Threshold conditions for arbitrary cascade models on arbitrary networks

Knowledge and Information Systems

Volumn 33, Issue 3, 2012, Pages 549-575

  Prakash, B Aditya ^a   Chakrabarti, Deepayan ^b   Valler, Nicholas C ^c   Faloutsos, Michalis ^c   Faloutsos, Christos ^d  

^a Carnegie Mellon University   (United States)

^b YAHOO RESEARCH   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Arbitrary graphs; Cascades; Epidemics; Tipping points; Virus propagation models

Indexed keywords

CASCADES (FLUID MECHANICS); COMPLEX NETWORKS; EIGENVALUES AND EIGENFUNCTIONS; EPIDEMIOLOGY; TOPOLOGY; VIRUSES;

ARBITRARY GRAPHS; CONNECTIVITY MATRIX; DESIGN AND EVALUATIONS; EPIDEMICS; EXTENSIVE SIMULATIONS; THRESHOLD CONDITION; TIPPING POINT; VIRUS PROPAGATION;

COMPUTER VIRUSES;

EID: 84869081518     PISSN: 02191377     EISSN: 02193116     Source Type: Journal    
DOI: 10.1007/s10115-012-0520-y     Document Type: Article

References (54)

1. Albert R, Jeong H, Barabási AL (2000) Error and attack tolerance of complex networks. Nature 407(6794): 378-482.
2. Anderson RM, May RM (1991) Infectious diseases of humans. Oxford University Press, Oxford.
3. Barrat A, Barthélemy M, Vespignani A (2010) Dynamical processes on complex networks. Cambridge University Press, Cambridge.
4. Barrett CL, Bisset KR, Eubank SG, Feng X, Marathe MV (2008) Episimdemics: an efficient algorithm for simulating the spread of infectious disease over large realistic social networks.
5. Bass FM (1969) A new product growth for model consumer durables. Manag Sci 15(5): 215-227.
6. Bikhchandani S, Hirshleifer D, Welch I (1992) A theory of fads, fashion, custom, and cultural change in informational cascades. J Political Econ 100(5): 992-1026.
7. Buldyrev SV, Parshani R, Paul G, Stanley HE, Havlin S (2010) Catastrophic cascade of failures in interdependent networks. Nature 464(7291): 1025-1028.
8. Castellano C, Pastor-Satorras R (2010) Thresholds for epidemic spreading in networks. Phys Rev Lett 105.
9. Chakrabarti D, Leskovec J, Faloutsos C, Madden S, Guestrin C, Faloutsos M (2007) Information survival threshold in sensor and P2P networks. In: IEEE INFOCOM.
10. Chakrabarti D, Wang Y, Wang C, Leskovec J, Faloutsos C (2008) Epidemic thresholds in real networks. ACM TISSEC 10(4).
11. Chen Q, Chang H, Govindan R, Jamin S, Shenker SJ, Willinger W (2002) The origin of power laws in internet topologies revisited. In: IEEE INFOCOMM. http://topology. eecs. umich. edu/data. html.
12. Chen W, Wang C, Wang Y (2010) Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: KDD.
13. Chung F, Lu L, Vu V (2003) Eigenvalues of random power law graphs. Ann Comb 7(1).
14. Cohen R, Havlin S, ben Avraham D (2003) Efficient immunization strategies for computer networks and populations. Phys Rev Lett 91(24): 247901.
15. Dodds PS, Watts DJ (2004) A generalized model of social and biological contagion. J Theor Biol 232: 587-604.
16. Easley D, Kleinberg J (2010) Networks, crowds, and markets: reasoning about a highly connected world. Cambridge University Press, Cambridge.
17. Eubank S, Guclu H, Anil Kumar VS, Marathe MV, Srinivasan A, Toroczkai Z, Wang N (2004) Modelling disease outbreaks in realistic urban social networks. Nature 429(6988): 180-184.
18. Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the internet topology. In: SIGCOMM, pp 251-262.
19. Ganesh A, Massoulié L, Towsley D (2005) The effect of network topology on the spread of epidemics. In: INFOCOM.
20. Goldenberg J, Libai B, Muller E (2001) Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark Lett 3(12): 211-223.
21. Gomez Rodriguez M, Leskovec J, Krause A (2010) Inferring networks of diffusion and influence. In: Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, ACM, New York, NY, USA (KDD '10), pp 1019-1028.
22. Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83(6): 1420-1443.
23. Gruhl D, Guha R, Liben-Nowell D, Tomkins A (2004) Information diffusion through blogspace. In: WWW '04. http://www2004. org/proceedings/docs/1p491. pdf.
