The basic insight of social network analysis is that social structure is an emergent property of the networks of relationships in which individuals (and other social actors, such as organizations) are embedded (Simmel [1922] 1955; Radcliffe-Brown 1940). Therefore, if one wants to understand social structure, one should study social networks. While research on social networks may use quantitative or qualitative or mixed methods, social network analysis itself is fundamentally neither quantitative nor qualitative, nor a combination of the two. Rather, it is structural. That is to say, the basic interest of social network analysis is to understand social structure, by studying social networks. Observing or calculating quantitative aspects of social networks, such as the average number of individuals with whom an individual is directly connected, or qualitative aspects, such as the nature of social ties among individuals, can be useful analytic techniques, but the fundamental quest is to understand the structure of the network, which is neither a quantity nor a quality.

As it has developed, social network analysis has become increasingly mathematical: That is, it employs formalisms and analytic techniques taken from mathematics and developed further for social network analysis by mathematicians. Many people think of social network analysis as primarily a quantitative approach to social science, because they mistakenly equate “quantitative” and “mathematical.” But, as Harrison White (1963a:79) pointed out, “Mathematics has grown much ‘beyond’ quantity...,” and the branch of mathematics principally used by social network analysis – graph theory – represents structures (or the lack thereof), not quantities. The same point was made much earlier by Radcliffe-Brown (1957), in his lecture series given at the University of Chicago in 1937:

Interest in social network analysis has grown massively in recent years. This growth has been matched by an increasing sophistication in the technical tools available to users. Models and Methods in Social Network Analysis (MMSNA) presents the most important of those developments in quantitative models and methods for analyzing social network data that have appeared during the 1990s. It is a collection of original chapters by leading methodologists, commissioned by the three editors to review recent advances in their particular areas of network methods.

As is well-known, social network analysis has been used since the mid-1930s to advance research in the social and behavioral sciences, but progressed slowly and linearly, until the end of the century. Sociometry (sociograms, sociomatrices), graph theory, dyads, triads, subgroups, and blockmodels – reflecting substantive concerns such as reciprocity, structural balance, transitivity, clusterability, and structural equivalence – all made their appearances and were quickly adopted by the relatively small number of “network analysts.” It was easy to trace the evolution of network theories and ideas from professors to students, from one generation to the next. The field of network analysis was even analyzed as a network (see, for example, Mullins 1973, as well as analyses by Burt in 1978, and Hummon and Carley in 1993). Many users eventually became analysts, and some even methodologists. A conference of methodologists, held at Dartmouth College in the mid-1970s, consisted of about thirty researchers (see Holland and Leinhardt 1979) and really did constitute a “who's who” of the field – an auspicious, but rather small gathering.