Statistical Methods and Network Simulation: The Role of Limited Information in Edge Formation

Snjiders et. al. (2009, 2013) have contributed to an approach integrating agent based models and empirical network data in which instead of empirical data “validating” the simulation, the simulation estimates the empirical parameters. One assumption is that agents have information about the other actors in the network, i.e. that any two agents could potentially form a tie. This assumption means that the model is limited to modeling relatively small empirical networks. Another potential solution is to consider how information about potential matches might be limited. In a loosely related area, Bearmann et. al. (2004) looked at the potential generating mechanisms of a specific type of social network: sexual histories. They found that limiting potential matches (excluding those closest in one’s network) generated social networks that closely matched empirical data.

We use agent based simulations to consider the effects of assuming full versus limited information in evolving social networks. First, we limit information in a network’s evolution based on the existing network, partitioning the list of potential new friends between those within one’s local network (e.g. 3-step acquaintances) and a small sample of strangers. We test whether limiting information about potential matches generates more realistic graphs in terms of the average path length, clustering, edge distribution, and connectivity, as community size increases. The question of limited information is then extended to sexual history networks, again, partitioning potential matches into those in one’s local network and a small sample of the general population. The evolution of social networks is based on an exponential graph models while the sexual histories implement a Gale Shapely Matching Algorithm, as seen in the literature on the stable matching problem.