Post on 08-May-2020
Emergence of Scaling in Random Networks
Albert-László Barabási & Réka AlbertScience, 286 (1999)
Scale-free Networks
Log k
Log
P(k
)
Log
P(k
)
Log k
Log
P(k
)en.wikipedia.org
Log k
Log
P(k
)en.wikipedia.org nealcaren.web.unc.edu
Log k
Log k
Log
P(k
)en.wikipedia.org
biomedicalcomputationreview.org
nealcaren.web.unc.edu
Log k
World wide web Protein
Interation
k
biomedicalcomputationreview.org(Barabasi, 1999)
The Model
„rich-get-richer“„preferrential attachment“
+
+
+
+
+
1. „preferential attachment“
→power law:
2. „growth“:
→ stationary:
The Model
scale invariance!
NetLogo Model
1. „preferential attachment“
→power law:
2. „growth“:
→ stationary:
Model Analysis
scale invariance!
The exponent
(Barabasi, 1999)
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
Erdös Renyi Model (1960)
N = const.