Dynamics of online social networks

Threshold effects in networks trigger global cascades which may generate the failure of such systems. This phenomenon was observed in the case of iWiW, a very popular Hungarian online social network which collapsed due to the cascading abandon of the service by its users, driven by exogenous and endogenous factors. In this research, we analyze the dataset of iWiW and try to characterize some of the dynamical features of the networks, basing our study on the timestamped interactions between users. We first look at the degree distribution of the network and then focus on identifying some of the ego-centered networks. We will then detect the communities in each ego-centered network with the Louvain algorithm and analyze the rank correlation between the registration dates and the last login dates of users inside the communities, comparing the obtained coefficients with the expected rank correlations for a null model. We find out that communities have some effect in governing the dynamics of the system. Then, we look at some metadata (city, age, gender, education level) to see if and how the characteristics of the users inside a community overlap with the respective ego and we find that the overlaps are not related to the rank correlations previously found. After that, we still look at the rank correlations for the nodes in some specific paths in the network and show that there is a strong tendency towards anticorrelation. We then develop a criterion according to which a node is considered as part of a departure cascade or not; applying the criterion to all the nodes, we are able to reconstruct the entire cascades history and look at some of their main statistical properties. Lastly, we illustrate the results of the simulations of a simple model that can explain some general dynamical features of such cascading effects on online social networks.