- Email: [email protected]
Bonding number in scientific disciplines
Social Networks 20 Ž1998. 239–246
Bonding number in scientific disciplines Sofıa ´ Liberman ) , Kurt Bernardo Wolf
1
Centro Internacional de Ciencias AC, AÕ. UniÕersidad sr n, 62210 CuernaÕaca, Morelos, Mexico
Abstract We propose a measure of the internal bonding of a research community. This bonding number appears to be constant over time Ž1982–1994. and distinguishes clearly between scientific disciplines Žphysics, mathematics, biotechnology and anthropology.. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Multiple authorship in scientific articles is on the increase in most branches of science ŽStokes and Hartley, 1989.. So is scientific productiÕity in most academic institutions, measured by the total number of refereed papers in international journals Žde Solla Price, 1963.. The latter and its year-to-year increase are important because they provide one of the main ‘objective’ arguments to individual researchers, research groups and university institutes when lobbying for resources. In a young university research community, the productivity of scientific institutes grows rapidly; some authors have characterized this growth as exponential ŽCrane, 1972; de Solla Price and Beaver, 1966; Meadows, 1974.. This is due in part to the increasing number of researchers working at the institution, in part to the growing number of coauthorships of each of its members, and in part to the actual betterment of their scientific expertise. See Fig. 1, where we plot the productivity of four institutes of the National Autonomous University of Mexico ŽUNAM. over the period 1982–1994. Moreover, productivity varies widely between disciplines, as do the impact factors of their journals ŽGarfield, 1983., and their prevailing work habits and ethics ŽMerton, 1979.. Quite understandably, the allocation of resources according to the bare productiv)
Corresponding author. Facultad de Psicologıa, de Mexico. E-mail: ´ Universidad Nacional Autonoma ´ ´ [email protected]. 1 Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, UNAMrCuernavaca, Apartado ´ Postal 48-3, 62251 Cuernavaca, Morelos, Mexico. E-mail: [email protected]. ´ 0378-8733r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 8 7 3 3 Ž 9 8 . 0 0 0 0 3 - 3
240
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
Fig. 1. Productivity Žnumber of articles. in four institutes ŽPhysics, Mathematics, Biotechnology, Anthropology. during the years 1982–1994, and their exponential adjusted curves.
ity numbers is a source of much dispute between competing university institutes. Scientometric indicators such as the mean worldwide productivity or the number of articles per member, are frequently invoked to obtain these resources and buy collaboration ŽLiberman and Wolf, 1990.. In Fig. 2 we compare the articles published in 1984 and 1994 for each of the four institutes graphically, indicating the number of authors of each article by the vertices of a polygon. The figure shows that while the number of articles has increased over time, the pattern of published collaboration is visibly constant and characteristic of each discipline. Most evident is the prevalence of multi-author publications in biotechnology, versus the very individual work of mathematicians. In this article we propose one scientometric indicator, the bonding number s , which was obtained from the yearly publication data of four scientific institutes Žrepresenting fields of science.. In Section 2 we recall some results in the literature on multiple authorship as a scientific communication mode which enhances the benefits for each author and of the research group. In Section 3 we introduce the definition of scientific bonds as contacts publicly manifested, and the extraction of the bonding number from the accessible data bases that are published yearly. When the yearly bonding number is fitted by an exponential curve, the value of the exponent is near zero. In other words, s is found to be nearly constant over the past 10 years for each of the disciplines. Yet, s has recognizably distinct values for each of the disciplines, with dispersion comparable
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
241
Fig. 2. Patterns of productivity in four disciplines for the years 1984 and 1994. Dots are articles of one author, n-sided polygons indicate articles of n coauthors.
