Milen Nikolov

Fig. 1: Acknowledgements across scholars network (about 3000 nodes). Our analysis shows that, network growth mechanisms (G) contributes the largest reduction in distance between the predicted and observed degree distributions. The success (S) and turnover (T) mechanisms seem to have similar effects. They also appear to be highly correlated since their combination has the smallest impact compared to the other two-way combinations. Nevertheless, the combination of the three mechanisms provides a dramatic improvement compared to the null model and leaves little to be contributed by other mechanisms. More details regarding these mechanisms can be found in our preprint available upon request.

Over the last decade, distributions of various social attributes across the population have been extensively studied using dynamically evolving graph models. Typically individuals form a set of nodes and the social relationships between them are captured a set of weighted edges. As people leave or enter the social network for various reasons (deaths and births, closing and opening accounts, etc.), and as their relationships change (new friendships emerge, new papers are coauthored, etc.) the model graph evolves. Distribution of popularity, status, and activity in social networks is then modeled by the nodes' indegrees, and outdegrees over time.

Analyzing the resulting graphs and data reveals that individual outcomes often follow highly skewed long-tailed distributions - most individuals have little, while a few individuals have a lot. In particular, this pattern has been observed for the distribution of popularity, status, and activity in social networks: freindship connections, authorship of scientific papers, number of posts in online media, etc.

However, in our daily social interactions, although we encounter a large variety of people, we tend to perceive most of them as "average" in terms of personality traits, cognitive abilities, and interpersonal skills. We rarely come across "extremes." Indeed, social and behavioral scientists usually assume that the distribution of individual heterogeneity follows a "bell-shaped curve". I.e. it matches a Gaussian (or normal) distribution. This paradigm is well-reflected in the design of aptitude tests, intelligence tests, and psychometric scales; it is also well-embedded in the most common statistical methods in social science research.

What are then the mechanisms underlying the emergence of inequalities in our evolving graphs degree distributions?

To answer this question, we first compiled a set of social interaction mechanisms that have been observed by social scientists to occur within communities (i.e. homopholy, transitivity, network growth, etc.). We also identified new plausible social mechanisms. Next, we encoded the mechanisms as concrete rules governing the social graph evolution. Based on the rules, we are able to derive analytically the resulting network degree distributions in some cases; in others, we simulate the mechanisms and collect the resulting network data series capturing degree dstribution as the graph evolves. Finally, we gathered data for three social networks at different scales: llinois US-China Adolescence Study (couple of hundred nodes); the acknowledgements network from articles published in the period 2000-2009 in ten prominent sociological journals (about 3000 nodes); and CouchSurfing (539,856 nodes). We used Kolmogorov-Smirnov (KS) among others test statistics to evaluate the statistical distance between our mechanisms' generated degree distributions and the degree distributions found in the data (when modeled as a graph). Fig. 1 shows some of our findings. For more details, our preprint, data and code are available upon request.