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Even though the heterogeneity of centrality in social networks is well documented, its role and effect on network stability in real life remains unclear. The literature roughly suggests that network structure is such that networks have an “inner” highly-connected nucleus and, in contrast, sparse outer shells. But to what extent is the existence of this nucleus 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, as a network grows and forms, theoretically speaking, network structure should be dependent on the patterns of change of degree centrality, i.e., social mobility between centrality shells. What is the role of social mobility in the formation of the nucleus-to-periphery profile, and is it related to network lifetime? Here, we explore these questions using data collected covering over a decade of activity from more than 10, 000 networked communities, with more than 134,000 users. We find that:  (i)  social mobility is, on average, negative but that,  (ii)  the higher the social mobility of the members of the network, the more stable and long-living the network is. Further,  (iii)  the network is, indeed, composed of two phases - a large but ephemeral sparsely connected “cloud” of actors, that nucleates around a  highly stable  nucleus of users. Lastly, (iv) networked communities which maintain a specific nucleus-to-periphery ratio  η , i.e., a ratio of the size of the nucleus to periphery of around    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$ \eta =\frac{1}{4} $$\end{document}   η  =   1  4, have a greater chance of survival. We find that deviations from this nucleus-to-periphery ratio predict a collapse of network activity, especially in the case of younger communities.   Electronic supplementary material  The online version of this article (10.1007/s41109-018-0102-3) contains supplementary material, which is available to authorized users.

Centralized nucleation in online networks leads to high social inequality