to that of other productivity indicators. The concluding Section 4 offers some remarks for future research. 2. Multiple authorship In previous studies we asserted that the establishment of contacts between individual researchers may be a precondition for productivity ŽLiberman and Wolf, 1997.. Attending scientific meetings is the ideal situation for establishing or activating scientific links with other colleagues of different institutions who are interested in the same research topics. Such contacts often become long-term relationships, which may be eventually reflected in joint coauthorship of scientific communications. The effect of multiple authorship has been traditionally considered as diluted productivity, since each coauthor only ‘does part of the paper’ ŽMeadows, 1974.. We cannot assume this is strictly true because there are no uniform criteria for apportioning participation by seniority, status, amount of work, or recognition. Scientists consider it fair to give credit equally, even if they privately acknowledge that the basic idea, the
242
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
computer algorithms and simulations, graphs, and the writing of the text of the article are due to one or another coauthor. Only in single-author papers is the credit entirely unambiguous; such papers are appreciated more in curricular evaluations, even if the probability is higher that they may contain errata or errors unrecognized by the referee, and uncorrected for lack of a second close reader of the manuscript. The habit of multiple authorship enhances the scientific value of an article for various reasons. Ža. Each author increases his curriculum vitae by an amount larger than the ‘fraction of article’ corresponding to him; Žb. joint publication widens the base of knowledge from the extant literature and is assumed to be ‘better informed’; and Žc. the basic ideas, calculations and conclusions, having presumably been subject to discussion and consensus, are more trustworthy. The first reason is an understandable tactic of each coauthor to enhance his own curricular score and, by itself, does nothing to increase the productivity of the larger community and, in fact, may be seen as an unwanted side-effect of the increasing institutional pressure to publish Žor perish.. The other two reasons are real gains in the value of the article and the competence of the research group. Various disciplines have very different ways to produce publishable results. Experimental work in a complex laboratory requires the collaboration of a large team, while the formulation and proof of a mathematical theorem may be done by a single researcher working alone. This is normally recognized by peer evaluation committees, but politicians and administrators of science are often unaware, unwilling or incapable of making the distinction when competing institutes vie for university funds. From the point of view of social psychology, multiple authorship reflects interaction and can be proposed as an indicator of the communication within the research group; if the authors habitually publish together, they constitute a recognizably coherent research unit, and collaboration is highly prized by university authorities who like to see interpersonal activity in their institutions ŽCrane, 1972; de Solla Price and Beaver, 1966.. Working in a research team also transmits indispensable tacit skills for scientific collaboration ŽPolanyi, 1958, 1970.. In the process of joint publication, older researchers train by example the younger generation in the canons and mores of science: ideas and calculations must be subject to scrutiny by discussion without implying personal confrontation, credit to previous work should be apportioned honestly, claims and conclusions ought to be written in a muted and modest manner, etc. Scientific collaboration attaches somewhat different values to discussions, disputes, conflicts, controversy, authority, fraud and piracy, than are common in other human endeavors. Disciplines such as biotechnology, where multiple authorship is the rule, have thus a bias towards homogenization of such values and variant individuals Žsingle authors. will not be abundant. Where production by single authors prevails, as in mathematics, ‘lonely geniuses’ are more common. 3. Contacts, bonds, and bonding number The establishment of contacts between researchers at scientific meetings has been formalized as a mathematical model whose input parameters are mean values of data obtained from questionnaires answered by working scientists ŽLiberman and Wolf,
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
243
1997.. Briefly, a contact was defined as any piece of scientific information exchanged face to face Žpresent in the briefcase or memory of the recipient. whose gain influences the subsequent work of the respondent. In spite of the private Žand subjective. nature of the ‘number of contacts’, the output from the model Žas that of any mathematical model. includes purportedly objective predictions and criteria, such as the cost per contact and the economic break-even point between convening an international meeting at the home country or sending a national delegation to a foreign meeting. Scientific contacts become bonds when the face-to-face interaction materializes into later coauthorship of specialized articles, published and therefore registered Žand observable. in scientific journals. Contacts may be private, but bonds are public. Contacts can persist in the recipient’s memory as enlargement and sharpening of expertise; bonds persist in the corpus of scientific literature, where they can be accessed from the yearly reports of university institutes, and from the database of the Institute for Scientific Information ŽGarfield, 1983.. We define the number of bonds contained in an article as its number of links Žbetween pairs of authors.. If there are n authors, the number of bonds will be the number of ways of choosing two objects from a collection of n distinct objects without regard to order. This is the combination of n objects in sets of two, given by the binomial coefficient n Ž n y 1. n s . 2 2 ŽEach of the n authors has n y 1 coauthors; divide by two to count each link once.. Thus, articles of 2, 3, 4, . . . authors contain 1, 3, 6, . . . bonds; articles of a single author contain no bonds. One may count total numbers and means of bonds of various sets of articles to arrive at other analyses, such as the number of bonds per researcher Žcountable in the articles of his curriculum., the number of bonds per institute Žfrom its yearly reports., per journal, per discipline, etc. and study their change with time; bonds may be further classified with binary labels such as intra- vs. inter-institutional bonds Žfor any one institute., ternary labels such as North–North, North–South, and South– South bonds Žfor developed vs. developing countries., etc. A paper signed by more than one author evinces that there has been effective scientific communication taking place. From the data contained in the yearly reports of four research institutes of a Mexican university, we examine the prevalence of bonding in four disciplines. We consider our study directed towards the mathematical model, rather than to any specific evaluation of the subject institutes; the exact and life sciences results are probably representative of the discipline worldwide, attested by the frequency of international collaboration in the database, while anthropology may suffer from some isolation. From the yearly reports we easily count A n , the number of articles of n authors of that year. The total number of authors contained in the report is thus
ž/
Nauthors s ÝnA n , n
and the number of bonds accounted is 1 Nbonds s Ýn Ž n y 1 . A n . 2 n
244
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
Fig. 3. Bonding numbers s obtained from the yearly reports of the four institutes ŽPhysics, Mathematics, Biotechnology, Anthropology., during the years 1982–1994, and their exponential adjusted curves. The salient feature is the constancy of s for each discipline over time and the difference of its values for different disciplines. ŽThe case of anthropology in 1983 is clearly anomalous and was taken out of the data when calculating the mean values of s over the whole period..
