Modeling, analysis, control, and management of complex social networks represent an important area of interdisciplinary research in an advanced digitalized world. In the last decade social networks have produced significant online applications which are running on top of a modern Internet infrastructure and have been identified as major driver of the fast growing Internet traffic. The "Second International Workshop on Modeling, Analysis and Management of Social Networks and Their Applications" (SOCNET 2018) held at Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, on February 28, 2018, has covered related research issues of social networks in modern information society. The Proceedings of SOCNET 2018 highlight the topics of a tutorial on "Network Analysis in Python" complementing the workshop program, present an invited talk "From the Age of Emperors to the Age of Empathy", and summarize the contributions of eight reviewed papers. The covered topics ranged from theoretical oriented studies focusing on the structural inference of topic networks, the modeling of group dynamics, and the analysis of emergency response networks to the application areas of social networks such as social media used in organizations or social network applications and their impact on modern information society. The Proceedings of SOCNET 2018 may stimulate the readers' future research on monitoring, modeling, and analysis of social networks and encourage their development efforts regarding social network applications of the next generation.