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He focused on the largest component, the clustering coefficient, and the mean distance between authors, all of which are consistent with the small-world model. He showed also the network in Slovenia is growing exponentially. Here, the hypothesis dealing with the clustering level, the second property of the small-world model, is:.

H1 : The co-authorship networks in the Slovenian scientific community have a high clustering level driven by transitive closure processes where co-authors of co-authors become, or remain, co-authors. The idea of cumulative advantage implies that excellent scientists are rewarded far more than others in their field. Said et al. This feature was found to be a consequence of two generic mechanisms: 1 networks expand continuously with the addition of new vertices; and 2 new vertices attach preferentially to vertices that are already well connected.

They presented a model based on these properties and reproduced the observed stationary scale-free distributions. The model was widely accepted and also criticized e. They also lay the foundations for fruitful applications of scale-free networks. The implications of scale-free distributions were used to delineate the structure of scientific co-authorship networks e. We examine these arguments further by asking if authors who are already well connected, as evidenced by their current number of co-authorships, will attract even more co-authorships as time goes by.

As noted earlier, the concept of preferential attachment reduces the generation of co-authorship to a single mechanism. However, the phenomenon of collaboration is far more complex. Using SAOM, they operationalized preferential attachment by separating the collaboration of researchers within the scientific discipline from their collaboration with scientists from abroad. They showed that some features of the preferential attachment principle were confirmed but in different ways in the three considered scientific disciplines, and not at all in biotechnology.

Here we test the following hypothesis dealing with the preferential attachment mechanisms using higher quality data:. H2 : New co-authorship collaborations of Slovenian researchers are more likely for authors who have more current co-authorships and for excellent researchers. For co-authorships, this holds both for collaboration within Slovenia and with researchers abroad. The hypothesis that individual and organizational contexts drive the formation of scientific co-authorship networks was confirmed by Kronegger et al.

They showed that the four disciplines were affected in different ways by the organization of local institutions and disciplinary publishing cultures. Here, based on their analyses we test the same hypothesis for all scientific fields and most scientific disciplines in the Slovenian scientific system. H3 : Individual and organizational contexts in Slovenia drive the formation of scientific co-authorship networks. Since our data are non-directed networks, a modification to the models of Snijders , is required. The choice by ego of alter is a multinomial choice, and the acceptance decision by alter is a binary choice.

The probability models for these choices are based on a linear predictor similar to generalized linear models. The coefficients parameters given in Table 4 are the estimated parameters in these linear predictors. Given the first hypothesis, we included in the model a clustering component to capture the idea of small dense parts being present in the network. As clustering can be viewed as a consequence of transitive closure, we added to the model the effect of transitivity in triplets.

Co-authors of co-authors will have a larger probability to become direct co-authors; and if they are already direct co-authors, they will have a larger probability of remaining compared to pairs of authors who are not co-authors of co-authors. Also, as co-authorship can also be driven by departmental and institutional affiliation, we operationalized this by working in the same organizational research group and by working in the same scientific discipline when analyzing fields.

In the first place, it is tested whether the current degree number of co-authorships has a positive effect on the number of new co-authorships. Since the collaboration network is symmetric, there is no distinction between the actors at both sides of the tie. Therefore, individual variables are included without an ego-alter differentiation.

As the degree captures only collaborations inside national networks scientific fields or scientific disciplines on national level , we also included collaboration outside the national collaboration network in the model. As this variable was highly skewed we used its logarithm.

Individual context was considered by scientific excellence. As controlling variables, we included gender and having a PhD. Period 2, — in , Slovenia became a member of the EU. These researchers collaborated with another 48, authors not registered with ARRS. Together, they published , publications that are, according to the evaluation criteria of ARRS, treated as scientific outputs. The data about discipline memberships were provided by the researchers themselves when they applied for an identification number.

Technology driven physics 30 , Communications technology 31 , Landscape design 45 and Ethnic studies 57 were excluded because of having too small numbers of researchers. This was measured by Jaccard coefficients between consecutive periods. Law 51 was excluded due to a deviating data structure: each wave had a few papers having a very high number of authors in contrast to the usual number of authors for this discipline. Historiography 60 was excluded due to high proportion of missing values in variables for actor properties.

The NCKS Research programme 72 , in addition to Interdisciplinary research 73 , was excluded as it lacks an established field structure Interdisciplinary studies. The last column in the last panel in both Tables 2 and 3 presents the share of researchers not having any co-authored publication during the observed time period within each scientific field or discipline.

