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  1. Dynamic phenomena and human activity in artificial society • Andrzej Grabowski1, Robert Kosiński1,2 and Natalia Kruszewska3 • Central Institute for LabourProtection – National ResearchInstitute • Faculty of Physics, Warsaw University of Technology • Institute of Mathematics and Physics, University of Technology and Life Sciences

  2. Introduction • The structure of the network • Human dynamics in artificial society • Dynamic phenomena in social network • Conclusions

  3. What is MMORPG? 1 2 3 4 5

  4. Second Life In May 2007 first embassy of Swiss was established in virtual world of Second Life. 1 2 3 4 5

  5. World of Warcraft Over 8x106 users! 1 2 3 4 5

  6. What is MMORPG? MMORPG (Massive Multiplayer On-line Role Playing Game) is a network game in which players enter a virtual world as characters playing roles invented by themselves gaining virtual life. This virtual world takes the form of a game server connected to the Internet, on which accounts are registered for users who log in through a special game client programs. Thousands of people can play on one server. They become a virtual society, so they share the common culture, area, identity and interactions in the network of interpersonal relationships. All individuals can add, by mutual consent, other people to their databases of friends. In this way undirected friendship network is formed. 1 2 3 4 5

  7. Basic properties of the network GC – Giant Component SW – small world network (φ = 0.01) RG – Random Graph BA – Barabasi-Albert network 1 2 3 4 5 The Giant Component contains almost all active individuals (we consider an individual as active when it regularly appears in the virtual world); only 252 individuals with k>0 do not belong to GC.

  8. Degree distribution 1 2 3 4 5 The graph shows power law regime. Such a power law is common in many types of networks, also in social networks. It is interesting that the same value of the exponent is observed in the model of a growing network with a linear preferential attachment.

  9. Clustering coefficient 1 2 3 4 5 The local clustering coefficient C(k) is negatively correlated with node degree k, showing the existence of a power law. The power-law relation C(k) is similar to the relationship observed in hierarchical networks.

  10. The power-law relation Ci~ki-αis similar to the relationship observed in hierarchicalnetworks.Such power laws hint at the presence of a hierarchical architecture: when small groups organize themselves into increasingly larger groups ina hierarchical manner, local clustering decreases on different scales according to such a power law. 1 2 3 4 5

  11. Degree correlations 1 2 3 4 5 The network under investigation is assortative mixed by degree; such a correlation is observed in many social networks. In social networks it is entirely possible, and is often assumed in sociological literature, that similar people attract one another.

  12. Degree correlations social networks technical networks 1 2 3 4 5

  13. Distribution of sizes of network components 1 2 3 4 5

  14. Results of a poll • In order to investigate the relation between networks of acquaintances in the virtual and real worlds, we carried out a survey among active players (360 personswere interested in filling it).We asked questions like: • how many people from your list of friends did you know before you start to play - Nb, and • with how many people who you got to know in the virtual world and add to your list of friends, do you maintain social contact in the real one - Na. 1 2 3 4 5

  15. Results of a poll Nb turns out to be realtive small, so the network did not develop only as a growing graph of underlaying social acquaintance network in the real one. The declared contacts established in real world as a result of meeting in game Na is almost three times greater. It indicates that on-line games have bigger influence on the network of acquaintances in the real world than in opposite case. When compare this data with the number of people in friendlist (18.4), we can see that it has significant importance for real network of friends. 1 2 3 4 5

  16. Results of a poll – comparision with Grono 1 2 3 4 5

  17. Human dynamics „The origin of bursts and heavytails in human dynamics” Albert-La´szlo´ Baraba´si, NATURE 435, 12 MAY 2005 1 2 3 4 5

  18. Human dynamics Henderson, T. & Nhatti, S.Modelling user behavior in networked games. Proc. 9th ACMInt. Conf. OnMultimetia 212–220 (ACM Press, New York, 2001). 1 2 3 4 5 Faloutsos, M., P. Faloutsos, and C.Faloutsos, 1999, Comput.Commun. Rev. 29, 251. Kumar, R., P. Raghavan, S. Rajalopagan, and A. Tomkins,1999, Proceedings of the 9th ACM Symposium on Principlesof Database Systems, p. 1. Adamic, L. A., and B. A. Huberman, 1999, Nature (London)401, 131

