In 1973, Small published a paper that was as groundbreaking in its own way as Garfield’s 1955 paper introducing citation indexing for science. This paper, “Co-citation in the scientific literature: a new measure of relationship between two documents,” introduced A new era in describing the specialty structure of science11. Small measured the similarity of two documents in terms of the number of times they were cited together, in other words their co-citation frequency. He illustrated his method of analysis with an example from recent papers in the literature of particle physics. Having found that such co-citation patterns indicated “the notion of subject similarity” and “the association or co- occurrence of ideas,” he suggested that frequently cited papers, reflecting key concepts, methods, or experiments, could beused as a starting point for a co-citation analysis as an objective way to reveal the social and intellectual, or the socio- cognitive, structure of a specialty area. [...] Small found co-citation analysis pointed to the specialty as the natural organizational unit of research, rather than traditionally defined and larger fields. Small also saw the potential for co- citation analysis to make, by analogy, movies and not merely snapshots. “The pattern of linkages among key papers establishes a structure or map for the specialty which may then be observed to change through time,” he stated. “Through the study of these changing structures, co-citation provides a tool for monitoring the development of scientific fields, and for assessing the degree of interrelationship among specialties.”

When Eugene Garfield introduced the concept of a citation index for the sciences in 1955, he emphasized its several advantages over traditional subject indexing. Since a citation index records the references in each article indexed, a search can proceed from a known work of interest to more recently published items that cited that work. Moreover, a search in a citation index, either forward in time or backward through cited references, is both highly efficient and productive because it relies upon the informed judgments of researchers themselves, reflected in the references appended to their papers, rather than the choices of indexing terms by cataloguers who are less familiar with the content of each publication than are the authors. Garfield called these authors “an army of indexers” and his invention “an association-of-ideas index.” He recognized citations as emblematic of specific topics, concepts, and methods: “the citation is a precise, unambiguous representation of a subject that requires no interpretation and is immune to changes in terminology.” In addition, a citation index is inherently cross-disciplinary and breaks through limitations imposed by source coverage.

To summarize, a research front consists of a group of highly cited papers that have been co-cited above a set threshold of similarity strength and their associated citing papers. In fact, the research front should be understood as both the co-cited core papers, representing a foundation for the specialty, and the citing papers that represent the more recent work and the leading edge of the research front. The name of the research front can be derived from a summarization of the titles of the core papers or the citing papers. The naming of research fronts in Thomson Reuters Essential Science IndicatorsSM relies on the titles of core papers. In other cases, the citing papers have been used: just as it is the citing authors who determine in their co-citations the pairing of important papers, it is also the citing authors who confer meaning on the content of the resulting research front. Naming research fronts is not a wholly algorithmic process, however. A careful, manual review of the cited or citing papers sharpens accuracy in naming a research front.

In 1965, Price published “Networks of scientific papers,” which used citation data to describe the nature of what he termed “the scientific research front.” Previously, he had used the term “research front” in a generic way, meaning the leading edge of research and including the most knowledgeable scientists working at the coalface. But in this paper, and using the short-lived field of research on N-rays as his example, he described the research front more specifically in terms of its density of publications and time dynamics as revealed by a network of papers arrayed chronologically and their inter-citation patterns. Price observed that a research front builds upon recently published work and that it displays a tight network of relationships.

Both Small and Marshakova- Shaikevich contrasted co-citation with bibliographic coupling, which had been described by Myer Kessler in 196315. Bibliographic coupling measures subject similarity between documents based on the frequency of shared cited references: if two works often cite the same literature, there is a probability they are related in their subject content. Co-citation analysis inverts this idea: instead of the similarity relation being established by what the publications cited, co-citation brings publications together by what cites them. With bibliographic coupling, the similarity relationships are static because their cited references are fixed, whereas similarity between documents determined by co-citation can change as new citing papers are published. Small has noted that he preferred co-citation to bibliographic coupling because he “sought a measure that reflected scientists’ active and changing perceptions16.”

The method of measuring co-citation similarity and the threshold of co-citation strength employed in creating research fronts has changed over the years. Today, we use cosine similarity, calculated as the co-citation frequency count divided by the square root of the product of the citation counts for the two papers. The minimum threshold for co-citation strength is a cosine similarity measure of .1, but this can be raised incrementally to break apart large clusters if the front exceeds a maximum number of core papers, which is set at 50. Trial and error has shown this procedure yields consistently meaningful research fronts.

In “Citation indexes for sociological and historical research,” published in 1963, he stated that citation indexing provided an objective method for defining a field of inquiry. That assertion rested on the same logical foundation that made information retrieval in a citation index effective: citations revealed the expert decisions and self-organizing behavior of researchers, their intellectual as well as their social associations. In 1964, with colleagues Irving H. Sher and Richard J. Torpie, Garfield produced his first historiograph, a linear mapping through time of influences and dependencies, illustrated by citation links, concerning the discovery of DNA and its structure5. Citation data, Garfield saw, provided some of the best material available for building out a picture of the structure of scientific research as it really was, even for sketching its terrain.

Garfield and Small both continued their research and experiments in science mapping over the decade and thereafter. In two papers published in 1985, Small introduced an important modification to his method for defining research fronts: fractional co-citation clustering. By counting citation frequency fractionally, based on the length of the reference list in the citing papers, he was able to adjust for differences in the average rate of citation among fields and therefore remove the bias that whole counting gave to biomedical and other “high citing” fields. As a consequence, mathematics, for example, emerged more strongly, having been underrepresented by integer counting.

Price hailed the work of Small and Griffith, remarking that while co-citation analysis of the scientific literature into clusters that map on a two dimensional plane “may seem a rather abstruse finding,” it was “revolutionary in its implications.”He asserted: “The finding suggests that there is some type of natural order in science crying out to be recognized and diagnosed. Our method of indexing papers by descriptors or other terms is almost certainly at variance with this natural order. If we can successfully define the natural order, we will have created a sort of giant atlas of the corpus of scientific papers that can be maintained in real time for classifying and monitoring developments as they occur.”