We consider the model realistic for author numbers that are not unreasonably large Žone experimental physics article had 23 authors and would count for 253 bonds!., so we restricted their range to 1 F n F 10. The effect of this bound will be commented upon after we interpret the data. The ratio we find of interest to characterize a discipline is the number of bonds per author,
s s NbondsrNauthors . On the basis of the figures published in references ŽBoldu, ´ 1987; Bosch et al., 1987; Instituto de Biotecnologıa, ´ UNAM, 1995; Instituto de Investigaciones Antropologicas, ´ UNAM, 1996., the values we find including the data of the years 1982–1994 are the following: Discipline s Physics 2.91 Mathematics 0.91 Biotechnology 3.90 Anthropology 0.69
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
245
These numbers of bonds subsume the connectivity patterns of Fig. 2. In Fig. 3 we show the value of s for each year in the period 1982–1994. The bound to 10 authors for the evaluation of Nbonds eliminates a few articles in physics and in biotechnology. Raising this bound beyond 10 raises the mean but also disperses the data points beyond significance. Lowering the bound, on the other hand, will lower and coalesce the means of physics and biotechnology, also entailing loss of significance of s . We regard the bound n F 10 as a good compromise. Within the random variability characteristic of publication data, the salient feature of the number of bonds is its constancy over the 12 years of the database. This may seem surprising in view of the increase both in the productivity Žnumber of articles. and in the mean number of coauthors. Other ‘events’ such as the availability of stipends from the Mexican Sistema Nacional de Investigadores since 1984, that was then ‘predicted’ that it would induce researchers to team up and publish more, in fact show up in various standard scientometric indicators very slightly ŽPerez ´ Angon ´ and Torres Vega, 1996.. Here we see that such changes in productivity andror economic inducement, have had no visible influence on the bonding number. We regard this as an indication that the bonding number is a stable characteristic; it measures the degree of collaboration between scientists in each discipline.
4. Conclusions Productivity may increase over time, but the amount of communication per author reflected in the bonding number s has been roughly constant through the period of 12 years for which publication data are available. In the four institutes we analyzed, the value of s is distinct and can be taken to characterize the working pattern in each discipline. Anthropologists and mathematicians have the habit to work andror publish alone, while physicists, and especially biotechnologists habitually include all the names of participants in the laboratory research group. The results are consistent with the following hypothesis: university researchers work honestly to the fullest of their ability. Although they increasingly team up to write multiple-authored articles, they spend more time on each article because each bond with each of his coauthors implies a constant share of his attention and his time. If this is true, it means that there is more work packed into each article; broadly speaking, that each paper reflects a more solid piece of research. Bonding numbers can be extracted from reports of institutes, groups with a grant, or individual curricula. This hypothesis leads to the prediction that there should be an observably higher bonding number in the curricula of research group leaders, because these individuals tend to coauthor many of the papers with their associates. The application of this indicator to individuals is currently under study, since research excellence by itself does not show up in indicators, although collaboration patterns do. We surmise that the bonding number should be a good indicator of changes in the communication of individuals and departments, within institutes whose baseline value of s we have provided in this paper.
