Indirect Estimation of Shortest Path Distributions with Small-World Experiments

The distribution of shortest path lenghts is a useful characterisation of the connectivity in a network. The small-world experiment is a classical way to study the shortest path distribution in real-world social networks that cannot be directly observed. However, the data observed in these experiments are distorted by two factors: attrition and routing (in)efficiency. This leads to inaccuracies in the estimates of shortest path lenghts. In this paper we propose a model to analyse small-world experiments that corrects for both of the aforementioned sources of bias. Under suitable circumstances the model gives accurate estimates of the true underlying shortest path distribution without directly observing the network. It can also quantify the routing efficiency of the underlying population. We study the model by using simulations, and apply it to real data from previous small-world experiments.