# Scientific Production and Productivity for Characterizing an Author’s Publication History: Simple and Nested Gini’s and Hirsch’s Indexes Combined

## Abstract

**:**

## 1. Introduction

## 2. Methodology

- I will focus on full-length peer-reviewed articles (as opposed to notes, comments, or letters) to rely on a prior scrutiny of their originality by peer reviewers.
- I will focus on English, to emphasize international dissemination. Note that citations of an article by non-English articles are also included in this analysis.
- I will focus on net citations, after eliminating self-citations (citations of the author’s other papers) and reciprocal citations (citations of papers by all coauthors and colleagues), by deleting records in which the same author appears in both the citing publication and the cited article. Although this will exclude some legitimate self-citations, it also mitigates the problem of excessive citation of one’s own papers. I will also delete records in which the same affiliation appears in the citing publication and the cited article. Although this will exclude some legitimate citations of the work of colleagues that provide important context, it also mitigates the problem of excessive reciprocal citation. Here, I define reciprocal citations as situations in which coauthors cite each other’s work. This will mitigate “apostle” effects (i.e., inflating citations by relying on temporal linkages such as citations of a supervisor’s or manager’s papers) and network effects (i.e., boosting citations by relying on personal linkages). Note that coauthors refer to any kind of publication (e.g., citations of articles by coauthors in books, symposium proceedings, or research notes) and colleagues refer to all researchers affiliated at any time with the author whose PH is being studied (e.g., citations of articles by colleagues in the same PhD courses).

#### 2.1. Definitions and Assumptions

- Production = the number of articles up to a given point in time, used as a total (stock) variable to estimate the researcher’s total scientific activity, where core production (as defined in Section 2.2) de-emphasizes the most frequently cited articles.
- Productivity = a marginal (flow) variable used to evaluate production per unit time or changes over time in scientific activity, where core productivity de-emphasizes the most popular articles.
- A multidisciplinary PH = the author submits their manuscripts to journals belonging to different disciplines; it will be measured by a Gini index applied to disciplines related to published manuscripts. The opposite would be a unidisciplinary PH.
- A multitopical PH = the author submits their manuscripts to many different journals belonging to the same discipline; it will be measured using a Gini index applied to journals related to the author’s published manuscripts. The opposite would be a unitopical PH.
- An intentional PH = the author deliberately submits their manuscripts in order to shape their PH; it is related to the choice of journal publication, it will be applied to disciplines (i.e., multi- or unidisciplinary) and journals (i.e., multi- or unitopical), and it will be measured by the Gini index.
- A successful PH = publications are cited many times by other papers within the same journal and within the same discipline (i.e., intratopical), by different journals within the same discipline (i.e., intertopical), or by different journals from different disciplines (i.e., interdisciplinary); it is related to the actions of other researchers (i.e., to cite or not to cite a given article), it will be applied to interdisciplinary and intertopical PHs, and it will be measured by H indexes.
- An orthodox PH = the author publishes in a single discipline and in many journals, and the vast majority of the citations are in few disciplines but in many different journals; it is intentional and successful, and it will be measured by combining H indexes and G indexes.
- A heterodox PH = the author publishes in a single discipline and in a few journals devoted to that discipline, so that the vast majority of citations are in few disciplines and few journals; it is intentional and successful, and it will be measured by combining H indexes and G indexes.
- An interdisciplinary PH = the author publishes in many disciplines and journals, and the vast majority of citations are in many different disciplines and journals; it is intentional and successful, and it will be measured by combining H indexes and G indexes.
- An intertopical PH = the author publishes in a single discipline and in many journals, and the vast majority of citations are in many journals within this discipline; it is intentional and successful, and it will be measured by combining H indexes and G indexes.

- Each journal represents a single topic within a discipline: that is, a journal cannot be attached to two different topics. See Section 5 for suggestions of future research to account for exceptions to this assumption.
- Each journal is linked to the most representative discipline: that is, a journal cannot be attached to two different disciplines. See Section 5 for suggestions of future research to account for exceptions to this assumption.

#### 2.2. Scientific Production and Productivity

_{ltn}, where l = linear, t = total, and n = net citations) will be calculated by applying the following formula to the number of articles per author as the independent variable (here, a generic scalar variable x) and to the number of citations per author for articles in a decreasing order as the dependent variable (here, the fitting curve lp(x)):

_{0}− a

_{1}x

_{0}and a

_{1}come from a linear regression of the total number of net citations over the total number of articles x. This procedure uses continuous variables to replace the calculation the H index based on discrete variables (i.e., Max

_{i}Min [f(i), i], where f(i) represents the number of citations in decreasing order from the largest to the smallest value for each article i and i is the counter for the article number). For example, H

_{ltn}is the value of x such that a

_{0}− a

_{1}x = x with a

_{0}and a

_{1}positive parameters (i.e., the solution is x = a

_{0}/(1+a

_{1})). In graphical terms, this solution is represented by the intersection between the line y = x (i.e., the 45 degree line) and the linear polynomial fitting curve.