246
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
References Boldu, 1938–1987. Instituto de Fısica, UNAM, Mexico City. ´ J.L. ŽEd.., 1987. Produccion ´ Academica ´ ´ Bosch, C., de la Pena, 1943–1987—Memoria. Instituto ˜ J.A., Prieto, C. ŽEds.., 1987. Instituto de Matematicas ´ de Matematicas, UNAM, Mexico City. ´ Crane, D., 1972. Invisible Colleges. Diffusion of Knowledge in Scientific Communities. Chicago University Press. de Solla Price, D.J., 1963. Little Science. Big Science. Columbia University Press. de Solla Price, D.J., Beaver, D., 1966. Collaboration in an invisible college. Am. Psychol. 21, 101–107. Garfield, E., 1983. Citation Indexing. ISI Press, Philadelphia. Instituto de Biotecnologıa, ´ UNAM, 1995. Informes Anuales del Instituto de Biotecnologıa ´ 1986–1994. UNAM, Cuernavaca. Instituto de Investigaciones Antropologicas, UNAM, 1996. Catalogo de Publicaciones. UNAM, Mexico City. ´ ´ Liberman, S., Wolf, K.B., 1990. Las redes de comunicacion Aportes de Investigacion, ´ cientıfica. ´ ´ Vol. 41. CRIM-UNAM, Mexico. Liberman, S., Wolf, K.B., 1997. The flow of knowledge: scientific contacts in formal meetings. Social Networks 19, 271–283. Meadows, A.J., 1974. Communication in Science. Butterworth, London, pp. 29–34. Merton, R.K., 1979. The Sociology of Science. Chicago University Press. Perez en America Latina. Boletın ´ Angon, ´ M.A., Torres Vega, G., 1996. Produccion ´ cientıfica ´ ´ ´ Acad. Invest. Cientıfica 28, 19–24. ´ Polanyi, M., 1958. Personal Knowledge. Routledge and Kegan Paul, London. Polanyi, M., 1970. Science, Faith and Society. University of Chicago Press. Stokes, T.D., Hartley, J.A., 1989. Coauthorship, social structure and influence within specialities. Soc. Stud. Sci. 19, 101–125.
Bonding number in scientific disciplines Sofıa ´ Liberman ) , Kurt Bernardo Wolf
1
Centro Internacional de Ciencias AC, AÕ. UniÕersidad sr n, 62210 CuernaÕaca, Morelos, Mexico
Abstract We propose a measure of the internal bonding of a research community. This bonding number appears to be constant over time Ž1982–1994. and distinguishes clearly between scientific disciplines Žphysics, mathematics, biotechnology and anthropology.. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Multiple authorship in scientific articles is on the increase in most branches of science ŽStokes and Hartley, 1989.. So is scientific productiÕity in most academic institutions, measured by the total number of refereed papers in international journals Žde Solla Price, 1963.. The latter and its year-to-year increase are important because they provide one of the main ‘objective’ arguments to individual researchers, research groups and university institutes when lobbying for resources. In a young university research community, the productivity of scientific institutes grows rapidly; some authors have characterized this growth as exponential ŽCrane, 1972; de Solla Price and Beaver, 1966; Meadows, 1974.. This is due in part to the increasing number of researchers working at the institution, in part to the growing number of coauthorships of each of its members, and in part to the actual betterment of their scientific expertise. See Fig. 1, where we plot the productivity of four institutes of the National Autonomous University of Mexico ŽUNAM. over the period 1982–1994. Moreover, productivity varies widely between disciplines, as do the impact factors of their journals ŽGarfield, 1983., and their prevailing work habits and ethics ŽMerton, 1979.. Quite understandably, the allocation of resources according to the bare productiv)
Corresponding author. Facultad de Psicologıa, de Mexico. E-mail: ´ Universidad Nacional Autonoma ´ ´ [email protected]. 1 Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, UNAMrCuernavaca, Apartado ´ Postal 48-3, 62251 Cuernavaca, Morelos, Mexico. E-mail: [email protected]. ´ 0378-8733r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 8 7 3 3 Ž 9 8 . 0 0 0 0 3 - 3
240
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
Fig. 1. Productivity Žnumber of articles. in four institutes ŽPhysics, Mathematics, Biotechnology, Anthropology. during the years 1982–1994, and their exponential adjusted curves.
