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 η=14, 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.
Bibliographical noteFunding Information:
We wish to thank Daniel Shapira (BGU), Jacob Goldenberg (IDC) and Miki Assaf (HUJ) for fruitful discussions. The data that were analyzed in this paper are available in: https://drive.google.com/open?id=1Gg9lQlWSviLrLAEGpR1q0vwA6UOR6IWN Data description: User posting activity in user-created forums (communes). Each row corresponds to one post. Variables: mainmsg: is the post the initial seed of the discussion tree? (0 = no, 1 = yes). place: the depth of the post within the tree (should be divided by 2). commune: a numerical id of the forum (commune). msgid: a numerical id of the post. date: the date the post was made. time: the time the post was made. userid: a numerical id of the user generating the post. thread: a numerical id of the thread of the post. parentmsg: the numerical id of the parent message. parentuser: the numerical id of the user which generated the parent post. numdate: the number of days at the date of the post since 01/01/2003.
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