_{ctn}, where c = cubic, t = total, and n = net) will be calculated as follows

_{0}− b

_{1}x + b

_{2}x

^{2}− b

_{3}x

^{3}

_{0}, b

_{1}, b

_{2}, and b

_{3}come from a cubic regression of the total number of net citations over the total number of articles x. For example, H

_{ctn}is the value of x such that b

_{0}− b

_{1}x + b

_{2}x

^{2}− b

_{3}x

^{3}= x with b

_{0}, b

_{1}, b

_{2}, and b

_{3}as positive parameters. That is, the solution is x = [1/(6b

_{3})] {2b

_{2}− 2 × 2

^{1/3}[b

_{2}

^{2}− 3 (1+ b

_{1}) b

_{3}]/F − 2

^{2/3}F}, with F = (−2 b

_{2}

^{3}+9 b

_{2}b

_{3}+ 9 b

_{1}b

_{2}b

_{3}− 27 b

_{0}b

_{3}

^{2}+ Z)

^{1/3}, where Z = √[(2b

_{2}

^{3}− 9(1 + b

_{1}) b

_{2}b

_{3}+ 27b

_{0}b

_{3}

^{2})

^{2}− 4(b

_{2}

^{2}− 3(1 + b

_{1}) b

_{3})

^{3}]). In graphical terms, this solution is represented by the intersection between the line y = x (i.e., the 45 degree line) and the cubic polynomial fitting curve.

_{ltn}) and total core production (i.e., H

_{ctn}), respectively. By analogy, the same procedure (i.e., linear and cubic fitting curves) applied to a subset of the articles (e.g., articles published in a specified period) estimates the average productivity (i.e., H

_{ltn10}) and the average core productivity (i.e., H

_{ctn10}), respectively. Similarly, the same procedure (i.e., linear and cubic fitting curves) applied to citations standardized per year estimates the total production (i.e., H

_{lyn}) and the total core production (i.e., H

_{cyn}) per year, respectively.

_{0}− a

_{1}x) = x (i.e., two parameters) would produce similar results. Moreover, the obtained H values are continuous and do not change abruptly when the number of citations of a single article changes; that is, they solve the problem of the discontinuity that could potentially be created by an additional citation received by the marginal article [69], because they account for the citations received by the entire set of published articles [70]. Finally, linear fitting gives too much weight to fashionable articles (i.e., articles with many citations in a few years), whereas a cubic fitting disregards them by giving more weight to articles with few citations in many years. Consequently, a linear fitting (i.e., H

_{ltn}or H

_{lyn}) seems to be most representative for total scientific production, whereas a cubic fitting (i.e., H

_{ctn10}or H

_{cyn10}) seems to be most representative for the average core scientific productivity.

#### 2.3. PH Characterization

_{ltg}), and by calculating the percentage difference between H

_{ltg}and H

_{ltn}(i.e., [H

_{ltg}− H

_{ltn}]/H

_{ltg}), this approach provides a measure of the relative importance of networking activity in a PH.

_{t}is not used here, since successful, unsuccessful, intentional, and unintentional features do not refer to the PH per se, but rather to characterizations of the PH such as inter- or intratopical and inter- or intradisciplinary characterization.

_{ljn}as a linear fitting of points where citations are in journals other than the journal that published the cited article (i.e., an intertopical measure). To do so, I computed H

_{ldn}as a linear fitting of points where citations are in disciplines other than the discipline of the cited article (i.e., an interdisciplinary measure), and calculated the G values for journals (G

_{j}) and disciplines (G

_{d}) by applying the following formulas.

_{j}= [1/(2 × 0.5 N

^{2}) Σ

_{i}Σ

_{k}|j

_{i}− j

_{k}|]/[(N − 1)/N]

_{d}= [1/(2 × 0.5 N

^{2}) Σ

_{i}Σ

_{k}|d

_{i}− d

_{k}|]/[(N − 1)/N]

_{d}(i.e., a multidisciplinary measure) and G

_{j}(i.e., a multitopical measure); j represents the journal title, j

_{i}− j

_{k}= 0 if articles i and k appear in the same journal and j

_{i}− j

_{k}= 1; otherwise, d represents the discipline name; and d

_{i}− d

_{k}= 0 if articles i and k belong to the same discipline and d

_{i}− d

_{k}= 1 otherwise. See an analysis of H indexes based on citations by different citers [73]. Note that this classification cannot be criticized as ambiguous (i.e., either the journal is the same or it is different), although it could be criticized because it overestimates PH differentiation (e.g., a heterodox post-Keynesian economist publishes in very few journals, such as the Cambridge Journal of Economics or the Journal of Post Keynesian Economics or the Review of Political Economy, but not in a single journal). However, heterogeneity of PHs can be estimated by comparing percentages.

_{d}and G

_{j}for a given H

_{ldn}and H

_{ljn}(i.e., a decrease in the inequality of articles for a given number of citations). Moreover, I define a PH as an unsuccessful intradisciplinary and intratopical PH if the author publishes in a single discipline and in few journals, and is also cited by authors in few different journals. I define a PH as an unsuccessful intradisciplinary and intertopical PH if the author publishes in a single discipline and in many journals, but is nonetheless cited by authors in few different journals. This is represented by a decrease of H

_{ldn}and H

_{ljn}for a given G

_{d}and G

_{j}(i.e., a decrease in the number of citations at a given inequality of articles). This case could depict an intradiscipline reputation if G

_{j}is large while H

_{ljn}is small; that is, it is possible that the author publishes in many journals because editors expect many citations of papers in their journal and consequently an increase in its impact factor, but this does not happen because papers are published without suitable scrutiny to ensure their quality. Similarly, I define an unsuccessful interdisciplinary and intertopical PH if the author publishes in many disciplines and in many journals, but is cited by authors in journals in few different disciplines. This is represented by a reduction of H

