Mathematical modelling of the statistics of communication in social networks

Abstract

Chat rooms are of enormous interest to social network researchers as they are one of the most interactive internet areas. To understand the behaviour of users in a chat room, there have been studies on the analysis of the Response Waiting Time (RWT) based on traditional approaches of aggregating the network contacts. However, real social networks are dynamic and properties such as RWT change over time. Unfortunately, the traditional approach focuses only on static network and neglecting the temporal variation in RWT which may have lead to misrepresentation of the true nature of RWT. In order to determine the true nature of RWT, we analyse and compare the RWT of three online chat room logs (Walford, IRC and T-REX) putting into consideration the dynamic nature of RWT. Our research shows that the distribution of the RWT exhibits multi-scaling behaviour, which signi cantly a ects the current views on the nature of RWT. This is a shift from simple power-law distribution to a more complex pattern. The previous study on users RWT between pairs of people claims that the RWT has a power-law distribution with an exponent of 1. However, our research shows that multi-scaling behaviour and the exponent has a wider range of values which depend on the environment and time of day. The di erent exponents observed on di erent time scales suggest that the time context or environment has a signi cant in uence on users RWT. Furthermore, using the chat characterise, we predicted the factors which could minimize response waiting time and improving the friendship connection during online chat sessions. We apply our ndings to design an algorithm for chat thread detection. Here, we proposed two variations of cluster algorithm. The rst algorithm involves the traditional approach while in the second one, the temporal variations in RWT was taken into consideration to capture the dynamic nature of a text stream. An advantage of our proposed method over the previous models is that previous models have involved highly computationally intensive methods and often lead to deterioration in the accuracy of the result whereas our proposed approach uses a simple and e ective sequential thread detection method, which is less computationally intensive