۱- Introduction

۲- Historical notes

۳- Distributed algorithms for network analysis

۴- Evolution of opinions and belief systems

۵- Conclusions and acknowledgements

References

Abstract

In this paper, we provide an overview of recent works on dynamics of social networks and distributed algorithms for their exploration, contributed by Dr. Roberto Tempo (1956–۲۰۱۷) and his colleagues. These works, based on the recent achievements in multi-agent systems theory and distributed randomized algorithms, contribute in bridging the gap between the two classical sciences of Social Network Analysis and Systems and Control. The topics covered by this survey include distributed algorithms for analysis of complex social networks and novel dynamic models, describing opinion formation processes in such networks.

Introduction

Originating from studies on sociometry [1], Social Network Analysis (SNA) has grown into an interdisciplinary theory, being an indispensable part of modern Network Science. SNA employs numerous mathematical tools, coming from graph theory, algorithm theory, probability theory and statistics. Whereas the important role of “cybernetical” (system, control and information-theoretic) methods in social and behavioral sciences has been foreseen by Wiener [2], the fruitful interaction among SNA and systems theory has started quite recently with introducing distributed algorithms for analysis of social networks and novel dynamical models, describing processes over such networks (e.g. evolution of individual opinions, attitudes and beliefs under social influence). The rapidly developing subfield of control theory, studying social networks by system-theoretic methods, is very young and still has no name. One of the pioneers of this new area, Roberto Tempo was very passionate about filling the gap between control and societal studies. Among his last works there were tutorial papers [3,4] making an attempt to systematize the most mature results and achievements of “social systems theory”, opening this novel area to a broad interdisciplinary research community.