#PAGE_PARAMS# #ADS_HEAD_SCRIPTS# #MICRODATA#

MSP-N: Multiple selection procedure with ‘N’ possible growth mechanisms


Autoři: Pradumn Kumar Pandey aff001;  Mayank Singh aff002
Působiště autorů: Computer Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttrakhand, India aff001;  Computer Science and Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat, India aff002
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0224383

Souhrn

Network modeling is a challenging task due to non-trivial evolution dynamics. We introduce multiple-selection-procedure with ‘N’ possible growth mechanisms (MSP-N). In MSP-N, an incoming node chooses a single option among N available options to link to pre-existing nodes. Some of the potential options, in case of social networks, can be standard preferential or random attachment and node aging or fitness. In this paper, we discuss a specific case, MSP-2, and shows its efficacy in reconstructing several non-trivial characteristic properties of social networks, including networks with power-law degree distribution, power-law with an exponential decay (exponential cut-off), and exponential degree distributions. We evaluate the proposed evolution mechanism over two real-world networks and observe that the generated networks highly resembles the degree distribution of the real-world networks. Besides, several other network properties such as high clustering and triangle count, low spectral radius, and community structure, of the generated networks are significantly closer to the real-world networks.

Klíčová slova:

Aging – Clustering coefficients – Community structure – Eigenvalues – Network analysis – Protein interaction networks – Social networks – Operator theory


Zdroje

1. Newman M. Networks: an introduction. Oxford University Press; 2010.

2. Barabási AL, Albert R, Jeong H. Scale-free characteristics of random networks: the topology of the world-wide web. Physica A: statistical mechanics and its applications. 2000;281(1):69–77.

3. Asur S, Ucar D, Parthasarathy S. An ensemble framework for clustering protein–protein interaction networks. Bioinformatics. 2007;23(13):i29–i40. doi: 10.1093/bioinformatics/btm212 17646309

4. Wu J, Vallenius T, Ovaska K, Westermarck J, Mäkelä TP, Hautaniemi S. Integrated network analysis platform for protein-protein interactions. Nature methods. 2009;6(1):75–77. doi: 10.1038/nmeth.1282 19079255

5. Amaral LAN, Scala A, Barthelemy M, Stanley HE. Classes of small-world networks. Proceedings of the national academy of sciences. 2000;97(21):11149–11152. doi: 10.1073/pnas.200327197

6. Newman ME. The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences. 2001;98(2):404–409. doi: 10.1073/pnas.98.2.404

7. Leskovec J, Mcauley JJ. Learning to discover social circles in ego networks. In: Advances in neural information processing systems; 2012. p. 539–547.

8. Barabási AL, Albert R. Emergence of scaling in random networks. Science. 1999;286(5439):509–512. doi: 10.1126/science.286.5439.509 10521342

9. Bollobás B, Riordan O. The diameter of a scale-free random graph. Combinatorica. 2004;24(1):5–34. doi: 10.1007/s00493-004-0002-2

10. Broder A, Kumar R, Maghoul F, Raghavan P, Rajagopalan S, Stata R, et al. Graph structure in the web. Computer networks. 2000;33(1):309–320. doi: 10.1016/S1389-1286(00)00083-9

11. Chung F, Lu L. The average distances in random graphs with given expected degrees. Proceedings of the National Academy of Sciences. 2002;99(25):15879–15882. doi: 10.1073/pnas.252631999

12. Kleinberg J. Small-world phenomena and the dynamics of information. Advances in neural information processing systems. 2002;1 : 431–438.

13. Milgram S. The small world problem. Psychology today. 1967;2(1):60–67.

14. Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’networks. Nature. 1998;393(6684):440–442. doi: 10.1038/30918 9623998

15. Martinez ND. Artifacts or attributes? Effects of resolution on the Little Rock Lake food web. Ecological Monographs. 1991; p. 367–392. doi: 10.2307/2937047

16. Barabási AL, Albert R. Emergence of scaling in random networks. Science. 1999;286(5439):509–512. doi: 10.1126/science.286.5439.509 10521342

17. Huxham M, Beaney S, Raffaelli D. Do parasites reduce the chances of triangulation in a real food web? Oikos. 1996; p. 284–300. doi: 10.2307/3546201

18. Newman ME, Girvan M. Finding and evaluating community structure in networks. Physical review E. 2004;69(2):026113. doi: 10.1103/PhysRevE.69.026113

19. Barabási AL, et al. Scale-free networks: a decade and beyond. Science. 2009;325(5939):412. doi: 10.1126/science.1173299 19628854

20. Eguiluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. Scale-free brain functional networks. Physical review letters. 2005;94(1):018102. doi: 10.1103/PhysRevLett.94.018102 15698136

21. Luce RD, Perry AD. A method of matrix analysis of group structure. Psychometrika. 1949;14(2):95–116. doi: 10.1007/bf02289146 18152948

22. Li W, Schuurmans D. Modular community detection in networks. In: Twenty-Second International Joint Conference on Artificial Intelligence; 2011.

