1. Quantifying Social Group Evolution Gergely Palla, Albert-Laszlo Barabasi, and Tamas Vicsek Nature Vol 446 April 2007 Presented by: Liang Ding Finance Department, KSU

2. Introduction Complex community structure Social and communication network is subject to constant evolution The knowledge of the mechanisms governing the underlying community dynamics is limited

3. Intro cond Aim: to uncover basic relationships characterizing community evolution An algorithm based on clique percolation

4. data 1. the monthly list of articles in the Cornell University Library e-print condensed matter achieve spanning 142 months, with over 30,000 authors; 2. the record of phone calls of a mobile phone company spanning 52 weeks, 4 million users.

6. To check overlap the average weight of the links inside communities the average weight of the inter- community links; For co-author is 2.9; for phone-call is 5.9 Indicating that the intensity of collaboration /communication within a group is significantly higher than with contacts belonging to a different group

7. To check homogeneity

8. The basic events in the life of a community

9. Basic quantities characterizing a community Size: s Age: Auto-correlation function: C(t)

10. Characteristic features of community evolution

11. The stationarity As the average correlation between subsequent states.

13. The relationship between the lifetime, the stationarity and the community size

15. The time evolution of four communities from the co-authorship network show: A typical small and stationary community undergoes minor changes, but lives for a long time; A large non-stationary community whose members change dynamically, resulting in significant fluctuations in both size and composition, has a quite extended lifetime

16. Could the inspection of a community itself predict its future? w out: the total weight of this member ’ s connections to outside of the community; w in: the total weight of this member ’ s connections to members belonging to the same community; Calculate the probability that the member will abandon the community as a function of the w out /(w in +w out ) ratio

18. Take the idea from individuals to communities

19. summary Large groups persist for longer if they are capable of dynamically altering their membership; Small groups displays the opposite tendency; The time commitment of members to a given community can be used for estimating the community ’ s lifetime.