Abstract
International scientific collaboration, a fundamental phenomenon of science, has been studied from several perspectives for decades. In the spatial aspect of science, cities have generally been considered by their publication output or by their citation impact. Only a minority of scientometric studies focus on exploring collaboration patterns of cities. In this visualisation, we go beyond the well-known approaches and map international scientific collaboration patterns of the most prominent science hubs considering both the quantity and the impact of papers produced in the collaboration. The analysis involves 245 cities and the collaboration matrix contains a total number of 7718 international collaboration links. Results show that US–Europe co-publication links are more efficient in terms of producing highly cited papers than those international links that Asian cities have built in scientific collaboration.
Keywords
1. Introduction
International scientific collaboration, a fundamental phenomenon of science, has been studied from several perspectives for decades [1,2]. There is evidence that international scientific collaboration started in the 19th century; however, due to the rapid globalisation of science, it has gained significance only in recent decades, and its growth rate is still accelerating [3,4]. Analysis of the spatial aspects of the science system, including that of international scientific collaboration, by using bibliometric data is in the scope of spatial scientometrics [5]. Spatial scientometric analysis most often focuses on examining international scientific collaboration between countries and regions but has shown little interest in examining the city level. One reason for this discrepancy is that cities are considered the most inhomogeneous spatial elements of the science system, where organisations are generally conducting research and producing publications independently from each other. Furthermore, problems stemming from the non-standardised territorial demarcation of cities make the results of spatial scientometric analysis at the city level rather uncertain (this problem and its solution are more thoroughly explained by Maisonobe et al. [6]).
Despite the aforementioned problems, several spatial scientometric studies focusing on cities have been published in the last two decades. One part of these studies examines the position of cities as nodal points of the science system based on total publication output (quantity approach) [7–9], while another part focuses on mapping cities as centres of excellence in terms of their citation impact (quality approach) [10]. Only a minority of spatial scientometric studies are interested in exploring collaboration patterns of cities, by, for example, examining internal collaborations [11] or mapping collaboration networks on the basis of co-authored papers [12].
2. Data collection and methods
In this visualisation, we go beyond analysing cities’ international scientific collaboration patterns that are based on the well-known approaches and rather present how efficient the collaborations between cities are. The analysis involves 245 cities in which authors produced at least 10,000 publications during 2014–2016. The names of cities can be found in the addresses reported by the authors of publications. We focused on only those city-to-city collaborations that produced at least 300 publications during the aforementioned period of analysis (i.e. an average of 100 publications per year). The collaboration matrix of 245 × 245 cities contains a total number of 7718 international collaboration links that meet the above criteria. Efficiency of the collaboration between each city dyad corresponds to the ratio of highly cited papers to all papers produced by co-authors affiliated with those cities between 2014 and 2016. We assume that the higher the efficiency of the collaboration between two cities is, the more likely it is that researchers affiliated with those cities conduct joint research resulting in new scientific breakthroughs.
We group city-to-city links along two dimensions (see the summary statistics in Table 1): the 80th percentile is used to partition by number of collaborations and fraction of highly cited papers. The groups contain 4997 links (low collaboration, low efficiency indicated by dark blue in Figure 1), 1180 links (low collaboration, high efficiency indicated by light blue), 1178 links (high collaboration, low efficiency indicated by light red) and 363 links (high collaboration, high efficiency indicated by dark red). We colour the edges by these four groups, set East–West edge curves positive (clockwise) for links with collaborative papers exceeding the 80th percentile and negative (counterclockwise) otherwise and plot the edges on top of each other.
Summary statistics of efficiency distribution across groups.

Visualisation of efficiency of international scientific collaboration of cities.
3. Discussion and conclusion
The strength of the scientific collaboration between two cities in terms of the number of co-authored papers is significantly influenced by the total publication output of organisations located in those cities; the geographical proximity; the historical, cultural and linguistic ties; and their scientific field profile [9,13]. However, these factors do not or only partly provide appropriate explanations for the varying efficiency of collaborations between certain city dyads.
International scientific collaboration between cities characterised by high collaboration and high efficiency (indicated by dark red in Figure 1): Figure 1 shows that the higher the number of co-authored papers between two cities (more precisely: between authors affiliated with those cities) is, the more likely it is that the efficiency of the collaboration approximates the average value. For example, the London–Paris collaboration link is the highest in the world in terms of the number of co-authored papers (more than 6800 papers produced between 2014 and 2016), but the efficiency of the collaboration (7.617) is around the average value (9.062). The scientific collaboration between Northern American, Western European and Australian cities having high total publication output generally produces a large number of co-authored papers from which many co-authored papers become highly cited, and for this reason the efficiency of these collaborations approximates (or is slightly above) the average value.
