Sustainable Online Communities Exhibit Distinct Hierarchical Structures Across Scales of Size

Online communities exist in many forms and sizes, and are a source of considerable influence for individuals and organizations (1, 2). Yet, there is limited insight into why some online communities are sustainable, while others cease to exist (3). We find that communities that fail to maintain a typical hierarchical social structure which balances cohesiveness across size scales do not survive, and can be distinguished from communities that exhibit such balance and prevail in the long term. Moreover, in an analysis of 10,122 real-life online communities with a total of 134,747 members over a period of more than a decade, we find that mapping the community social circle structure in the first 30 days of its lifetime is sufficient to forecast the survival of the community up to ten years in the future. By varying calibration time frames, the aspects of the social structure that allows for predictive power emerge and fixate within the first couple of months in a community’s lifetime. A community can exhibit a variety of social structure configurations. However, in actuality, not all hypothetical structures may be observed: Only those configurations that promote survival at each scale are likely to be observed, while other communities with sub-optimal structure configurations are expected to fade away. Indeed, in our data, we find that communities that thrive are those that exhibit distinct structural network features that are scalable across sizes: We identify a “valley of stability” that marks a range of structures for which communities preserve sustainability. These findings suggest an analogy to the stability of physical matter: Only structures that exist in an optimal balance between contradictory forces across scales of size survive for relatively long periods. While the hierarchical nature of social communities is well documented [e.g., (4-9)], its association with network stability has yet to be established. This hierarchy captures valuable information on the stability of networks and can indicate the "health" level of that network and be an important predictor of stability. Individuals gain benefits from group membership (10), a major benefit being the common relevance of group members to one another and the consequent resource exchange within the group. An important factor in the stability of a social group is its level of cohesiveness (11). A well-functioning cohesive group supplies information, security, and a variety of other important resources to its members (12, 13). In addition, previous studies have shown that access to outside connections and social circles leads to benefits and information that are associated with the outside world [e.g., finding a job through weak ties (15), or exposure to innovation (9, 16)]. In general, investment in a few links with non-kin “friends” that connect unrelated families can potentially increase efficiency for information exchange (17). Obviously, each member of a group would want to benefit from both global and local connections, but there is a basic constraint: group members have limited time and effort to spend on maintaining relations. This leads to a natural tradeoff between connection choices. Community stability is, therefore, a consequence of a subtle balance between local (direct) and global (more exploratory) benefits. The members of each existing small clique may decide to spend their resources to interact strictly with other members of their clique. This allows them to benefit from their group’s resources and protection, but increases the risk of fragmentation of the clique from the rest of the community. Alternatively, they may choose to focus on relationships outside the clique to seek new opportunities and exposure to new ideas, and to increase their scope. This, in turn, may result in risking their own clique’s long-term stability. A compromise between these competing sets of needs would be a mix of the two approaches: group members connect to larger external circles, but only to those that their own clique peers also connect to. Consequently, cliques are able to maintain their cohesive structure, while at the same time to overlap with other cliques, simultaneously conserving the cohesiveness of the whole community. The result is a hierarchical structure in which the extended social circles are an aggregation of smaller scale circles, but integrity is conserved for both scales. The generalization to higher scales is straightforward. For each scale, members of the social circle of that scale will balance between relationships within or outside it. In fact, we maintain that unlike common approaches which rely on a dichotomy between the individualand aggregate-level structure—identifying and using social sub-communities across varying size scales as the units of analysis is a much more useful and constructive approach. This type of multi-scale cohesiveness facilitates long-term sustainability for the community. A mapping of the profile of the cohesiveness across scales is, therefore, a measure of the community's health in terms of social stability. In order to examine this conjecture, we developed a mapping approach to detect the social circles across scales and then, from the mapping, calculated a cohesiveness-vs.-scales profile. We defined a social circle's cohesiveness as the overlap of interests among its members and operationalized it by using the clustering coefficient as the measure of interest overlap (18). Then we tested whether the cohesiveness-vs.scales profile is a good diagnostic of community stability and evaluated its predictive power. We used a multi-scale approach to map social circles (i.e., sub networks) per given scale level of cohesiveness. Let S M be the social circles’ mapping of a social network of N individuals for a given scale S, where S is a positive integer number representing the radius of a cohesiveness sphere. The mapping } { ,S S C M   is the set of social circles } { ,S C for a given S such that S S M C  ,  if the two following conditions are satisfied: (i) For each and every pair of individuals i and j in the network that belong to social circle S C ,  , the shortest path S C j i d , ,  between them within the social circle S C ,  satisfies: S d S C j i  , ,  . (ii) There is no inclusion relationship between social circle S C ,  and S C ,  of mapping S M for   ,  , and    . Namely, for any two social circles S S M C  ,  and S S M C  ,  for which    , the condition is S S C C , ,    and S S C C , ,    . Figure 1 illustrates a simple example of a mapping for a hypothetical network with ten nodes. In the figure, it is possible to see how small circles of high cohesiveness merge into larger ones of lower cohesiveness. For instance, the tightest cohesiveness sphere 1  S , condition (i), results in the mapping 1 M , which is the mapping of the fully connected groups in the community, i.e., the network cliques (4). In the figure, it is possible to see that 1 M includes three highcohesiveness circles, or cliques. Condition (ii) dictates that each separate circle is not fully contained within another clique although they can still partially overlap. If the basic a-priori units of analysis of the network are the nodes, the clique map ( 1 M ) is the mapping of the one-scalehigher “natural” components of the network (S=1 in Fig. 1). Next, 2 M is the mapping of the second-order cliques (S=2 in Fig. 1), and so on. The last stage includes only a single social circle—the entire community. Fig. 1. An example of social circles mapping for an illustrative ten-node network. The network itself, with no mapping, is shown at the top of the figure. The mapping level, S, is given above each correspending mapping. The full explanation of how the social circles mapping was calculated is given in the supplementary information, S1. Figure 2 illustrates the mapping process for a real-life sample of 43 community members in a community that was created to host discussions of users interested in a contemporary religious lifestyle. Figure 2A shows a plot of the network of interactions between the members of that community. The red area marks the one and only detected social circle at the level of 4  S , i.e., the whole community. In practice, the figure shows that the whole community is connected at a distance of either four connections or less. The one-step lower scale 3  S (Fig. 2B) shows a more granular picture of the structure, in which the average social circle size at that scale is around the size of a characteristic band (6). The social circles at this scale seem to be cohesive and practically woven into one another, a positive sign of stability. Some of the most popular topics in each separate social circle are given in Figure 2A–D. A post factum inspection of the figures and text reveals that the social circles mapping closely corresponds to topical mapping. Users form small groups of unique common denominators, which join into larger groups of more widespread common denominators. This happens across scales. The detailed analysis of the major topics within each detected social circle is described in Section S2.