This volume contains the lectures presented at the CCIII Course “Computational Social Science and Complex Systems” of the “Enrico Fermi” School held on 16–21 July 2018 in Varenna, Italy.

According to Stephen Hawking, the 21st century will be the century of complexity. Heterogeneous systems consisting of many interacting parts showing emergent phenomena are abundant and, indeed, at the turn of the millennium, the time seemed to be ripe for science to address the most relevant questions about their structure and dynamics. Paradigmatic examples of complex systems are human society and economics, where, in addition to the anyway challenging task of studying such systems, the property of adaption constitutes an additional difficulty, as the observers and the observed are coinciding in some cases.

The development of large-scale quantitative social science has been hindered for a long time by the lack of data. Traditional methods of data collection, like surveys, have in fact been very useful, however, they have severe limitations. The situation has radically changed recently due to the dramatic development of computing and information communication technology. We live now in a world of data deluge, where the question is not only how to obtain the data but rather how to sort out the important information from the plethora of data that can be accessed. Almost all our everyday activities leave digital fingerprints behind, enabling researchers to investigate interactions of people with high spatio-temporal resolution. Time-stamped mobile call records with position specification by antenna towers are just one example of such data sources. Another one from the field of finance is the detailed information about the limit order book of financial markets.

This Big Data has made it possible to study questions, which had been earlier impossible to deal with. From the large-scale structure of society to the temporal patterns of communication, from multi-scale dynamics of the stock market to the data-based categorization of investment strategies, from social contagion to disease spreading, many aspects of social and economic systems have become accessible. It is important to underline that many of these problems have immediate relation to applications.

The new situation has required new tools and new approaches. It has turned out that it is not possible to cope with the challenges induced by Big Data within one discipline like sociology or economics: There is a need for a multidisciplinary effort. New fields like econophysics, sociophysics, computational social science, and network science have emerged providing examples of co-operation occurring overcoming disciplinary borders. Physicists —besides economists, sociologists, computer scientists, etc.— have played an important role in this endeavor from the beginning.

Physics, especially statistical physics, contributes to the study of social and economic complex systems with an arsenal of tools, such as phase transitions and scaling, mean-field theory, random walks, correlation functions, pattern formation, non-linear dynamic systems, etc. However, the role of physics goes much beyond discovering possible analogies to physical systems and applying tools developed for investigating them. Perhaps even more important is the approach of physicists to tackle problems, which goes back to Galilei and Newton and which is widely acknowledged as the “scientific method”. It consists of a perpetual interplay between empirical observation, modeling, and theory, between induction and deduction, where empirical facts are always the decisive elements for the development or falsification of a theory.

The Summer Course of the International School of Physics “Enrico Fermi” on “Computational Social Science and Complex Systems” had the aim of presenting to PhD students and young researchers some of the recent developments in the interdisciplinary fields of computational social science and econophysics.

In the collected lectures of the School, a group of lectures have focused on recent problems investigated in computational social science. Specifically, Stefan Thurner discusses the study of virtual social systems. He shows that several sociological classics including the formation of social networks, the setting of gender differences, the growth of wealth inequality, etc. can be successfully investigated on the historical records of a society of computer game players. Markus Strohmaier considers the problems and potential of measuring social and political phenomena on the web. László Barabási and Federico Musciotto summarize Barabási’s lecture introducing the recently emerging “Science of success”. Barabási’s approach primarily focuses on the differences between the concepts of performance and success in modern society. Some recent results of the research area of market microstructure are discussed in Fabrizio Lillo’s lectures, where he discusses the interplay between order flow, intention of trading agents, and price dynamics of the traded asset. Both in computational social science and in the analysis and modeling of complex systems a crucial role is played by network science. Salvatore Miccichè and Rosario Mantegna present a primer on so-called “statistically validated networks”. These are networks where a selection of nodes and links is obtained under the condition that a specific statistical null hypothesis is rejected. With this methodology, one can highlight groups of nodes and links that are over-expressed (or under-expressed) with respect to a null hypothesis usually taking into account the intrinsic heterogeneity of the systems. Another crucial aspect of networks science concerns nature and properties of temporal networks. János Kertész briefly reviews the characteristics of temporal networks with special emphasis on small motifs and on the process of spreading. Temporal networks are also discussed in Alain Barrat’s lecture with an emphasis on the role of face-to-face interaction between individuals. Specifically, he focuses on the detection of face-to-face interactions recorded with using technologies such as Bluetooth, WiFi or RFID and on their analyses in terms of minimal models at different levels of description incorporating non-trivial longitudinal structures, mesoscopic structures, and correlated activity patterns. The role of the spatial structure of the population in the classic problem of disease spreading is discussed by Vittoria Colizza in her lecture where she discusses how to introduce the concept of meta-population in the standard modeling framework for the study of epidemic spread. Finally, the properties of spatio-temporal infrastructure networks are reviewed in the contribution of Louis Shekhtman and Shlomo Havlin, where they highlight how interdependent networks are characterized by abrupt first-order-like transitions where a cascade leads to a network collapse.

The Course was the first “Enrico Fermi” summer School on the interdisciplinary topic of computational social science with an emphasis on economic and social complex systems. This book records the lectures provided at the School and should be a useful reference for researchers interested in this area. We believe that beginning graduate students, young researchers and advanced research professionals will find this book useful for approaching some basic questions and many subtleties of the emerging field of computational social science.

We are grateful to the Italian Physical Society (SIF) and to Morgan Stanley Magyarország Elemzö KFT for their financial support. We wish to thank Prof. F. Mallamace and S. De Pasquale for their encouragement during the preparation for the School. Finally, we wish to thank Barbara Alzani (SIF), Ramona Brigatti, Elena Salvadore and Monica Bonetti (SIF) for their excellent cooperation before, during, and after the School period.

János Kertész, Rosario Nunzio Mantegna and Salvatore Miccichè