Nucleation of social groups: The role of centrality inequality and social mobility

Even though the heterogeneity of social networks centrality is well documented, its role and effect on network stability, is unclear. It is known that, universally, networks have an “inner” highly-connected nucleus and, in contrast, sparser outer shells. But, to what extent the existence of this nucleus is crucial for the survival of a network? To what extent is the outer shells, much-larger population, essential to the longevity of the network? Furthermore, network structure is very much dependent on the mobility between centrality shells, i.e., social mobility. What is, then, the role of social mobility in the formation of the nucleus-periphery profile and does it have an effect on network lifetime? Here, we explore these questions using data collected of more than 10K networked communities, with more than 134K users, for over a decade. We find that: (i) social mobility is, on average, negative and promotes instability, and (ii) the more positive social mobility is, the more stable the community. Further, (iii) the network is composed of two phases, a large but ephemeral sparsely-connected cloud of actors which nucleates around a highly stable nucleus of core users. Finally, (iv) networked communities which closely maintain a nucleation ratio, i.e., ratio between nucleus size and outer shells size, of 1 to 3, exhibit the best chances of survival. Deviations from this nucleation ratio translates into the collapse of the network, especially for younger communities.