1. Emergence of Scaling and Assortative Mixing by Altruism Li Ping The Hong Kong PolyU 2010.07.29

2. Outline Motivation and background Network model Statistical properties Summary

3. Motivations Networks are evolving in time Some topological features arising: Power – law degree distributions Assortativity mixing patterns …… What’s the origin of these properties?

4. Barabasi-Albert Model Rules: Growth & Preferential attachment Results: Power-law degree distribution!

5. Beyond Scaling-Assortativity Assortativity a negative or positive correlation in adjacent nodes with respect to a certain property Measurement or

6. 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

7. Existing Model for Social Networks BA growth mechanism Adding new nodes with probability Mixing Adding new edges between node 1 and 2 with probability 1- M. Catanzaro et al. Physica A 338(2004) 119-124

8. Our Model Growth rule: Each time, a new node is added in the existing network Altruistic attachment Preferentially choose a node to be an agent according to its degree Randomly choose a node to be the target from the neighborhood of the agent agent New node

9. N ＝ 150 ， m ＝ 3 AA or BA ？

10. Statistical Properties- Degree Distribution N ＝ 2000 ， m ＝ 3 ， with assortativity coefficient ＝ 0.081

11. Power Law Exponent for Different Network Size

12. Assortativity BAAA

13. Fragility and Robustness Randomly remove nodes Targeted remove nodes AA BA

14. Clustering Coefficients

15. 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…

16. Thank you for your attention!