Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29.
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Transcript of Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29.
![Page 1: Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29.](https://reader030.fdocuments.in/reader030/viewer/2022032806/56649efe5503460f94c128ba/html5/thumbnails/1.jpg)
Emergence of Scaling and Assortative Mixing by Altruism
Li Ping
The Hong Kong PolyU
2010.07.29
![Page 2: Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29.](https://reader030.fdocuments.in/reader030/viewer/2022032806/56649efe5503460f94c128ba/html5/thumbnails/2.jpg)
Outline
Motivation and background Network model Statistical properties Summary
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Motivations
Networks are evolving in time Some topological features arising:
Power – law degree distributionsAssortativity mixing patterns……
What’s the origin of these properties?
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Barabasi-Albert Model
Rules:Growth &Preferential attachment
Results:Power-law degree distribution!
![Page 5: Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29.](https://reader030.fdocuments.in/reader030/viewer/2022032806/56649efe5503460f94c128ba/html5/thumbnails/5.jpg)
Beyond Scaling-Assortativity
Assortativity a negative or positive correlation in
adjacent nodes with respect to a certain property
Measurement
€
r ∝ kik j − ki k jor
€
knn (k) = k 'P(k ' | k)k '∑
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Assortative (disassortative) Mixing in Real Networks
Internet
AS1998 AS2003 AS2008 -0.198 -0.14 -0.13
Erdos collaboration networks
Erdos971 Erdos981 Erdos991
0.2245 0.2251 0.2243
AssortCoeff
AssortCoeff
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Existing Model for Social Networks
BA growth mechanismAdding new nodes with probability
MixingAdding new edges between node 1
and 2 with probability 1-
M. Catanzaro et al. Physica A 338(2004) 119-124
€
pkik j
j
∑
€
(1− p)k1k j
j
∑P(k2 | k1)
€
p
€
p
![Page 8: Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29.](https://reader030.fdocuments.in/reader030/viewer/2022032806/56649efe5503460f94c128ba/html5/thumbnails/8.jpg)
Our Model
Growth rule: Each time, a new node is added in the existing network
Altruistic attachmentPreferentially choose a node to be an
agent according to its degreeRandomly choose a node to be the
target from the neighborhood of the agent
agent
New node
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N = 150 , m = 3
AA or BA?
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Statistical Properties-Degree Distribution
N = 2000 , m = 3 , with assortativitycoefficient = 0.081
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Power Law Exponent for Different Network Size
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Assortativity
BA AA
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Fragility and Robustness
Randomly remove nodes
Targeted remove nodes
AA
BA
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Clustering Coefficients
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Conclusion
Assortativity and scale - free properties can be reproduced by introducing altruistic attachment mechanism
AA network model shows some differences with respect to various statistical properties by numerical simulations
More things that AA tells us…
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Thank you for your attention!