov, F. Papadopoulos, M. Kitsak, A. Vahdat, and M. Boguñá, Hyperbolic geometry of complex networks, Phys. Rev. E 82, 036106 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.82.036106
30. F. Papadopoulos, M. Kitsak, M. Á. Serrano, M. Boguñá, and D. Krioukov, Popularity versus similarity in growing networks, Nature (London) 489, 537 (2012). NATUAS 0028-0836 10.1038/nature11459
31. K. Zuev, F. Papadopoulos, and D. Krioukov, Hamiltonian dynamics of preferential attachment, J. Phys. A 49, 105001 (2016). 1751-8113 10.1088/1751-8113/49/10/105001
32. P. Colomer-de-Simon and M. Boguná, Clustering of random scale-free networks, Phys. Rev. E 86, 026120 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.026120
33. K. Anand, D. Krioukov, and G. Bianconi, Entropy distribution and condensation in random networks with a given degree distribution, Phys. Rev. E 89, 062807 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.062807
34. L. Pietronero, E. Tosatti, V. Tosatti, and A. Vespignani, Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf, Physica A 293, 297 (2001). PHYADX 0378-4371 10.1016/S0378-4371(00)00633-6
35. V. Bimal, M. Alan, C. Meeyoung, and P. G. Krishna, On the evolution of user interaction in Facebook, in Proceedings of the 2nd ACM Workshop on Online Social Networks (WOSN '09) (ACM, New York, 2009), p. 37.
36. A. Smith, 6 new facts about Facebook, Pew Research Center, http://www.pewresearch.org/fact-tank/2014/02/03/6-new-facts-about-facebook.
37. S. Herculano-Houzel, B. Mota, and R. Lent, Cellular scaling rules for rodent brains, Proc. Natl. Acad. Sci. USA 103, 12138 (2006). PNASA6 0027-8424 10.1073/pnas.0604911103
38. S. Herculano-Houzel, The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost, Proc. Natl. Acad. Sci. USA 109, 10661 (2012). PNASA6 0027-8424 10.1073/pnas.1201895109