Bradford`s law describes the number of basic journals in a particular field or topic and has recently been applied to neurosurgery. The aim of this study was to use the currently accepted formulations of Bradford`s Law to identify basic journals of paediatric neurosurgery. Additional analysis was performed to compare regional dependence with citation density in North American and European neurosurgeons. Bradford`s law uses three parameters to model c to ck to ck2. ckp – 1 sequence using the Egghe formulation. Parameter c defines the core number of journals. The parameter k defines the Bradford multiplier. These parameters depend on the choice of p, which represents the number of zones. They can be solved with the following equations: Citation distribution of Bradford`s verbal formulation with respect to observed. The distribution of bradford over four zones is shown. The line shows that the adjustment of the first three zones of Bradford`s law, although uncommon in academic medicine, has recently been used by Madhugiri et al.  to identify basic journals for the entire field of neurosurgery. The objective of our current study was to establish a method for using Bradford`s law in the identification of basic journals of pediatric neurosurgery.
Using the verbal formulation of Bradford`s law, we found nine journals at their heart with a Bradford multiplier of 4. A separate analysis was conducted using Bradford`s Law to identify regional differences in citation density and preference between North American and European pediatric neurosurgeons. To our knowledge, this is the first study to date to analyze regional dependence on citation density. Bradford`s law of dispersion is a law of diminishing yield and dispersion. Bradford formulated the law in 1948, stating that for a particular field there are “very productive magazines, a greater number of more moderate producers, and an even greater number of ever-decreasing productivity” . For each issue or individual domain, the upper third (Zone 1 or Core) represents the journals most frequently cited in the literature on the subject and which are therefore of the greatest interest to researchers in the discipline. The middle third (zone 2) includes journals that had an average number of citations, and the bottom third (zone 3 or tail) includes the long tail of journals that are rarely cited and considered marginally important to the subject . Researchers have defined a topic in lexical, semantic, and subject diffusion terms , and some argue that problems may not play a role in defining the “topic,” provided it is applied consistently . All original research publications from 2009 to 2013 were analyzed for the top 25 pediatric journalistic neurosurgeons in North America and Europe selected to build regional citation databases of all journal references. Regional differences were compared at each database. Egghe`s formulation and the verbal formulation of Bradford`s law were used to create specific citation density areas and identify basic journals.
Egghe`s formulation has proven accurate for many different applications in bibliometric analysis . Egghe`s formulation can be used to create a graphical representation of the Bradford distribution. The following equations are used for this: With this method, we discovered that the distribution followed a pattern for certain p-values. Parameters c and k could be found for the first three areas that respond to the verbal formulation, while all areas beyond three did not reach the citation density expected for this Bradford multiplier. The closest agreement on the first three zones was for p = 4 (Fig. 3). With this formula, the core journals for pediatric neurosurgery have evolved to become the top nine journals with a Bradford multiplier of 4. The main journals of pediatric neurosurgery, organized by citations, are: the Journal of Neurosurgery, Neurosurgery, Epilepsia, Child`s Nervous System, Pediatric Neurosurgery, Neurology, Journal of Clinical Oncology, Cancer Research and New England Journal of Medicine. A Bradford legal analysis was also carried out for a group of 25 of Europe`s largest paediatric neurosurgeons. Citation density in this group was more closely correlated with Egghe`s formulation than with the North American dataset (Fig. 4). For continuity between group comparisons, bradford`s final model used was verbal formulation.
The verbal formulation of Bradford`s law for the European group showed five journals in the central area. The main journals in the European database, sorted by number of citations, are Child`s Nervous System, Journal of Neurosurgery, Neurosurgery, Pediatric Neurosurgery and Journal of Neurosurgery: Pediatrics. The citation database has been organized in descending order of the number of citations per journal (Table 3). The ordered distribution of the citation density can be seen in Fig. 1. The number of citations in the main journal, Journal of Neurosurgery, was used as Ym (1,553), and the total number of journals cited was used as T (2,231). Using these values in the Egghe formulation described above, we solved for the theoretical citation distribution for p = 3–8, where p is the number of zones. Bradford`s Law is a model first described by Samuel C. Bradford in 1934 that estimates the exponential diminishing return of reference searches in scientific journals.
One formulation is that when journals in an area are sorted by number of articles into three groups, each with about one-third of all articles, the number of journals in each group is proportional to 1:n:n².  There are a number of related formulations of the principle. The regional comparison showed a preference for the Journal of Neurosurgery and Child`s Nervous System, respectively, but four of the top five reviews were common to both groups. By applying the verbal wording of Bradford`s law to the North American citation database, a citation density pattern was identified in the first three areas. Journals located in the first most frequently cited area are presented as basic journals. There are a number of mathematical approaches to model Bradford`s distribution law to a particular data set [7-10]. Egghe`s extension of the Leimkhuler method was used in this study because it was the most widely used [7, 8, 10, 11]. This formulation is based on the use of exponential functions to predict zonal distribution and depends on the parameters of the citation database of the total number of citations of the top journal and the total number of journals.
However, no mathematical formulation has achieved consistent statistical significance . Our database of citations did not match the currently accepted formulations of Bradford`s Law, a topic common to many other scholars [6, 7, 11]. The observed distribution showed a greater number of citations in the first and last areas than expected, while the central areas contained fewer. Analysis of European pediatric neurosurgeons showed a less pronounced difference. The citation distribution expected by Egghe`s formulation did not correspond to the observed citation distribution identified by our citation database (Fig. 2). Egghe`s formulation would predict that all areas have roughly equal distribution of citation density, but our distribution did not meet this expectation.