ity numbers is a source of much dispute between competing university institutes. Scientometric indicators such as the mean worldwide productivity or the number of articles per member, are frequently invoked to obtain these resources and buy collaboration ŽLiberman and Wolf, 1990.. In Fig. 2 we compare the articles published in 1984 and 1994 for each of the four institutes graphically, indicating the number of authors of each article by the vertices of a polygon. The figure shows that while the number of articles has increased over time, the pattern of published collaboration is visibly constant and characteristic of each discipline. Most evident is the prevalence of multi-author publications in biotechnology, versus the very individual work of mathematicians. In this article we propose one scientometric indicator, the bonding number s , which was obtained from the yearly publication data of four scientific institutes Žrepresenting fields of science.. In Section 2 we recall some results in the literature on multiple authorship as a scientific communication mode which enhances the benefits for each author and of the research group. In Section 3 we introduce the definition of scientific bonds as contacts publicly manifested, and the extraction of the bonding number from the accessible data bases that are published yearly. When the yearly bonding number is fitted by an exponential curve, the value of the exponent is near zero. In other words, s is found to be nearly constant over the past 10 years for each of the disciplines. Yet, s has recognizably distinct values for each of the disciplines, with dispersion comparable
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
241
Fig. 2. Patterns of productivity in four disciplines for the years 1984 and 1994. Dots are articles of one author, n-sided polygons indicate articles of n coauthors.
to that of other productivity indicators. The concluding Section 4 offers some remarks for future research. 2. Multiple authorship In previous studies we asserted that the establishment of contacts between individual researchers may be a precondition for productivity ŽLiberman and Wolf, 1997.. Attending scientific meetings is the ideal situation for establishing or activating scientific links with other colleagues of different institutions who are interested in the same research topics. Such contacts often become long-term relationships, which may be eventually reflected in joint coauthorship of scientific communications. The effect of multiple authorship has been traditionally considered as diluted productivity, since each coauthor only ‘does part of the paper’ ŽMeadows, 1974.. We cannot assume this is strictly true because there are no uniform criteria for apportioning participation by seniority, status, amount of work, or recognition. Scientists consider it fair to give credit equally, even if they privately acknowledge that the basic idea, the
242
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
computer algorithms and simulations, graphs, and the writing of the text of the article are due to one or another coauthor. Only in single-author papers is the credit entirely unambiguous; such papers are appreciated more in curricular evaluations, even if the probability is higher that they may contain errata or errors unrecognized by the referee, and uncorrected for lack of a second close reader of the manuscript. The habit of multiple authorship enhances the scientific value of an article for various reasons. Ža. Each author increases his curriculum vitae by an amount larger than the ‘fraction of article’ corresponding to him; Žb. joint publication widens the base of knowledge from the extant literature and is assumed to be ‘better informed’; and Žc. the basic ideas, calculations and conclusions, having presumably been subject to discussion and consensus, are more trustworthy. The first reason is an understandable tactic of each coauthor to enhance his own curricular score and, by itself, does nothing to increase the productivity of the larger community and, in fact, may be seen as an unwanted side-effect of the increasing institutional pressure to publish Žor perish.. The other two reasons are real gains in the value of the article and the competence of the research group. Various disciplines have very different ways to produce publishable results. Experimental work in a complex laboratory requires the collaboration of a large team, while the formulation and proof of a mathematical theorem may be done by a single researcher working alone. This is normally recognized by peer evaluation committees, but politicians and administrators of science are often unaware, unwilling or incapable of making the distinction when competing institutes vie for university funds. From the point of view of social psychology, multiple authorship reflects interaction and can be proposed as an indicator of the communication within the research group; if the authors habitually publish together, they constitute a recognizably coherent research unit, and collaboration is highly prized by university authorities who like to see interpersonal activity in their institutions ŽCrane, 1972; de Solla Price and Beaver, 1966.. Working in a research team also transmits indispensable tacit skills for scientific collaboration ŽPolanyi, 1958, 1970.. In the process of joint publication, older researchers train by example the younger generation in the canons and mores of science: ideas and calculations must be subject to scrutiny by discussion without implying personal confrontation, credit to previous work should be apportioned honestly, claims and conclusions ought to be written in a muted and modest manner, etc. Scientific collaboration attaches somewhat different values to discussions, disputes, conflicts, controversy, authority, fraud and piracy, than are common in other human endeavors. Disciplines such as biotechnology, where multiple authorship is the rule, have thus a bias towards homogenization of such values and variant individuals Žsingle authors. will not be abundant. Where production by single authors prevails, as in mathematics, ‘lonely geniuses’ are more common. 3. Contacts, bonds, and bonding number The establishment of contacts between researchers at scientific meetings has been formalized as a mathematical model whose input parameters are mean values of data obtained from questionnaires answered by working scientists ŽLiberman and Wolf,
