Spiraling Facebook: an alternative Metropolis–Hastings random walk using a spiral proposal distribution

Sampling the content of an Online Social Network (OSN) is a major application area due to the growing interest in collecting social information e.g., email, location, age and number of friends. Large-scale social networks such as Facebook can be difficult to sample due to the amount of data and the privacy settings imposed by this company. Sampling techniques require the development of reliable algorithms able to cope with an unknown environment. Our main purpose in this manuscript is to examine whether it is possible to switch the normal distribution of the Metropolis–Hasting random walk (MHRW) by using a spiral approach as an alternative and reliable distribution. We propose a sampling algorithm, the Alternative Metropolis–Hasting random walk AMHRW, to study the effect of collecting digital profiles on two different datasets. We examine the soundness and robustness of the proposed algorithm through independent walks on two different representative samples of Facebook. We observe that normal distribution performance can be approximated by means of the use of an Illusion spiral. Similarly, we provide a formal convergence analysis to evaluate the performance of our independent walks and to evaluate whether the sample of draws has attained an equilibrium state. Finally, our preliminary results provide experimental evidence that collecting data with the AMHRW algorithm can be equally effective as the MHRW algorithm on large-scale networks