23. Pandey PK, Adhikari B. A parametric model approach for structural reconstruction of scale-free networks. IEEE Transactions on Knowledge and Data Engineering. 2017;29(10):2072–2085. doi: 10.1109/TKDE.2017.2725264

24. Dorogovtsev SN, Mendes JFF. Evolution of networks with aging of sites. Physical Review E. 2000;62(2):1842. doi: 10.1103/PhysRevE.62.1842

25. Dorogovtsev S, Mendes J, Samukhin A. Size-dependent degree distribution of a scale-free growing network. Physical Review E. 2001;63(6):062101. doi: 10.1103/PhysRevE.63.062101

26. Chakrabarti D, Faloutsos C. Graph mining: Laws, generators, and algorithms. ACM computing surveys (CSUR). 2006;38(1):2. doi: 10.1145/1132952.1132954

27. Toivonen R, Onnela JP, Saramäki J, Hyvönen J, Kaski K. A model for social networks. Physica A: Statistical Mechanics and its Applications. 2006;371(2):851–860. doi: 10.1016/j.physa.2006.03.050

28. Kossinets G, Watts DJ. Empirical analysis of an evolving social network. Science. 2006;311(5757):88–90. doi: 10.1126/science.1116869 16400149

29. Jackson MO. A survey of network formation models: stability and efficiency. Group Formation in Economics: Networks, Clubs, and Coalitions. 2005; p. 11–49.

30. Slikker M, van den Nouweland A. Network formation models with costs for establishing links. Review of Economic Design. 2000;5(3):333–362. doi: 10.1007/PL00013692

31. Bornholdt S, Rohlf T. Topological evolution of dynamical networks: Global criticality from local dynamics. Physical Review Letters. 2000;84(26):6114. doi: 10.1103/PhysRevLett.84.6114 10991137

32. Barabâsi AL, Jeong H, Néda Z, Ravasz E, Schubert A, Vicsek T. Evolution of the social network of scientific collaborations. Physica A: Statistical mechanics and its applications. 2002;311(3):590–614.

33. Pandey PK, Adhikari B. Context dependent preferential attachment model for complex networks. Physica A: Statistical Mechanics and its Applications. 2015;436 : 499–508. doi: 10.1016/j.physa.2015.04.038

34. Simon HA. On a class of skew distribution functions. Biometrika. 1955;42(3/4):425–440. doi: 10.2307/2333389

35. Price DdS. A general theory of bibliometric and other cumulative advantage processes. Journal of the American society for Information science. 1976;27(5):292–306. doi: 10.1002/asi.4630270505

36. Abello J, Buchsbaum AL, Westbrook JR. A functional approach to external graph algorithms. In: Algorithms—ESA’98. Springer; 1998. p. 332–343.

37. Faloutsos M, Faloutsos P, Faloutsos C. On power-law relationships of the internet topology. In: ACM SIGCOMM computer communication review. vol. 29. ACM; 1999. p. 251–262.

38. Huberman BA, Adamic LA. Internet: growth dynamics of the world-wide web. Nature. 1999;401(6749):131–131. doi: 10.1038/43604

39. Kumar R, Raghavan P, Rajagopalan S, Tomkins A. Trawling the Web for emerging cyber-communities. Computer networks. 1999;31(11):1481–1493. doi: 10.1016/S1389-1286(99)00040-7

40. Bi Z, Faloutsos C, Korn F. The DGX distribution for mining massive, skewed data. In: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining. ACM; 2001. p. 17–26.

41. Chakrabarti D, Zhan Y, Faloutsos C. R-MAT: A Recursive Model for Graph Mining. In: SDM. vol. 4. SIAM; 2004. p. 442–446.