As both approaches give the same results, the isolates were excluded from all further analyses. This tendency is also seen in the middle panel of Tables 2 and 3 average degrees. A similar trend is evident in the scientific disciplines see Table 3 where the variation between the percentages of excluded researchers across scientific disciplines inside each of the scientific fields is larger.

The only outlier is Technology driven physics with an extremely small number of researchers. As noted above, there are higher percentages of excluded researchers in the disciplines from the social sciences and the humanities.

Structures of Scientific Collaboration | The MIT Press

The scientific disciplines listed at the bottom of Table 3 and marked by EXC were excluded from all further analyses. All co-authorship ties were binarized: if two researchers had at least one joint publication a value of 1 was assigned, otherwise a value of 0 was used. It appears that, in their analyses, such ties remain in the network, which may be problematic in the case of co-authorship networks.

Yet, scientists collaborating at one point in time can maintain or dissolve their co-authorship tie at a later time. Consequently, we considered the possibility that ties can be created, maintained or deleted since this is a feature that characterizes co-authorship networks. The probabilities of tie creation and deletion depend on so-called effects explanatory variables that may depend on the network or be exogenously given , with their associated coefficients as parameters.

The set of effects chosen as the model specification followed from the hypotheses as elaborated in the preceding section. Preferential attachment was operationalized by five effects: degree of alter inside the co-authorship network, degree of alter with respect to collaboration with researchers outside the co-authorship network, scientific excellence, scientific age, and age similarity. The network was defined in three consecutive observations corresponding to the periods mentioned in Sect. Estimated parameters for the six scientific fields Italicized estimates are not statistically significant; there are standard errors in parentheses.

Using SAOM includes also an estimate of the cost of adding one more tie to the personal network of each researcher is obtained, an important characteristic seldom considered by scholars studying preferential attachment. This value is given by the third basic parameter degree.

This makes sense because tie formation incurs costs in terms of time, effort, and resources. Researchers can co-author with only a limited number of different authors as each new tie represents an additional time and cost burden. The next three parameters in Table 4 concern the clustering level as a dimension of the small-world process. Among these, the fourth parameter of the model, for the transitive triads effect, is positive and significant showing that scientists tend to form new co-authorship ties with the co-authors of their co-authors inside the scientific field.

It is positive and significant for all fields and all disciplines. The fifth and the sixth parameter that show the impact of belonging to the same research group and to the same discipline as a tendency to form new co-authorship ties are also positive and significant in five scientific fields. This holds for all but two scientific disciplines. The next three parameters in Table 4 concern preferential attachment in the six scientific fields in Slovenia.

As discussed in the previous section, this deals with a preference to create new ties with prominent researchers who already have a high number of co-authors. The parameter for alters number of co-authors within the scientific field network is negative and statistically significant in all scientific fields it is negative but not significant in the humanities.

This indicates that researchers do not tend to form new ties with those researchers who collaborate more within the national field. This is a partial contradiction of the second hypothesis.

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There is much greater diversity in the alters number of co-authors outside the scientific field. The parameters showing significant positive values are for Natural sciences and mathematics, Engineering sciences and technologies, Medical sciences, and Biotechnical sciences. A positive estimated parameter means that researchers are more likely to create new ties with those researchers within the field who collaborate with many authors from other fields or mostly with others from abroad.

This is partial confirmation for the second hypothesis. However, for Social science and Humanities, the sign of this parameter is negative significant for the social sciences and not significant for the humanities : among these researchers, collaboration with other researchers outside the field or outside Slovenia has a negative effect on tie formation with scientists working in the social sciences and in the humanities.

Yet publication excellence has a positive and significant effect on new tie formation within the Social sciences and the Humanities: researchers tend to create new co-authorship ties more often with those researchers who publish in the highest ranked scientific journals. We note that researchers from these two fields publish less often in the best scientific journals suggesting excellence is more valued for creating co-authorship ties.

The only negative and significant parameter for publishing excellence is in the Natural sciences and mathematics. This parameter is negative but not significant for other three fields. Regarding publication excellence, the results are mixed. It has no effect on co-authorship in the technical, medical and biological sciences.

