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Network Theory

Networks are a pertinent concept to contemporary society; communication, transportation, and other forms of connectivity among people and goods, as well as knowledge and other expressions of human creativity, appear to be organized according to principles that have been explored by network theory. The development of a comprehensive network theory implied several interdisciplinary digressions and cross-fertilization of concepts and methods from mathematics to anthropology and from physics to sociology along two centuries. The apparent nomadic inclination of network studies induced scientists in a range of disciplines to make sense of important social phenomena and orient their work toward a common theoretical perspective. Several scholars now agree that the study of networks, including the exploration of their variety and dynamics, is an important key to understanding the evolution and stability of physical and social structures. Network theory has its origins in graph theory and has developed in different areas of the social and natural sciences and led to current trends in theoretical and empirical network research.

The Idea of Network

The idea that connections among actors or components of a set are relevant for understanding its form and its properties has a long history. In the 18th century, the Swiss-born mathematician Leonhard Euler developed a new area of research involving the logic exploration and calculus of geometric graphics; his work and the subsequent studies of other mathematicians pose the bases for graph theory, the basic methodological references for the study of networks. Graph theory uses a specific terminology to describe networks (such as the term node to indicate the endpoint of a connection and the term line to represent the connection itself) and elaborated several principles to define networks properties. For example, a network characterized by a Euler trial offers the opportunity to complete a cycle of all the connected lines without passing more than one time from each node.

The mathematical study of networks, however, was initially based on abstract calculus and had limited empirical applications; only in the 20th century, with the spread of communication, transportation, and transmission systems, was graph theory successfully put into service of the physical and social sciences. Historically, three main phases of development of network research can be drawn. In the first phase, different disciplines involved in the area such as mathematics and social sciences autonomously develop a theoretical paradigm to study connections and social relations. In the second, historical phase graph theory is integrated in social studies with relevant contributions from mathematics and statistics, and the study of interaction networks establishes itself as a formal framework for thinking about the social world. Contemporary network theory is influenced by physics and computing sciences and employs theoretical concepts and methodological tools from social network analysis for the study of large networks such as the Internet, its evolution, and the socioeconomic phenomena generated by technological innovation. Advanced theoretical research concentrates on the formalization of properties of noncasual networks and dynamical evolution of complex networks with a specific concern in the area of computational biology and epidemiology.

The Origins

At the end of the 19th century, an eclectic German sociologist, Georg Simmel, was intrigued by the rapid social and technological changes that were transforming modern society. He observed that individuals were increasingly involved in relations of different sorts, from economic to affective and communicative relations, and that these contacts originated only partially from the preferences of the person. Participation in social circles, according to Simmel, implied rules and opportunities; the outcome of relations, though, was influenced by formal aspects such as the number of participants to the relation, the positivity/negativity of these relations, and the presence of groups of similar individuals (on the bases of age, gender, or social class and ethnic origin). He defined formal sets of relations as “forms” and predicted that the social sciences would investigate connections among individuals in order to discover the hidden properties that influence the formation and the transformation of social circles. Simmel's analysis, however, lacked formalization, and its theoretical relevance was not completely acknowledged until the middle of the 20th century.

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