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
243
1997.. Briefly, a contact was defined as any piece of scientific information exchanged face to face Žpresent in the briefcase or memory of the recipient. whose gain influences the subsequent work of the respondent. In spite of the private Žand subjective. nature of the ‘number of contacts’, the output from the model Žas that of any mathematical model. includes purportedly objective predictions and criteria, such as the cost per contact and the economic break-even point between convening an international meeting at the home country or sending a national delegation to a foreign meeting. Scientific contacts become bonds when the face-to-face interaction materializes into later coauthorship of specialized articles, published and therefore registered Žand observable. in scientific journals. Contacts may be private, but bonds are public. Contacts can persist in the recipient’s memory as enlargement and sharpening of expertise; bonds persist in the corpus of scientific literature, where they can be accessed from the yearly reports of university institutes, and from the database of the Institute for Scientific Information ŽGarfield, 1983.. We define the number of bonds contained in an article as its number of links Žbetween pairs of authors.. If there are n authors, the number of bonds will be the number of ways of choosing two objects from a collection of n distinct objects without regard to order. This is the combination of n objects in sets of two, given by the binomial coefficient n Ž n y 1. n s . 2 2 ŽEach of the n authors has n y 1 coauthors; divide by two to count each link once.. Thus, articles of 2, 3, 4, . . . authors contain 1, 3, 6, . . . bonds; articles of a single author contain no bonds. One may count total numbers and means of bonds of various sets of articles to arrive at other analyses, such as the number of bonds per researcher Žcountable in the articles of his curriculum., the number of bonds per institute Žfrom its yearly reports., per journal, per discipline, etc. and study their change with time; bonds may be further classified with binary labels such as intra- vs. inter-institutional bonds Žfor any one institute., ternary labels such as North–North, North–South, and South– South bonds Žfor developed vs. developing countries., etc. A paper signed by more than one author evinces that there has been effective scientific communication taking place. From the data contained in the yearly reports of four research institutes of a Mexican university, we examine the prevalence of bonding in four disciplines. We consider our study directed towards the mathematical model, rather than to any specific evaluation of the subject institutes; the exact and life sciences results are probably representative of the discipline worldwide, attested by the frequency of international collaboration in the database, while anthropology may suffer from some isolation. From the yearly reports we easily count A n , the number of articles of n authors of that year. The total number of authors contained in the report is thus
ž/
Nauthors s ÝnA n , n
and the number of bonds accounted is 1 Nbonds s Ýn Ž n y 1 . A n . 2 n
244
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
Fig. 3. Bonding numbers s obtained from the yearly reports of the four institutes ŽPhysics, Mathematics, Biotechnology, Anthropology., during the years 1982–1994, and their exponential adjusted curves. The salient feature is the constancy of s for each discipline over time and the difference of its values for different disciplines. ŽThe case of anthropology in 1983 is clearly anomalous and was taken out of the data when calculating the mean values of s over the whole period..
We consider the model realistic for author numbers that are not unreasonably large Žone experimental physics article had 23 authors and would count for 253 bonds!., so we restricted their range to 1 F n F 10. The effect of this bound will be commented upon after we interpret the data. The ratio we find of interest to characterize a discipline is the number of bonds per author,
s s NbondsrNauthors . On the basis of the figures published in references ŽBoldu, ´ 1987; Bosch et al., 1987; Instituto de Biotecnologıa, ´ UNAM, 1995; Instituto de Investigaciones Antropologicas, ´ UNAM, 1996., the values we find including the data of the years 1982–1994 are the following: Discipline s Physics 2.91 Mathematics 0.91 Biotechnology 3.90 Anthropology 0.69
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
245
These numbers of bonds subsume the connectivity patterns of Fig. 2. In Fig. 3 we show the value of s for each year in the period 1982–1994. The bound to 10 authors for the evaluation of Nbonds eliminates a few articles in physics and in biotechnology. Raising this bound beyond 10 raises the mean but also disperses the data points beyond significance. Lowering the bound, on the other hand, will lower and coalesce the means of physics and biotechnology, also entailing loss of significance of s . We regard the bound n F 10 as a good compromise. Within the random variability characteristic of publication data, the salient feature of the number of bonds is its constancy over the 12 years of the database. This may seem surprising in view of the increase both in the productivity Žnumber of articles. and in the mean number of coauthors. Other ‘events’ such as the availability of stipends from the Mexican Sistema Nacional de Investigadores since 1984, that was then ‘predicted’ that it would induce researchers to team up and publish more, in fact show up in various standard scientometric indicators very slightly ŽPerez ´ Angon ´ and Torres Vega, 1996.. Here we see that such changes in productivity andror economic inducement, have had no visible influence on the bonding number. We regard this as an indication that the bonding number is a stable characteristic; it measures the degree of collaboration between scientists in each discipline.