International scientific collaboration between cities characterised by high collaboration and low efficiency (indicated by light red in Figure 1): The scientific collaborations between the major Latin American cities (e.g. Sao Paulo, Rio de Janeiro and Mexico City), Chinese cities (e.g. Beijing, Shanghai and Hong Kong) and other East Asian cities (e.g. Tokyo, Osaka, Seoul and Singapore), but primarily with Western cities, have recently been significant; however, the efficiency of these collaborations generally remains below average. Emerging Latin American and Chinese cities have established high scientific collaboration in terms of the number of co-authored papers with many cities located in developed countries, but only few of these collaborations (at least in terms of proportion) have produced new scientific breakthroughs (indicated by the low number of highly cited papers). Surprisingly, many international scientific collaboration links built by major Japanese cities (and that of some other cities located in highly developed East Asian countries) also belong to this group. In the past two decades, Japanese cities have established increased scientific collaboration with Chinese cities (e.g. the Tokyo–Beijing link is one of the strongest in the world in terms of the number of co-authored papers), particularly in the field of engineering and several disciplines in natural sciences. The geographical proximity between Japanese and Chinese (and other East Asian) cities and the increasing economic and scientific cooperation of the countries they are located in give significant impetus to scientific collaboration between them, resulting in the production of a large number of co-authored papers. However, despite most co-authored papers being produced in research fields having high citation impact (e.g. 58% of all Tokyo–Beijing co-authored papers were produced in five sub-disciplines of physics), only few of these papers have received sufficient numbers of citations to become highly cited (for a citation analysis of different scientific disciplines, see Patience et al. [14]).
International scientific collaboration between cities characterised by low collaboration and high efficiency (indicated by light blue in Figure 1): Collaborations between cities having the highest efficiency are generally based upon a fewer number of co-authored papers (approximately an amount of 300–450 papers during a 3-year period), while typical geographical patterns cannot be detected. The Toulouse–Copenhagen collaboration produces the highest efficiency (27.213) in the world exceeding the average value by three times. The efficiency of the collaboration between Warsaw and Nijmegen (26.380), Padua and Toronto (25.989) and Helsinki and Montreal (25.868) is also very high. None of the geographical proximity (as in the case of the London–Paris, and the Seattle–Vancouver, BC, collaboration links); the historical, cultural and linguistic ties (as in the case of the Copenhagen–Stockholm, and the Paris–Montreal collaboration links); or the size of the output (as in the case of the Beijing–Tokyo, and the London–Boston collaboration links) are factors influencing the efficiency of these collaborations. It is, however, more important to know which are the most productive scientific disciplines in those cities. For example, in each aforementioned case, the most productive discipline is ‘Astronomy and Astrophysics’ (40%–50% of all co-authored papers are produced in that field) of which the ratio of highly cited papers to all papers is generally very high. Because in these collaborations the number of co-authored papers is low, the attitude of individual researchers located in those cities becomes even more important (i.e. the collaboration between two or some star researchers becomes more visible).
International scientific collaboration between cities characterised by low collaboration and low efficiency (indicated by dark blue in Figure 1): Most international scientific collaborations of city dyads produce only a few numbers of co-authored papers (i.e. 300–600 papers during a 3-year period) with low efficiency. In these cases, pronounced geographical patterns cannot be found.
In this article, we mapped the international scientific collaboration links of cities producing at least 10,000 papers during 2014–2016. The collaboration matrix of 245 × 245 cities contains a total number of 7718 links that we classified into four groups based on the size of the collaborations and the highly cited paper ratio (i.e. the efficiency) of the links. Previous studies and our research both suggest that the efficiency of a collaboration link is significantly influenced by several factors (e.g. the total publication output of cities, and the linguistic, historical, cultural and economic ties between the countries in which cities are located) [13], but one of the most important ones seems to be the disciplinary profile of cities. Thus, the examination of the connection between the efficiency of cities’ international scientific collaboration and their disciplinary profile outlines further research directions.
Footnotes
Data sources
All data were obtained from the Web of Science’s (owned by Clarivate Analytics) Science Citation Index Expanded, Social Sciences Citation Index and Arts & Humanities Citation Index databases.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work of Balázs Lengyel has received funding from the National Research, Development and Innovation Office (NKFI 116163).
Software
We used ‘R’ for both network visualisation and mapping.
