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In sociology, social complexity is a conceptual framework used in the analysis of society. Contemporary definitions of complexity in the sciences are found in relation to systems theory, in which a phenomenon under study has many parts and many possible arrangements of the relationships between those parts. At the same time, what is complex and what is simple is relative and may change with time.
Current usage of the term "complexity" in the field of sociology typically refers specifically to theories of society as a complex adaptive system. However, social complexity and its emergent properties are central recurring themes throughout the historical development of social thought and the study of social change. The early founders of sociological theory, such as Ferdinand Tönnies, Émile Durkheim, Max Weber, Vilfredo Pareto, and Georg Simmel, all examined the exponential growth and increasing interrelatedness of social encounters and exchanges. This emphasis on interconnectivity in social relationships and the emergence of new properties within society is found in theoretical thinking in multiple areas of sociology. As a theoretical tool, social complexity theory serves as a basis for the connection of micro- and macro-level social phenomena, providing a meso-level or middle-range theoretical platform for hypothesis formation. Methodologically, the concept of social complexity is theory-neutral, meaning that it accommodates both local (micro) and global (macro) phenomena in sociological research.
The American sociologist Talcott Parsons carried on the work of the early founders mentioned above in his early (1937) work on action theory. By 1951, Parsons places these earlier ideas firmly into the realm of formal systems theory in The Social System. For the next several decades, this synergy between general systems thinking and the further development of social system theories is carried forward by Parson's student, Robert K. Merton, and a long line of others, in discussions of theories of the middle-range and social structure and agency. During part of this same period, from the late 1970s through the early 1990s, discussion ensues in any number of other research areas about the properties of systems in which strong correlation of sub-parts leads to observed behaviors variously described as autopoetic, self-organizing, dynamical, turbulent, and chaotic. All of these are forms of system behavior arising from mathematical complexity. By the early 1990s, the work of social theorists such as Niklas Luhmann began reflecting these themes of complex behavior.
One of the earliest usages of the term "complexity", in the social and behavioral sciences, to refer specifically to a complex system is found in the study of modern organizations and management studies. However, particularly in management studies, the term often has been used in a metaphorical rather than in a qualitative or quantitative theoretical manner. By the mid-1990s, the "complexity turn" in social sciences begins as some of the same tools generally used in complexity science are incorporated into the social sciences. By 1998, the international, electronic periodical, Journal of Artificial Societies and Social Simulation, had been created. In the last several years, many publications have presented overviews of complexity theory within the field of sociology. Within this body of work, connections also are drawn to yet other theoretical traditions, including constructivist epistemology and the philosophical positions of phenomenology, postmodernism and critical realism.
Methodologically, social complexity is theory-neutral, meaning that it accommodates both local and global approaches to sociological research. The very idea of social complexity arises out of the historical-comparative methods of early sociologists; obviously, this method is important in developing, defining, and refining the theoretical construct of social complexity. As complex social systems have many parts and there are many possible relationships between those parts, appropriate methodologies are typically determined to some degree by the research level of analysis differentiated by the researcher according to the level of description or explanation demanded by the research hypotheses.
At the most localized level of analysis, ethnographic, participant- or non-participant observation, content analysis and other qualitative research methods may be appropriate. More recently, highly sophisticated quantitative research methodologies are being developed and used in sociology at both local and global levels of analysis. Such methods include (but are not limited to) bifurcation diagrams, network analysis, non-linear modeling, and computational models including cellular automata programming, sociocybernetics and other methods of social simulation.
Main article: Dynamic network analysis
Complex social network analysis is used to study the dynamics of large, complex social networks. Dynamic network analysis brings together traditional social network analysis, link analysis and multi-agent systems within network science and network theory. Through the use of key concepts and methods in social network analysis, agent-based modeling, theoretical physics, and modern mathematics (particularly graph theory and fractal geometry), this method of inquiry brought insights into the dynamics and structure of social systems. New computational methods of localized social network analysis are coming out of the work of Duncan Watts, Albert-László Barabási, Nicholas A. Christakis, Kathleen Carley and others.
New methods of global network analysis are emerging from the work of John Urry and the sociological study of globalization, linked to the work of Manuel Castells and the later work of Immanuel Wallerstein. Since the late 1990s, Wallerstein increasingly makes use of complexity theory, particularly the work of Ilya Prigogine. Dynamic social network analysis is linked to a variety of methodological traditions, above and beyond systems thinking, including graph theory, traditional social network analysis in sociology, and mathematical sociology. It also links to mathematical chaos and complex dynamics through the work of Duncan Watts and Steven Strogatz, as well as fractal geometry through Albert-László Barabási and his work on scale-free networks.
Main article: Computational sociology
The development of computational sociology involves such scholars as Nigel Gilbert, Klaus G. Troitzsch, Joshua M. Epstein, and others. The foci of methods in this field include social simulation and data-mining, both of which are sub-areas of computational sociology. Social simulation uses computers to create an artificial laboratory for the study of complex social systems; data-mining uses machine intelligence to search for non-trivial patterns of relations in large, complex, real-world databases. The emerging methods of socionics are a variant of computational sociology.
Computational sociology is influenced by a number of micro-sociological areas as well as the macro-level traditions of systems science and systems thinking. The micro-level influences of symbolic interaction, exchange, and rational choice, along with the micro-level focus of computational political scientists, such as Robert Axelrod, helped to develop computational sociology's bottom-up, agent-based approach to modeling complex systems. This is what Joshua M. Epstein calls generative science. Other important areas of influence include statistics, mathematical modeling and computer simulation.
Main article: Sociocybernetics
Sociocybernetics integrates sociology with second-order cybernetics and the work of Niklas Luhmann, along with the latest advances in complexity science. In terms of scholarly work, the focus of sociocybernetics has been primarily conceptual and only slightly methodological or empirical. Sociocybernetics is directly tied to systems thought inside and outside of sociology, specifically in the area of second-order cybernetics.
In the first decade of the 21st century, the diversity of areas of application has grown as more sophisticated methods have developed. Social complexity theory is applied in studies of social cooperation and public goods; altruism; education; global civil society  collective action and social movements; social inequality; workforce and unemployment; policy analysis; health care systems; and innovation and social change, to name a few. A current international scientific research project, the Seshat: Global History Databank, was explicitly designed to analyze changes in social complexity from the Neolithic Revolution until the Industrial Revolution.
As a middle-range theoretical platform, social complexity can be applied to any research in which social interaction or the outcomes of such interactions can be observed, but particularly where they can be measured and expressed as continuous or discrete data points. One common criticism often cited regarding the usefulness of complexity science in sociology is the difficulty of obtaining adequate data. Nonetheless, application of the concept of social complexity and the analysis of such complexity has begun and continues to be an ongoing field of inquiry in sociology. From childhood friendships and teen pregnancy to criminology and counter-terrorism, theories of social complexity are being applied in almost all areas of sociological research.
In the area of communications research and informetrics, the concept of self-organizing systems appears in mid-1990s research related to scientific communications. Scientometrics and bibliometrics are areas of research in which discrete data are available, as are several other areas of social communications research such as sociolinguistics. Social complexity is also a concept used in semiotics.