It has a negative effect in the natural sciences. For these four fields, this aspect of the preferential attachment hypothesis is not confirmed. We also tested whether young researchers form new co-authorship ties with older, established researchers usually their mentors. The most salient effects are in the natural sciences and mathematics. The age similarity is not significant in all scientific fields. This result does not follow the standard hypothesis claiming young researchers form new co-authorship ties with scientifically excellent older scientists. Next, we examine the effects of the controlling variables.

As expected, having a PhD has a positive effect on tie formation in all scientific fields. Researchers are more likely to establish ties with male colleagues within the technical, medical and biotechnical sciences. The only negative effect is in the social sciences: researchers are more likely to create new ties with female researchers within the field. This effect is not significant in the natural sciences and the humanities. No doubt this reflects demographic differences: the proportion of female researchers is the highest in the social sciences.

A general summary of the results of fitting the stochastic-actor-oriented model is straightforward. In all six scientific fields, Slovenian researchers form new co-authorship ties in ways consistent with clustering inside the co-authorship networks: co-authors of co-authors will tend to become co-authors.

The preferential attachment mechanism is more complex than the advocates of a single global autonomous mechanism claim. First, the distance between the researchers who collaborate matters for tie formation. Alters high degree of co-authorship inside the field has a negative effect on new tie formation in all scientific fields, but high alters degree of collaboration outside the field reveals a gap between the social sciences and humanities and the other four fields.

Alters higher degree of outside collaboration has a negative effect on new tie formation and publication excellence has a positive effect in the social sciences and humanities but the opposite effect exists in the other four fields.

Doing this was not straightforward because the estimated parameters are not directly comparable across disciplines due to variations in the size of the disciplines. While the starting point is the set of these estimated parameters, we transformed them to measure the importance of the estimated parameters using the proposed method of Indlekofer and Brandes These values ignore the sign of the estimated parameters for disciplines. These measures were standardized before obtaining the Euclidean distances for each pair of disciplines. The clustering used Wards hierarchical clustering procedure Ward Averages of the importance coefficients according to the estimated parameters for each obtained cluster.

The overall summary for the five clusters is shown in Table 5. The averages of the importance coefficients for each obtained cluster and each parameter are easy to summarize. First, for all clusters, the overall coefficients for transitive triads and belonging to the same research group are positive.

The first of these results indicates the presence of a small-world clustering phenomenon and the second is for the impact of the institutional feature of belonging to the same research group. Second, the overall coefficients for the degree of alter is negative, contradicting the primary operationalization of preferential attachment, for all clusters. Third, the overall coefficients for all clusters except HUM,SOC are positive for the degree of alters outside the national disciplinary disciplines.

This supports one aspect of the preferential attachment idea. Finally, these overall coefficients for the scientific excellence of alters are negative for all clusters except HUM,SOC. We note that these summary coefficients for the residual cluster follow all of these patterns but with the smallest values. These results are consistent with the results reported earlier and will not be summarized further. Given this overall summary for the clusters, the next issue is whether the disciplines within the clusters have the same patterns of signs for the estimated parameters.

Evidence for this assessment comes from the reported coefficients in Table 6. For all of the first four clusters, the coefficients for transitive triads and membership of the same research group follow the general pattern for all disciplines. Every discipline has the same pattern for the degree of alter and the degree outside the discipline. Regarding scientific excellence, we note that all estimated coefficients have the same sign as for the overall cluster.

For the third cluster HUM, SOC , its disciplines have the same estimated coefficient pattern for degree of alter and scientific excellence as for the cluster as a whole. The same holds for degree outside the disciple but with only one exception out of 22 disciplines. Regarding scientific excellence, two disciplines have the wrong sign and three others have estimated coefficient values very close to 0. Overwhelmingly for the first four clusters of disciplines, the pattern of coefficient signs of the clusters are followed also by all the disciplines they contain.

The overall summary regarding the substantive hypotheses is not driven by just a few disciplines: the phenomena hold at the disciplinary level. Given the heterogenous nature of the RESID cluster, we cannot expect to see the same level of consistency. Even so, there is complete consistency for the disciplines regarding transitive triads. For membership in the same research group, there are only three inconsistencies out of 22 disciplines and these have negative values that are borderline.

For the degree of alter, there are only four exceptions out of 22 disciplines. Even here, there is considerable consistency of the disciplines with the overall pattern. However, this is not the case for scientific excellence as half of the estimated coefficients have the wrong sign at the disciplinary level. We emphasize that small world clustering and preferential attachment phenomena hold at the disciplinary level even in the residual cluster.