_{ldn}and H

_{ljn}for a given G

_{d}and G

_{j}(i.e., a decrease in the number of citations at a given inequality of articles). This case could depict an intratopical reputation if G

_{d}is large while H

_{ldn}is small (i.e., it is possible that the author publishes in few journals because the author knows the editors). Finally, I calculated the areas as percentages using the following equations, with the specified different colors applied in the two-dimensional graphs presented in Section 4 to characterize the PHs:

_{ltg}− H

_{ltn})]/(H

_{ltg})

_{ltn}− H

_{ljn}) × (1 − G

_{j})]/(H

_{ltn})

_{ljn}− H

_{ldn}) × (G

_{j}− G

_{d})]/(H

_{ltn})

_{ldn}× G

_{d}]/(H

_{ltn})

_{d}= 0, then the yellow area is given by [H

_{ljn}× G

_{j}]/(H

_{ltn}) in order to depict only intentional interdisciplinary PHs.

## 3. Data

- Year
- Author
- Affiliation: institute/university, city, country
- Source: journal title
- Subjects: health, life, physical, social sciences, and multidisciplinary
- Disciplines: five in health sciences (medicine, veterinary, nursing, dentistry, and health professions), five in life sciences (pharmacology & toxicology, biological, neurology, agricultural, and immunology), nine in physical sciences (chemistry, physics & astronomy, and mathematics, Earth & planetary, energy, environmental, materials, engineering, and computing & information), and eight in social sciences (psychology, economics & econometrics & finance, arts & humanities, business & management & accounting, decision, politics, architecture, and sociology)

## 4. Application of the Indexes

_{ltn}= 6.29) by standardizing for an average of four authors per article, and within the 0.0008% best scientists from 2007 to 2016 (based on H

_{cyn10}= 2.57) by standardizing for an average publication life cycle of five years. In addition, similar calculations for the second and third analyses PHs (Table A3 and Table A4, respectively) suggest that H indexes per year should be used to compare careers of senior researchers. See Supplemental Materials III for the calculation of the H indexes. Indeed, H

_{ltn}for the second PH is slightly larger than H

_{ltn}for the third PH (i.e., 10.00 > 8.34), whereas H

_{lyn}for the second PH is considerably smaller than H

_{lyn}for third PH (i.e., 1.52 < 4.17).

_{lyn}= 2.43 being smaller than H

_{cyn10}= 2.57. These results are also externally consistent. For example, calculations for the third PH (Table A4) show 11.2 English articles per author and H

_{lyn}= 4.17, with the third author’s index being 7.5 times better than the index achieved by the first analysed author (Table A1), after standardization of citations per year. Moreover, the present results are clearly better than those calculated using traditional versions of the H index: six for the first representative author for 22 years versus 11 for the third representative author for 33 years, where the latter is only 1.83 times the former. Finally, these results can be easily interpreted. Indeed, if 2.57 articles are cited 2.57 times per year per author, there are several implications: for four authors, the same H index could be achieved only if 10.3 articles were cited 10.3 times per year, which, over a period of 10 years, means that the 10.3 articles would each be cited 103 times. These results can also be simply justified. Indeed, it is difficult to support the belief that citation of one article with 10 authors only one time will directly or indirectly benefit science or society to the same extent as 10 articles with a single author, each cited 10 times.

_{d}is large (i.e., the author publishes in many disciplines), G

_{j}is large (i.e., the author publishes in many journals), H

_{ljn}is slightly larger than H

_{ldn}, and H

_{ldn}is large (i.e., the vast majority of citations are in different disciplines). Moreover, I define a PH as (intradisciplinary and intratopical) heterodox (e.g., Figure 6) if G

_{d}is 0 (i.e., the author publishes in a single discipline), G

_{j}is small (i.e., the author publishes in few journals), and H

_{ljn}is small (i.e., the vast majority of citations are in the same journals). Finally, I define a PH as (intradisciplinary and intertopical) orthodox (e.g., Figure 7) if G

_{d}is 0 (i.e., the author publishes in a single discipline), G

_{j}is large (i.e., the author publishes in many journals), and H

_{ljn}is large (i.e., the vast majority of citations are in different journals). In other words, an orthodox PH can be either intra- or interdisciplinary.

_{ldn}is greater than 0. Indeed, in a heterodox PH, H

_{ljn}= 0 only if each article is cited by an article in the same journal, whereas a more likely citation by an article in a different journal from a small group of journals is excluded. Similarly, in an intradisciplinary orthodox PH, H

_{ldn}= 0 only if each article is cited by an article in the same discipline, whereas a less likely citation by an article in a different discipline is excluded.

_{ltn}or H

_{cyn10}, one should also characterize each PH by comparing the areas of the four colors or calculating the ratios based on the areas of the four colors. In particular, in terms of interdisciplinarity, the three analyzed PHs can be ranked as follows: first PH (i.e., 0.539 × 6.29 = 3.39) > third PH (i.e., 0 × 8.34 = 0) = second PH (i.e., 0 × 9.91 = 0). In terms of heterodoxy, the three analyzed PHs can be ranked as follows; second PH (i.e., 0.036 × 9.91 = 0.36) > first PH (i.e., 0.003 × 6.29 = 0.02) > third PH (i.e., 0.001 × 8.34 = 0.01). In terms of orthodoxy, the three analyzed PHs can be ranked as follows: third PH (i.e., 0.819 × 8.34 = 6.83) > second PH (i.e., 0.538 × 9.91 = 5.33) > first PH (i.e., 0.041 × 6.29 = 0.26).