42. Christensen K, Donangelo R, Koiller B, Sneppen K. Evolution of random networks. Physical Review Letters. 1998;81(11):2380. doi: 10.1103/PhysRevLett.81.2380

43. Krapivsky PL, Redner S, Leyvraz F. Connectivity of growing random networks. Physical review letters. 2000;85(21):4629. doi: 10.1103/PhysRevLett.85.4629 11082613

44. Ohtsuki H, Hauert C, Lieberman E, Nowak MA. A simple rule for the evolution of cooperation on graphs and social networks. Nature. 2006;441(7092):502–505. doi: 10.1038/nature04605 16724065

45. Krapivsky PL, Redner S. Organization of growing random networks. Physical Review E. 2001;63(6):066123. doi: 10.1103/PhysRevE.63.066123

46. Dorogovtsev SN, Goltsev AV, Mendes JFF. Pseudofractal scale-free web. Physical Review E. 2002;65(6):066122. doi: 10.1103/PhysRevE.65.066122

47. Dorogovtsev SN, Goltsev AV, Mendes JFF. Ising model on networks with an arbitrary distribution of connections. Physical Review E. 2002;66(1):016104. doi: 10.1103/PhysRevE.66.016104

48. Dorogovtsev SN, Mendes JFF. Effect of the accelerating growth of communications networks on their structure. Physical Review E. 2001;63(2):025101.

49. Leskovec J, Krevl A. SNAP Datasets: Stanford Large Network Dataset Collection; 2014. http://snap.stanford.edu/data.

50. Singh M, Sarkar R, Goyal P, Mukherjee A, Chakrabarti S. Relay-linking models for prominence and obsolescence in evolving networks. In: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM; 2017. p. 1077–1086.

51. Singh M, Sarkar R, Goyal P, Mukherjee A, Chakrabarti S. Sic Transit Gloria Manuscriptum: Two Views of the Aggregate Fate of Ancient Papers. arXiv preprint arXiv:151108310. 2015;.

52. Zhu H, Wang X, Zhu JY. Effect of aging on network structure. Phys Rev E. 2003;68 : 056121. doi: 10.1103/PhysRevE.68.056121

53. Kumar R, Raghavan P, Rajagopalan S, Sivakumar D, Tomkins A, Upfal E. Random graph models for the web graph. In: FOCS; 2000. p. 57–65.

54. König MD, Tessone CJ, Zenou Y. From assortative to dissortative networks: the role of capacity constraints. Advances in Complex Systems. 2010;13(04):483–499. doi: 10.1142/S0219525910002700

55. Battiston P. Constrained Network Formation. Italian Economic Journal. 2016;2(3):347–362. doi: 10.1007/s40797-016-0040-0

56. Barabási AL, Albert R, Jeong H. Mean-field theory for scale-free random networks. Physica A: Statistical Mechanics and its Applications. 1999;272(1):173–187.

57. Leskovec J, Kleinberg J, Faloutsos C. Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining. ACM; 2005. p. 177–187.

58. Girvan M, Newman ME. Community structure in social and biological networks. Proceedings of the national academy of sciences. 2002;99(12):7821–7826. doi: 10.1073/pnas.122653799

59. Blondel V, Guillaume J, Lambiotte R, Lefebvre E. Fast Unfolding of Community Hierarchies in large network. J Stat Mech P. 2008;1008.

60. Jamakovic A. Characterization of complex networks: application to robustness analysis. 2008;.

61. Chung FR, Graham FC. Spectral graph theory. 92. American Mathematical Soc.; 1997.


Článek vyšel v časopise

PLOS One


2019 Číslo 12
Nejčtenější tento týden
Nejčtenější v tomto čísle
Kurzy

Zvyšte si kvalifikaci online z pohodlí domova

BONE ACADEMY 2025
nový kurz
Autoři: prof. MUDr. Pavel Horák, CSc., doc. MUDr. Ludmila Brunerová, Ph.D, doc. MUDr. Václav Vyskočil, Ph.D., prim. MUDr. Richard Pikner, Ph.D., MUDr. Olga Růžičková, MUDr. Jan Rosa, prof. MUDr. Vladimír Palička, CSc., Dr.h.c.

Cesta pacienta nejen s SMA do nervosvalového centra
Autoři: MUDr. Jana Junkerová, MUDr. Lenka Juříková

Svět praktické medicíny 2/2025 (znalostní test z časopisu)

Eozinofilní zánět a remodelace
Autoři: MUDr. Lucie Heribanová

Hypertrofická kardiomyopatie: Moderní přístupy v diagnostice a léčbě
Autoři: doc. MUDr. David Zemánek, Ph.D., MUDr. Anna Chaloupka, Ph.D.

Všechny kurzy
Kurzy Podcasty Doporučená témata Časopisy
Přihlášení
Zapomenuté heslo

Zadejte e-mailovou adresu, se kterou jste vytvářel(a) účet, budou Vám na ni zaslány informace k nastavení nového hesla.

Přihlášení

Nemáte účet?  Registrujte se

#ADS_BOTTOM_SCRIPTS#