The first hypothesis about the presence of clustering as a dimension of a small-world structure was confirmed emphatically. The evidence regarding the second hypothesis concerning preferential attachment as the driving mechanism of co-authorship was decidedly mixed. Yet, in the main, our results contradict the hypothesis of a single preferential attachment mechanism for the formation of collaborative ties.

The current number of co-authorships inside the field or discipline has a negative effect on new tie formation in all scientific fields and nearly all scientific disciplines. Our results show the distance between researchers who collaborate matters also. Regarding this, the social sciences and humanities differ from the other four fields. Alters higher degree of collaboration outside of Slovenia has a negative effect on new tie formation in the social sciences and humanities but a positive effect in the other fields. A high degree of collaboration outside the national disciplinary field, a revised notion of preferential attachment, has a positive impact on tie formation for the natural, technical, medical and biotechnical sciences.

Clearly, preferential attachment mechanisms are more subtle than can be summarized by stating that researchers who currently have a large number of co-authors will see an increase in their number of collaborators, at least for the science dynamics in smaller national scientific systems. Another difference between the social sciences and the humanities compared with the other four fields is that publication excellence had a positive effect on the formation of collaborative ties in the social sciences and humanities but a negative effect in the other fields.

However, the standard hypothesis that young researchers form new co-authorship ties with scientifically excellent older scientists was not confirmed. Researchers from all fields but the humanities were more likely to form new ties with younger colleagues. The third hypothesis was confirmed and the evidence demonstrates that the scientific fields and disciplines are affected by the organization of local institutions and publishing cultures.

We note that our findings regarding the effects of small-world phenomena, preferential attachment, institutional arrangements hold for virtually all disciplines as well as for broad fields. The differences between the two basic pools of scientific knowledge i. In the former socialist era, due to ideological pressure on the social sciences and the humanities, these disciplines were less internationalized and much less oriented to publishing in high-ranking international journals. In part, this helps account for some of the differences between the two groups of fields. Yet, those social scientists and humanists who already engaged in excellent publication activity can be very attracted to research collaboration with their disciplinary colleagues.

No single approach, be it sociological, social network analytic or based on conceptions drawn from physics, can be useful by itself. Multiple approaches are needed to account for the complex phenomenon of scientific collaboration, especially for national scientific systems. While science can be viewed as a general phenomenon it is also conditioned by local institutional contexts. Therefore, some older, mostly prominent researchers were missing along with some other researchers.

In other classification systems, some of these disciplines are not classified in the natural sciences. Preferential attachment, in its simple form, uses degree centrality to capture an aspect of researcher motivation for seeking new collaborative ties. For individuals having no interest in network analysis, it is highly unlikely that they are aware of their betweenness values in a network.


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We did not include betweenness as a predictor for this reason. Even so, this idea is worth considering in future research.

Primarily, this is collaboration with researchers from abroad since there are very little collaboration between different fields in Slovenia. The difference can be attributed to having, in this study, larger scientific groups with better data and a more elaborated model specification. Alternative transformations were examined also. Skip to main content Skip to sections. Advertisement Hide. Download PDF. Scientific collaboration dynamics in a national scientific system.

Open Access. First Online: 07 April Introduction Scientific collaboration in modern science appears to be one of the key factors for increasing publication productivity and quality. Co-authorship networks and citation networks are very useful instruments for studying collaboration in science.

Both have positive impacts on scientific productivity. Scientific disciplines still represent a crucial institutional and organizational framework within which scientific activities take place. There are several international, national, and informal classifications of scientific disciplines. Since we analyzed the co-authorship networks of the Slovenian scientific system, we started with the classification into scientific fields and scientific disciplines used by the Slovenian Research Agency henceforth: ARRS , the main policy authority in Slovenian science. It is presented in Table 1 together with the number of scientific disciplines assigned to each scientific field.

As a result, we ignored it in our analyses of co-authorship network dynamics. Table 1 Seven scientific fields in the Slovenian Research Agencys classification system with the number of scientific disciplines. ID Scientific field No. According to analyses of the collaboration styles of researchers belonging to different scientific disciplines and fields, co-authorship represents an important differentiating indicator between them.

The differences in the percentages of co-authored publications among the seven scientific fields in Slovenia are shown in Fig. There is a large gap between the average levels of co-authorship in the natural, technical, medical and biotechnical sciences, and the average co-authorship levels in the humanities and the social sciences.

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Structures of Scientific Collaboration (Inside Technology)

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