_{ltn}are likely to be observed, by introducing some form of compensation (e.g., a smaller H

_{ltn}with large red or blue areas could be preferred to a larger H

_{ltn}with small red or blue areas). This is why I have focused on intentional and successful interdisciplinary and heterodoxy criteria in this study.

## 5. Discussion

_{ltn}and H

_{cyn10}, respectively), which requires the ability to disentangle networking from research activity (i.e., H

_{ltg}vs. H

_{ltn}) so that these activities can be separately and positively evaluated. The research activity should then be evaluated by potentially favoring or contrasting PHs according to basic intentional characteristics such as heterodox vs. orthodox articles and intra- vs. interdiscipline articles (expressed as proportions), and these should be distinguished from unsuccessful or unintentional characteristics.

- Many proposals for modifying the original H index have been accounted for [85], including the elimination of self- and reciprocal citations, an increased weighting of highly cited articles, a focus on peer-reviewed scientific journals, the use of fractional citations to account for the number of authors (i.e., awarding authors a fraction of a point instead of a full point for multi-author articles), an increased sensitivity to variability of the overall citation profile, and a consideration of the life cycle of an article.
- Discrimination against interdisciplinary and heterodox PHs can be reduced by mitigating the bias created by conventional rankings, without relying on the application of advanced methodologies to complex datasets, as in the case of applying empirically based scaling factors to different disciplines [86], comparisons with the performance of other researchers in the same field [87], or comparison with the average number of citations per paper in a given discipline [25]
- Most of the main questions left open by the original description of the H index have been tackled [88], including the attribution of an article to a given discipline, since this is done by the author. This is done while retaining the practicality and simplicity that made the original H metric so appealing to a large audience.
- Indicators are distinguished according to the goals being pursued by amending well-established procedures such as years from publication rather than academic age (i.e., the duration of a researcher’s career at the time of the analysis [89]), and the indicators can be applied at different levels of aggregation (e.g., at department or university levels).
- Indicators are based on information that is available at an individual level, including citations that would be disregarded by the original H index [70], and the indicators can be easily computed.
- Rankings can also be obtained when the publication period is prior to the citation period under consideration (e.g., neglecting citations older than 22 years rather than articles published more than 22 years ago). Indeed, I chose the third PH in Section 4 as a reference example to show how this feature of the proposed model works.

- Results depend on the dataset used, and many alternatives could be applied [10]. However, the Scopus dataset for the last 22 years is both authoritative and comprehensive, and the same criticism could be raised for other datasets.
- The focus is on past (retrospective) real performance rather than on future expected (prospective) performance [90,91]. However, using impact factors to account for expected future performance would require a reliance on debatable information, such as the 2-year vs. 5-year impact factors described by Sangwal [57], from a dispersed and always in-progress dataset, as in the case of the temporal evolution of impact factors that is discussed by Finardi [92]. In addition, there are potentially opposite interpretations. For example, the presence of few citations in journals with a high impact factor could be a negative feature, because it would represent the lack of ability to exploit an important audience.
- Insights are not based on axiomatization, in which many alternatives could be suggested [93]. However, the formulas are easy to implement and straightforward to interpret.
- Characterization of the PHs depended on the simplifying assumption that a journal could not belong to two or more disciplines [25]. Although factor analysis could be used to univocally sort journals into single hypothetical disciplines in terms of estimated correlations, this is unrealistic in practice because researchers may be unable to perform this analysis without support from suitable software. However, accounting for multidisciplinary journals remains a challenge for future research

## 6. Conclusions

## Supplementary Materials

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Datasets

**Table A1.**Descriptive statistics and Scopus categories for the first analyzed PH, as a representative interdisciplinary and intertopical orthodox PH. Each row represents a single publication; multiple publications in the same journal and same year are represented by separate rows.

Year | Disc | AN | Number of Citations | ||||
---|---|---|---|---|---|---|---|

Gross | Net | ||||||

Total | Total | By Different Journals | By Different Disciplines | ||||

Environmental & Resource Economics | 2016 | Eco | 1 | 0 | 0 | 0 | 0 |

Applied Mathematical Modeling | 2016 | Mat | 1 | 0 | 0 | 0 | 0 |

Applied Soft Computing Journal | 2016 | Com | 1 | 3 | 1 | 0 | 0 |

Science of the Total Environment | 2016 | Env | 1 | 6 | 4 | 1 | 1 |

Sustainability (Switzerland) | 2016 | Env | 1 | 1 | 1 | 0 | 0 |

Sustainability (Switzerland) | 2016 | Env | 17 | 2 | 2 | 1 | 0 |

Sustainability (Switzerland) | 2016 | Env | 21 | 0 | 0 | 0 | 0 |

Journal of Happiness Studies | 2015 | Hum | 1 | 0 | 0 | 0 | 0 |

Sustainability (Switzerland) | 2015 | Env | 16 | 4 | 4 | 2 | 1 |

Sustainability Science | 2015 | Env | 1 | 1 | 0 | 0 | 0 |

Coastal Engineering | 2014 | Eng | 8 | 27 | 16 | 8 | 4 |

Journal of Hydrology | 2014 | Env | 2 | 0 | 0 | 0 | 0 |

Environmental Modeling and Assessment | 2013 | Env | 1 | 0 | 0 | 0 | 0 |

Environmental Modeling and Software | 2013 | Com | 2 | 11 | 11 | 6 | 6 |

Natural Hazards | 2013 | Env | 1 | 2 | 2 | 2 | 2 |

Environmental Management | 2011 | Env | 1 | 4 | 3 | 3 | 3 |

Journal of Happiness Studies | 2011 | Hum | 1 | 3 | 2 | 2 | 2 |

Water Resources Management | 2010 | Env | 1 | 15 | 15 | 13 | 11 |

International Journal of Hospitality Management | 2009 | Man | 1 | 16 | 16 | 14 | 12 |