24. Hayashi Y, Minoura M, Matsukubo J (2003) Recoverable prevalence in growing scale-free networks and the effective immunization. arXiv: cond-mat/0305549 v2.
25. Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42.
26. Hethcote HW, Yorke JA (1984) Gonorrhea transmission dynamics and control. Springer Lecture notes in biomathematics 46.
27. Hirsch MW, Smale S (1974) Differential equations, dynamical systems and linear algebra. Academic Press, New York.
28. Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, Cambridge.
29. Kempe D, Kleinberg J, Tardos E (2003) Maximizing the spread of influence through a social network. In: KDD.
30. Kephart JO, White SR (1993) Measuring and modeling computer virus prevalence. In: IEEE computer society symposium on research in security and privacy.
31. Kleinberg J (2007) The wireless epidemic. Nature 449.
32. Kumar R, Novak J, Raghavan P, Tomkins A (2003) On the bursty evolution of blogspace. In: WWW.
33. Lad M, Zhao X, Zhang B, Massey D, Zhang L (2003) Analysis of BGP update surge during slammer worm attack. In: 5th International workshop on distributed computing (IWDC). http://citeseer. ist. psu. edu/lad03analysis. html.
34. Lappas T, Terzi E, Gunopoulos D Mannila H (2010) Finding effectors in social networks. In: SIGKDD.
35. Leskovec J, Adamic LA, Huberman BA (2006) The dynamics of viral marketing. In: EC. ACM Press, New York, NY, USA, pp 228-237.
36. Leskovec J, Backstrom L, Kleinberg J (2009) Meme-tracking and the dynamics of the news cycle. In: ACM SIGKDD.
37. Maymounkov P, Mazières D (2002) Kademlia: a peer-to-peer information system based on the XOR metric. In: Revised papers from the first international workshop on peer-to-peer systems, Springer, London, UK (IPTPS '01), pp 53-65. http://dl. acm. org/citation. cfm?id=646334. 687801.
38. McCuler CR (2000) The many proofs and applications of perron's theorem. SIAM Rev 42.
39. McKendrick AG (1926) Applications of mathematics to medical problems. In: Proceedings of Edin. Math. Society, vol 14, pp 98-130.
40. Milnes HW (Aug-Sept 1963) Conditions that the zeros of a polynomial lie in the interval [-1, 1] when all zeros are real. Am Math Mon 70(7).
41. NDSSL (2007) Synthetic data products for societal infrastructures and protopopulations: data set 2. 0. NDSSL-TR-07-003. http://ndssl. vbi. vt. edu/Publications/ndssl-tr-07-003. pdf.
42. Newman MEJ (2002) Spread of epidemic disease on networks. Phys Rev E 66(1): 016128. doi: 10. 1103/PhysRevE. 66. 016128.
43. Newman MEJ (2005) Threshold effects for two pathogens spreading on a network. Phys Rev Lett 95(10): 108701.
44. Pastor-Santorras R, Vespignani A (2001) Epidemic spreading in scale-free networks. Phys Rev Lett 86: 14.
45. Pathak N, Banerjee A, Srivastava J (2010) A generalized linear threshold model for multiple cascades. In: ICDM.
46. Prakash BA, Tong H, Valler N, Faloutsos M, Faloutsos C (2010) Virus propagation on time-varying networks: theory and immunization algorithms. In: ECML-PKDD.
47. Prakash BA, Beutel A, Rosenfeld R, Faloutsos C (2012) Winner takes all: competiting viruses or ideas on fair-play networks. In: WWW.
48. Richardson M, Domingos P (2002) Mining knowledge-sharing sites for viral marketing. In: SIGKDD.
49. Rogers EM (2003) Diffusion of innovations, 5th ed. Free Press. http://www. amazon. ca/exec/obidos/redirect?tag=citeulike09-20& path=ASIN/0743222091.
50. Saito K, Kimura M, Ohara K, Motoda H (2012) Efficient discovery of influential nodes for sis models in social networks. Knowl Inf Syst (KAIS) 30(3): 613-635.
51. Vojnovic M, Gupta V, Karagiannis T, Gkantsidis C (2008) Sampling strategies for epidemic-style information dissemination. In: IEEE INFOCOM.
52. Watts DJ, Strogatz SH (1998) Collective dynamics of 'small-world' networks. Nature 393: 440-442.
53. Website (November 15, 2011) Mainline bittorrent website. http://www. bittorrent. com/.
54. Zhao J, Wu J, Feng X, Xiong H, Xu K (2011) Information propagation in online social networks: a tie-strength perspective. Knowl Inf Syst 1-20. doi: 10. 1007/s10115-011-0445-x.