Dynamic phenomena and human activity in artificial society

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Dynamic phenomena and human activity in
artificial society

• Andrzej Grabowski1, Robert Kosinski1,2 and
  Natalia Kruszewska3
• Central Institute for Labour Protection
  National Research Institute
• Faculty of Physics, Warsaw University of
  Technology
• Institute of Mathematics and Physics, University
  of Technology and Life Sciences

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1. Introduction
2. The structure of the network
3. Human dynamics in artificial society
4. Dynamic phenomena in social network
5. Conclusions

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What is MMORPG?
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Second Life
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World of Warcraft
Over 8x106 users!
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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.
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Basic properties of the network
GC Giant Component SW small world
network (f 0.01) RG Random Graph BA
Barabasi-Albert network
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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 kgt0 do not belong to
GC.
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Degree distribution
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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.
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Clustering coefficient
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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.
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The power-law relation Ciki-a is similar to the
relationship observed in hierarchical networks.
Such power laws hint at the presence of a
hierarchical architecture when small groups
organize themselves into increasingly larger
groups in a hierarchical manner, local clustering
decreases on different scales according to such a
power law.
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Degree correlations
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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.
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Degree correlations
social networks
technical networks
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Distribution of sizes of network components
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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 persons were 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.

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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.
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Results of a poll comparision with Grono
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Human dynamics
The origin of bursts and heavy tails in human
dynamics Albert-Laszlo Barabasi, NATURE 435,
12 MAY 2005
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Human dynamics
Henderson, T. Nhatti, S. Modelling user
behavior in networked games. Proc. 9th ACMInt.
Conf. On Multimetia 212220 (ACM Press, New York,
2001).
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1. Faloutsos, M., P. Faloutsos, and C.Faloutsos,
   1999, Comput. Commun. Rev. 29, 251.
2. Kumar, R., P. Raghavan, S. Rajalopagan, and A.
   Tomkins, 1999, Proceedings of the 9th ACM
   Symposium on Principles of Database Systems, p.
   1.
3. Adamic, L. A., and B. A. Huberman, 1999, Nature
   (London) 401, 131

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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.
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Human dynamics
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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.
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Life-span
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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.
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Human dynamics
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Average time daily devoted to the game is
positive correlated with life-span of an
individual.
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Human dynamics
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The relation between lifespan of an individual
and its connectivity.
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Social activity
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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.
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Social activity
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The activity of an individual is positively
correlated with its connectivity and the results
can be approximated with power law.
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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
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kiI the number of Ill neighbours
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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 Aiconst. The
average activity was the same in both
distributions, with the aim of obtaining better
comparable results.
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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
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Epidemic spreading
g 0.1
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Epidemic spreading, large b and g
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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.
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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
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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
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Rumour propagation
g 40
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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.

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Conclusions

1. 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.
2. 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.

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Thank you for your attention!
The End