Journal of Environmental Management | 2008 | Env | 1 | 8 | 7 | 6 | 6 |

Papers in Regional Science | 2003 | Eco | 3 | 2 | 1 | 1 | 1 |

Environment and Development Economics | 1998 | Eco | 1 | 1 | 1 | 1 | 1 |

Journal of Environmental Economics and Management | 1998 | Eco | 1 | 15 | 15 | 14 | 2 |

Economic Journal | 1995 | Eco | 1 | 1 | 1 | 1 | 1 |

Total | 122 | 102 | 75 | 53 |

**Table A2.**Summary of the H index values calculated for the first analyzed PH (Table A1) over the author’s whole career (i.e., the 22-year period from 1995 to 2016).

All Authors (24 Articles) | Production per Author (18.6 Articles) | Productivity per Author per Year (18.6 Articles) | ||
---|---|---|---|---|

H_{latg} = 8.42 | → | H_{ltg} = 7.34 | ||

H_{catg} = 6.84 | → | H_{ctg} = 5.75 | ||

↓ | ↓ | |||

H_{latn} = 7.62 | → | H_{ltn} = 6.29, H_{ltn10} = 6.02 | → | H_{lyn} = 2.43, H_{lyn10} = 2.56 |

H_{catn} = 6.67 | → | H_{ctn} = 5.28, H_{ctn10} = 4.93 | → | H_{cyn} = 2.60, H_{cyn10} = 2.57 |

↓ | ||||

H_{ljn} = 5.74 | ||||

H_{cjn} = 4.97 | ||||

↓ | ||||

H_{ldn} = 4.71 | ||||

H_{cdn} = 4.31 |

**Table A3.**Descriptive statistics and Scopus categories for the second analyzed PH, which is a representative intradisciplinary and intratopical heterodox PH. Each row represents a single publication; multiple publications in the same journal and same year are represented by separate rows.

Year | Disc | AN | Number of Citations | ||||
---|---|---|---|---|---|---|---|

Gross | Net | ||||||

Total | Total | By Different Journals | By Different Disciplines | ||||

Cambridge Journal of Economics | 2012 | Eco | 1 | 7 | 7 | 5 | 0 |

Cambridge Journal of Economics | 2012 | Eco | 1 | 8 | 7 | 5 | 0 |

Cambridge Journal of Economics | 2005 | Eco | 1 | 36 | 36 | 29 | 1 |

Journal of Post-Keynesian Economics | 2001 | Eco | 1 | 6 | 6 | 4 | 0 |

Cambridge Journal of Economics | 1994 | Eco | 1 | 1 | 1 | 1 | 0 |

Structural Change and Economic Dynamics | 1990 | Eco | 1 | 2 | 2 | 1 | 0 |

Cambridge Journal of Economics | 1989 | Eco | 1 | 19 | 19 | 8 | 2 |

Cambridge Journal of Economics | 1989 | Eco | 1 | 0 | 0 | 0 | 0 |

Cambridge Journal of Economics | 1988 | Eco | 1 | 38 | 35 | 33 | 5 |

Cambridge Journal of Economics | 1988 | Eco | 1 | 12 | 11 | 7 | 3 |

Cambridge Journal of Economics | 1986 | Eco | 1 | 0 | 0 | 0 | 0 |

Cambridge Journal of Economics | 1983 | Eco | 1 | 9 | 9 | 6 | 1 |

Review of Economic Studies | 1981 | Eco | 1 | 1 | 1 | 1 | 0 |

Cambridge Journal of Economics | 1977 | Eco | 1 | 11 | 11 | 8 | 0 |

Quarterly Journal of Economics | 1966 | Eco | 1 | 45 | 43 | 35 | 1 |

Review of Economic Studies | 1964 | Eco | 1 | 0 | 0 | 0 | 0 |

Oxford Economic Papers | 1960 | Eco | 1 | 7 | 7 | 5 | 0 |

Total | 201 | 195 | 148 | 13 |

**Table A4.**Descriptive statistics and Scopus categories for the third analyzed PH, as a representative intradisciplinary and intertopical orthodox PH. Each row represents a single publication; multiple publications in the same journal and same year are represented by separate rows. Note that in contrast with the other two PHs, all publications by this author occurred before 1995.