  19. Human dynamics On-line games, like MMORPGs, offer a great opportunity to investigate human dynamics, because much information about individuals is registered in databases. To analyze how long people are interested in a single task and how much time they devote to a single task, we studied cumulative time spent in the virtual world TG registered in the game database. Players can lose interest in playing the game and they can abandon their characters after some time. The lifespan of an individual TL is defined as the number of days since the time of an individual was created to the date of last logging. 1 2 3 4 5

  20. Human dynamics 1 2 3 4 5 The number of individuals who spent TG hours playing the game has the power-law form. Thus, the probability that a human will devote the time t to a single activity has a fat-tailed distribution.

  21. Life-span 1 2 3 4 5 The number of individuals whose activity in the virtual world lasted TL days. Average time TL equals 69 days. However, for individuals who are active for more than one month, the average time TL equals as many as 170 days.

  22. Human dynamics 1 2 3 4 5 Average time daily devoted to the game is positive correlated with life-span of an individual.

  23. Human dynamics 1 2 3 4 5 The relation between lifespan of an individual and its connectivity.

  24. Social activity 1 2 3 4 5 Social interactions with other players is an important part of each MMORPG. On the basis of the playing time, we calculate the activity A of individuals, i.e. the relative time daily devoted to interactions with others.

  25. Social activity 1 2 3 4 5 The activity of an individual is positively correlated with its connectivity and the results can be approximated with power law.

  26. Susceptible Ill Removed Epidemic spreading We investigate simple SIR (Susceptible, Ill, Removed) model. To distinguish the effectiveness of interactions between individuals we take into account human activity A: 1 2 3 4 5 kiI – thenumber of Illneighbours

  27. Epidemic spreading In order to investigate the influence of the human activity on the spreading process we have made computations for two different distributions of activity, real and uniform Ai=const. The average activity was the same in both distributions, with the aim of obtaining better comparable results. 1 2 3 4 5

  28. Epidemic spreading In the case of real distribution of social activity (empty marks) the magnitude of epidemic (V) is greater and the epidemic spreads faster. It is a result of presence of very active spuper-spreadrers in the network (individuals with large k and A). g = 0.9 1 2 3 4 5

  29. Epidemic spreading g = 0.1 1 2 3 4 5

  30. Epidemic spreading, large b and g 1 2 3 4 5

  31. Ignorant Spreader Stifler Rumour propagation The next phenomenon which we study is the process of rumor propagation in a real social network. Ignorants (IG) have not heard the rumor and hence are susceptible to be informed. Spreaders (SP) are active individuals who spread the rumor. Stiflers (ST) know the rumor but are no longer interested in spreading it. 1 2 3 4 5

  32. Ignorant Spreader Spreader Stifler Rumour propagation Similarly like in the case of epidemic spreading, we take into account social activity A of the individuals. As result of interactions with spreaders an ignorant individual turns into new spreader with probability and a spreader becomes a stifler if he/she encounters another spreader or a stifler with probability 1 2 3 4 5

  33. Rumour propagation In the case of real distribution of social activity (empty marks) the relative number of individuals affected by rumor (V) is greater, however the rumour spreads much slower. This is so because super-spreaders very quickly turn into stifler state. g = 5 1 2 3 4 5

  34. Rumour propagation g = 40 1 2 3 4 5

  35. 1 2 3 4 5

  36. Conclusions • We have shown that a friendship network maintained in the virtual world has similar properties (eg. large clustering, a low value of the average path length, assortative mixing by degree and a scale-free distribution of connectivity) to other social networks. • The power-law form of distributions PG(TG), PL(TL), k(TL), A(k) and other results indicate that such a scaling law is common in human dynamics and should be taken into account in models of the evolution of social networks and of human activity. 1 2 3 4 5

  37. Conclusions • We have found that taking into account real distribution of the social activity speeds up the process of epidemic spreading, however decreases the rate of rumor propagation. This is a result of e.g. different behavior of super-spreaders. • Our results indicate that the influence of human social activity on dynamic phenomena in social networks significantly depends on the type of this phenomenon and type of interaction rules. 1 2 3 4 5

  38. Thank you for your attention! The End