A new method to discretize time to identify the milestones of online social networks

Online social networks (OSNs) are complex time-varying networks due to the exponential growth in the number of users and the activities of those users. As the form of OSNs can change in each time frame, those working in domains such as community detection, event detection, big data analytics, recommender systems and marketing need to find a way to discretize time to identify the behavioural changes in the OSN over time. For dynamic domains, it is necessary to chunk the network into some time windows and monitor all these time windows. However, to date, many studies have only attempted to monitor a network using one-time window as one inseparable piece of information, which can lead to misinterpretation of the data. Existing methods predict the population growth of a network based on a whole growth rate, but a network has some distinct growth rates during its lifespan. Therefore, this study aims to propose a new method to discretize time to detect the milestones of OSNs. However, many parameters can affect OSN growth. Therefore, in this study, an OSN growth equation is formulated on the basis that the network follows a specific order and discipline in its growth. This study introduces a two-variable equation based on the number of users and the number of connections, which are two common variables in all OSNs, to identify behavioural changes in OSNs. Experiments conducted on six different datasets as well as on real Facebook and real Twitter data show that an OSN follows two different patterns during its lifespan. These two growth patterns differ markedly, and the point at which these two patterns meet is the milestone of the network.