Year | Disc | AN | Number of Citations | ||||
---|---|---|---|---|---|---|---|

Gross | Net | ||||||

Total | Total | By Different Journals | By Different Disciplines | ||||

Physical Review | 1953 | Phy | 1 | 7 | 7 | 7 | 2 |

Science | 1951 | Phy | 1 | 4 | 4 | 4 | 1 |

Science | 1949 | Phy | 8 | 1 | 1 | 1 | 0 |

Reviews of Modern Physics | 1948 | Phy | 1 | 56 | 56 | 56 | 13 |

Reviews of Modern Physics | 1946 | Phy | 2 | 85 | 85 | 84 | 12 |

Reviews of Modern Physics | 1945 | Phy | 2 | 249 | 249 | 244 | 75 |

Science | 1940 | Phy | 1 | 27 | 27 | 27 | 17 |

Journal of the Franklin Institute | 1937 | Phy | 2 | 254 | 251 | 246 | 76 |

Science | 1936 | Phy | 1 | 305 | 305 | 299 | 92 |

Journal of the Franklin Institute | 1936 | Phy | 1 | 101 | 101 | 99 | 31 |

Physical Review | 1936 | Phy | 2 | 29 | 29 | 28 | 9 |

Physical Review | 1935 | Phy | 3 | 6806 | 6805 | 6663 | 2058 |

Physical Review | 1935 | Phy | 2 | 319 | 318 | 311 | 96 |

Physical Review | 1931 | Phy | 3 | 28 | 28 | 26 | 6 |

Nature | 1923 | Phy | 1 | 10 | 10 | 10 | 3 |

Nature | 1921 | Phy | 1 | 10 | 10 | 10 | 3 |

Total | 8291 | 8286 | 8115 | 2495 |

**Table A5.**Descriptive statistics and Scopus categories for the randomly selected PH analyzed for the life sciences. Each row represents a single publication; multiple publications in the same journal and same year are represented by separate rows.

Year | Disc | AN | Number of Citations | ||||
---|---|---|---|---|---|---|---|

Gross | Net | ||||||

Total | Total | By Different Journals | By Different Disciplines | ||||

Agricultural Systems | 2017 | Agr | 10 | 1 | 0 | 1 | 0 |

Soil and Tillage Research | 2017 | Agr | 10 | 1 | 0 | 0 | 0 |

Geoderma | 2017 | Agr | 5 | 3 | 2 | 2 | 0 |

European Journal of Agronomy | 2017 | Agr | 5 | 2 | 1 | 1 | 0 |

Journal of Environmental Management | 2016 | Env | 6 | 5 | 3 | 3 | 1 |

Field Crops Research | 2016 | Agr | 7 | 4 | 1 | 1 | 1 |

European Journal of Agronomy | 2016 | Agr | 8 | 1 | 1 | 1 | 0 |

European Journal of Agronomy | 2016 | Agr | 8 | 3 | 0 | 0 | 0 |

Agronomy | 2016 | Agr | 7 | 9 | 3 | 2 | 1 |

Industrial Crops and Products | 2015 | Agr | 4 | 3 | 3 | 2 | 0 |

Ecological Indicators | 2015 | Env | 7 | 6 | 3 | 3 | 1 |

Geoderma | 2013 | Agr | 5 | 23 | 21 | 19 | 0 |

Soil Use and Management | 2013 | Agr | 5 | 4 | 0 | 0 | 0 |

Geoderma | 2012 | Agr | 4 | 15 | 10 | 6 | 0 |

Cold Regions Science and Technology | 2012 | Agr | 3 | 6 | 1 | 1 | 0 |

Soil and Tillage Research | 2010 | Agr | 8 | 17 | 9 | 8 | 0 |

Soil and Tillage Research | 2007 | Agr | 5 | 39 | 27 | 15 | 0 |

Total | 142 | 85 |

**Table A6.**Descriptive statistics and Scopus categories for the randomly selected PH analyzed for the health sciences. Each row represents a single publication; multiple publications in the same journal and same year are represented by separate rows.

Year | Disc | AN | Number of Citations | ||||
---|---|---|---|---|---|---|---|

Gross | Net | ||||||

Total | Total | By Different Journals | By Different Disciplines | ||||

Scientific Reports | 2017 | Med | 8 | 0 | 0 | 0 | 0 |

Briefings in Bioinformatics | 2017 | Med | 3 | 2 | 2 | 2 | 0 |

G3: Genes, Genomes, Genetics | 2017 | Med | 7 | 2 | 1 | 1 | 0 |

PLoS ONE | 2017 | Med | 7 | 0 | 0 | 0 | 0 |

Nucleic Acids Research | 2017 | Med | 4 | 4 | 2 | 2 | 0 |

BMC Genomics | 2017 | Med | 2 | 2 | 2 | 2 | 0 |

Bioinformatics | 2017 | Med | 3 | 2 | 2 | 2 | 0 |

Journal of Clinical Microbiology | 2016 | Med | 9 | 0 | 0 | 0 | 0 |

Frontiers in Molecular Biosciences | 2016 | Med | 6 | 1 | 0 | 0 | 0 |

International Journal of Systematic and Evolutionary Microbiology | 2016 | Med | 8 | 2 | 2 | 2 | 0 |

mSphere | 2016 | Med | 3 | 3 | 3 | 3 | 0 |

mBio | 2016 | Med | 15 | 8 | 7 | 7 | 0 |

Genome Announcements | 2016 | Med | 6 | 2 | 1 | 1 | 0 |

Gene | 2015 | Med | 4 | 3 | 0 | 0 | 0 |

Mobile DNA | 2015 | Med | 4 | 15 | 11 | 7 | 0 |

Scientific Reports | 2015 | Med | 6 | 7 | 4 | 3 | 0 |

Journal of Bacteriology | 2014 | Med | 4 | 8 | 6 | 6 | 0 |

Genome Announcements | 2014 | Med | 9 | 4 | 3 | 3 | 0 |

Gene | 2013 | Med | 7 | 11 | 9 | 9 | 0 |

Journal of Bacteriology | 2012 | Med | 9 | 5 | 5 | 5 | 0 |

PLoS ONE | 2012 | Med | 6 | 7 | 7 | 6 | 0 |

Genomics, Proteomics and Bioinformatics | 2011 | Med | 4 | 0 | 0 | 0 | 0 |

Total | 88 | 67 |

#### Appendix A.2. A Test Using Randomly Selected PHs

**Figure A1.**Characterization of a randomly chosen author for life sciences. Black area (17.1%) = networking; red area (0.9%) = intradisciplinary and intratopical heterodox; yellow area (48.7%) = intradisciplinary and intertopic orthodox; blue area (3.6%) = interdisciplinary and intertopical orthodox. G

