emergence of scaling in random networks -...
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Emergence of Scaling in Random Networks
Albert-László Barabási & Réka AlbertScience, 286 (1999)
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Scale-free Networks
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Log k
Log
P(k
)
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Log
P(k
)
Log k
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Log
P(k
)en.wikipedia.org
Log k
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Log
P(k
)en.wikipedia.org nealcaren.web.unc.edu
Log k
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Log k
Log
P(k
)en.wikipedia.org
biomedicalcomputationreview.org
nealcaren.web.unc.edu
Log k
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World wide web Protein
Interation
k
biomedicalcomputationreview.org(Barabasi, 1999)
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The Model
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„rich-get-richer“„preferrential attachment“
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+
+
+
+
+
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1. „preferential attachment“
→power law:
2. „growth“:
→ stationary:
The Model
scale invariance!
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NetLogo Model
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1. „preferential attachment“
→power law:
2. „growth“:
→ stationary:
Model Analysis
scale invariance!
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The exponent
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(Barabasi, 1999)
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Typical values for
problem Barabasi, 1999 Price, 1976
WWW 2.1
Citation network 3.0 2.5-3.0
Actor collaboration 2.3
Power grid 4.1
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Erdös Renyi Model (1960)
N = const.