Intelligibility of Erdös-Rényi random graphs and time varying social network modeling

The concept of social networks has been widely studied for different classic (socio-economic problems, trade networks, etc) and contemporary (World Wide Web, cell phone networks, smart city networks, IoT, etc.) settings. People, organizations, intelligent vehicles, mobile robots, wearable and embedded devices, all can be connected by means of appropriate information and communication technologies. In recent years, the area of social networks became very popular mainly through the development of social media and Internet social websites such as Facebook, Twitter, LinkedIn, ResearchGate, and many others. Graph theory offers suitable mathematical representations for social networking models. We describe in this paper some enumerative, stochastic and statistical tools allowing the analysis of time-varying social networks. Indeed, the study of social networks through the theory of random graphs and dynamic network analysis has enabled us to develop probabilistic and statistical approaches to calculate some indices and measures that characterize the dynamic behavior of such the networks through time.