4. Conclusions Productivity may increase over time, but the amount of communication per author reflected in the bonding number s has been roughly constant through the period of 12 years for which publication data are available. In the four institutes we analyzed, the value of s is distinct and can be taken to characterize the working pattern in each discipline. Anthropologists and mathematicians have the habit to work andror publish alone, while physicists, and especially biotechnologists habitually include all the names of participants in the laboratory research group. The results are consistent with the following hypothesis: university researchers work honestly to the fullest of their ability. Although they increasingly team up to write multiple-authored articles, they spend more time on each article because each bond with each of his coauthors implies a constant share of his attention and his time. If this is true, it means that there is more work packed into each article; broadly speaking, that each paper reflects a more solid piece of research. Bonding numbers can be extracted from reports of institutes, groups with a grant, or individual curricula. This hypothesis leads to the prediction that there should be an observably higher bonding number in the curricula of research group leaders, because these individuals tend to coauthor many of the papers with their associates. The application of this indicator to individuals is currently under study, since research excellence by itself does not show up in indicators, although collaboration patterns do. We surmise that the bonding number should be a good indicator of changes in the communication of individuals and departments, within institutes whose baseline value of s we have provided in this paper.
246
S. Liberman, K.B. Wolf r Social Networks 20 (1998) 239–246
References Boldu, 1938–1987. Instituto de Fısica, UNAM, Mexico City. ´ J.L. ŽEd.., 1987. Produccion ´ Academica ´ ´ Bosch, C., de la Pena, 1943–1987—Memoria. Instituto ˜ J.A., Prieto, C. ŽEds.., 1987. Instituto de Matematicas ´ de Matematicas, UNAM, Mexico City. ´ Crane, D., 1972. Invisible Colleges. Diffusion of Knowledge in Scientific Communities. Chicago University Press. de Solla Price, D.J., 1963. Little Science. Big Science. Columbia University Press. de Solla Price, D.J., Beaver, D., 1966. Collaboration in an invisible college. Am. Psychol. 21, 101–107. Garfield, E., 1983. Citation Indexing. ISI Press, Philadelphia. Instituto de Biotecnologıa, ´ UNAM, 1995. Informes Anuales del Instituto de Biotecnologıa ´ 1986–1994. UNAM, Cuernavaca. Instituto de Investigaciones Antropologicas, UNAM, 1996. Catalogo de Publicaciones. UNAM, Mexico City. ´ ´ Liberman, S., Wolf, K.B., 1990. Las redes de comunicacion Aportes de Investigacion, ´ cientıfica. ´ ´ Vol. 41. CRIM-UNAM, Mexico. Liberman, S., Wolf, K.B., 1997. The flow of knowledge: scientific contacts in formal meetings. Social Networks 19, 271–283. Meadows, A.J., 1974. Communication in Science. Butterworth, London, pp. 29–34. Merton, R.K., 1979. The Sociology of Science. Chicago University Press. Perez en America Latina. Boletın ´ Angon, ´ M.A., Torres Vega, G., 1996. Produccion ´ cientıfica ´ ´ ´ Acad. Invest. Cientıfica 28, 19–24. ´ Polanyi, M., 1958. Personal Knowledge. Routledge and Kegan Paul, London. Polanyi, M., 1970. Science, Faith and Society. University of Chicago Press. Stokes, T.D., Hartley, J.A., 1989. Coauthorship, social structure and influence within specialities. Soc. Stud. Sci. 19, 101–125.