Heterogeneity shapes groups growth in social online communities.

We study the time evolution of group sizes of an online community. The
empirical analysis shows that (i) groups grow linearly in time, (ii)
the growth values have heavy-tailed distribution and (iii) the number
of new groups grows linearly with time.
Based on these findings we propose a minimal model for the dynamics of
elements (groups) with associated counters (sizes). We show that the
elements intrinsic heterogeneity, introduced as a heavy-tailed
distribution of counters growth, shapes the statistical properties of
the system, such as the heavy-tailed distribution of counters and the
average growth of counters proportional to the value of counters.
Finally, we compare the model with a model of preferential growth and
emphasize that the model based on big-gets-bigger principle lacks
heterogeneity and introduces very strong correlation between size and
age, whereas the model based on broad heterogeneity performs close to
what is observed in the studied system.