_{d}= 0.22, G

_{j}= 0.93, H

_{ldn}= 0.23, H

_{ljn}= 1.17, H

_{ltn}= 1.37, H

_{ltg}= 1.65. Abbreviations: G

_{d}, Gini index for disciplines; G

_{j}, Gini index for journals; H, Hirsch indexes; d = discipline, g = gross, j = journal, l = linear, n = net, t = total.

**Figure A2.**Characterization of a randomly chosen author for health sciences. Black area (15.3%) = networking; red area (0.2%) = intradisciplinary and intratopical heterodox; yellow area (86.2%) = intradisciplinary and intertopic orthodox; blue area (0%) = interdisciplinary and intertopical orthodox. G

_{d}= 0, G

_{j}= 0.97, H

_{ldn}= 0.03, H

_{ljn}= 1.00, H

_{ltn}= 1.10, H

_{ltg}= 1.30. Abbreviations: G

_{d}, Gini index for disciplines; G

_{j}, Gini index for journals; H, Hirsch indexes; d = discipline, g = gross, j = journal, l = linear, n = net, t = total.

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**Figure 1.**Least-squares linear interpolation fitting for the H index per author (i.e., scientific production): H

_{ltn}= 6.29 (R

^{2}= 0.66; regression sum of squares = 389; sum of squares for the residuals = 195; F (2, 22) = 44 (p < 0.001) with 2 parameters and 24 observations). The red increasing line represents y = x; the blue decreasing line represents the fitted curve. Abbreviations: l = linear interpolation; t = total number of publications and citations in the period 1995 to 2016; n = net citations.

**Figure 2.**Least-squares cubic interpolation fitting for the H index per author (i.e., scientific core production): H

_{ctn}= 5.28 (R

^{2}= 0.95; regression sum of squares = 553; sum of squares for the residuals = 30; F (4, 20) = 120 (p < 0.001) with 4 parameters and 24 observations). The red increasing linear line represents y = x; the blue decreasing line represents the fitted curve. Abbreviations: c = cubic interpolation; t = total number of publications and citations in the period 1995 to 2016; n = net citations.

**Figure 3.**Least-squares linear interpolation fitting for the H index per author per year (i.e., scientific productivity): H

_{lyn10}= 2.56 (R

^{2}= 0.72; regression sum of squares = 30; sum of squares for the residuals = 11; F (2, 18) = 46 (p < 0.001) with 2 parameters and 20 observations). The red increasing linear line represents y = x; the blue decreasing line represents the fitted curve. Abbreviations: l = linear interpolation; y = publications and citations per year, n = net citations; 10 = 10 years (2007 to 2016).

**Figure 4.**Least-squares cubic interpolation fitting for the H index per author per year (i.e., scientific core productivity): H

_{cyn10}= 2.57 (R

^{2}= 0.97; regression sum of squares = 40; sum of squares for the residuals = 1; F (4, 16) = 158 (p < 0.001) with 4 parameters and 20 observations). The red increasing linear line represents y = x; the blue decreasing line represents the fitted curve. Abbreviations: c = cubic interpolation; y = publications and citations per year, n = net citations; 10 = 10 years (2007 to 2016).

**Figure 5.**Characterization of a representative interdisciplinary and intertopical orthodox PH. Black area (14.3%) = networking; red area (0.3%) = intradisciplinary and intratopical heterodox; yellow area (4.1%) = intradisciplinary and intertopical orthodox; blue area (53.9%) = interdisciplinary and intertopical orthodox. G

_{d}= 0.72, G

_{j}= 0.97, H

_{ldn}= 4.71, H

_{ljn}= 5.74, H

_{ltn}= 6.29, H

_{ltg}= 7.34. Abbreviations: G

_{d}, Gini index for disciplines; G

_{j}, Gini index for journals; H, Hirsch indexes; d = discipline, g = gross, j = journal, l = linear, n = net, t = total.

**Figure 6.**Characterization of a representative intradisciplinary and intratopical heterodox PH. Black area (0.9%) = networking; red area (3.6%) = intradisciplinary and intratopical heterodox; yellow area (53.8%) = intradisciplinary and intertopical orthodox; blue area (0%) = interdisciplinary and intertopical orthodox. G

_{d}= 0, G

_{j}= 0.59, H

_{ldn}= 2.11, H

_{ljn}= 9.04, H

_{ltn}= 9.91, H

_{ltg}= 10.00. Abbreviations: G

_{d}, Gini index for disciplines; G

_{j}, Gini index for journals; H, Hirsch indexes; d = discipline, g = gross, j = journal, l = linear, n = net, t = total.

**Figure 7.**Characterization of a representative intradisciplinary and intertopical orthodox PH. Black area (0%) = networking; red area (0.1%) = intradisciplinary and intratopical heterodox; yellow area (81.9%) = intradisciplinary and intertopical orthodox; blue area (0%) = interdisciplinary and intertopical orthodox. G

_{d}= 0, G

_{j}= 0.82, H

_{ldn}= 8.19, H

_{ljn}= 8.33, H

_{ltn}= 8.34, H

_{ltg}= 8.34. Abbreviations: G

_{d}, Gini index for disciplines; G

_{j}, Gini index for journals; H, Hirsch indexes; d = discipline, g = gross, j = journal, l = linear, n = net, t = total.

