Quantifying Social Group Evolution

Gergely Palla, Albert-Laszlo Barabasi, and Tamas VicsekNature Vol 446 April 2007

Presented by: Liang Ding Finance Department, KSU

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

Intro cond• Aim: to uncover basic relationships

characterizing community evolution

• An algorithm based on clique percolation

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.

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 /com

munication within a group is significantly higher than with contacts belonging to a different group

cwicc ww /

icw

To check homogeneity

The basic events in the life of a community

Basic quantities characterizing a

community• Size: s• Age: • Auto-correlation

function: C(t)

Characteristic features of community evolution

The stationarity• As the average

correlation between subsequent states.

The relationship between the lifetime, the stationarity and the

community size

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

Could the inspection of a community itself predict its

future?• wout: the total weight of this member’s

connections to outside of the community;

• win: 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 wout/(win+wout) ratio

Take the idea from individuals to communities

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.