**Table 1.**Summary of notation applied in calculations. Definitions of abbreviations: cubic (c) fitting vs. linear (l) fitting; total (t) citations vs. per year (y) citations; gross (g) citations vs. net (n) citations; 10 years (10) vs. total career (no letter).

G_{j} | Gini Index for Journals | |||
---|---|---|---|---|

G_{d} | Gini Index for Disciplines | |||

Fitting | Citations | Period | ||

Per author | H_{ltn10} | Linear | Total net | 10 years |

H_{ctn10} | Cubic | Total net | ||

H_{lyn10} | Linear | Net per year | ||

H_{cyn10} | Cubic | Net per year | ||

H_{ltn} | Linear | Total net | Total career | |

H_{ctn} | Cubic | Total net | ||

H_{lyn} | Linear | Net per year | ||

H_{cyn} | Cubic | Net per year | ||

H_{ltg} | Linear | Total gross | ||

H_{ctg} | Cubic | Total gross | ||

H_{ljn} | Linear | Total net in different journals | ||

H_{cjn} | Cubic | Total net in different journals | ||

H_{ldn} | Linear | Total net in different disciplines | ||

H_{cdn} | Cubic | Total net in different disciplines | ||

All authors | H_{latg} | Linear | Total gross | |

H_{catg} | Cubic | Total gross | ||

H_{latn} | Linear | Total net | ||

H_{catn} | Cubic | Total net |

**Table 2.**Summary of publication history (PH) characterizations in terms of key parameters. H

_{d}= H index for different disciplines, G

_{d}= G index for different disciplines, H

_{j}= H index for different journals, and G

_{j}= G index for different journals. Approximately, small G

_{d}= ≤ 0.2; small G

_{j}= ≤ 0.6; tiny H

_{d}≤ 1; small H

_{d}for 1 < H

_{d}≤ 3; tiny H

_{j}≤ 2; small H

_{j}for 2 < H

_{j}≤ 6.

Intentional | Unintentional | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

PH definitions | G_{d} | G_{j} | H_{d} | H_{j} | G_{d} | G_{j} | H_{d} | H_{j} | ||

Successful | Intradisciplinary | Intratopical | 0 | Small | Small | Small | ||||

Intratopical heterodox | 0 | Small | Tiny | Small | ||||||

Intertopical | 0 | Large | Small | Large | 0 | Small | Small | Large | ||

Intertopical orthodox | 0 | Large | Tiny | Large | ||||||

Interdisciplinary | Intertopical | Small | Large | Large | Large | 0 | Large | Large | Large | |

Intertopical orthodox | Large | Large | Large | Large | ||||||

Unsuccessful | Intradisciplinary | Intratopical | 0 | Small | Small | Tiny | ||||

Intradisciplinary | Intertopical | 0 | Large | Small | Tiny | |||||

Interdisciplinary | Intertopical | Small | Large | Tiny | Large |

**Table 3.**The estimated values of the H indexes per author for the first analyzed PH (Table A1). All values are for the net production or productivity (i.e., after removal of reciprocal citations). Abbreviations: c = cubic fitting; l = linear fitting; n = net number of citations; t = total articles; y = citations are divided by the number of years since publication.

H | The Last 10 Years (2007–2016) | H | Author’s Whole Career (1995–2016) |
---|---|---|---|

H_{ltn10} | 6.02 | H_{ltn} | 6.29 (Figure 1) |

H_{ctn10} | 4.93 | H_{ctn} | 5.28 (Figure 2) |

H_{lyn10} | 2.56 (Figure 3) | H_{lyn} | 2.43 |

H_{cyn10} | 2.57 (Figure 4) | H_{cyn} | 2.60 |

**Table 4.**Summary of potentially questionable practices by editors and authors: sources, behavior types, observations, and warning indicators.

Single Author | Many Authors | |
---|---|---|

Single editor | Intrajournal personal relationship Opportunistic behavior by the editor and the author Many articles in the same journal (Tall but narrow red area) | Bargaining power of the editor Tactical behavior by the editor Many citations in the same journal (Large red area, but orthodox topics) |

Many editors | Interdisciplinary reputation of the author Tactical behavior by editors Many articles in many journals (Tall but narrow yellow area) | |

Single author | Personal relationship Opportunistic behavior by authors Many citations in many journals (Large black area) |

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## Share and Cite

**MDPI and ACS Style**

Zagonari, F.
Scientific Production and Productivity for Characterizing an Author’s Publication History: Simple and Nested Gini’s and Hirsch’s Indexes Combined. *Publications* **2019**, *7*, 32.
https://doi.org/10.3390/publications7020032

**AMA Style**

Zagonari F.
Scientific Production and Productivity for Characterizing an Author’s Publication History: Simple and Nested Gini’s and Hirsch’s Indexes Combined. *Publications*. 2019; 7(2):32.
https://doi.org/10.3390/publications7020032

**Chicago/Turabian Style**

Zagonari, Fabio.
2019. "Scientific Production and Productivity for Characterizing an Author’s Publication History: Simple and Nested Gini’s and Hirsch’s Indexes Combined" *Publications* 7, no. 2: 32.
https://doi.org/10.3390/publications7020032