Mathematics and statistics related studies in Indonesia using co-authorship network analysis

As the fourth most populous country in the world, Indonesia has great potential because around 43% of its 250 million people are young or under 25 years old [1] and participation in formal education (higher education level) in 2017 increased 113.78% compared to 2005 [2]. Indonesian scholars also have published a numbers of articles in numerous international journal, but in fact, it still lacking in publications compared with other ASEAN countries such as Singapore, Malaysia, and Vietnam. Bibliometrics studies can identify and measure the contribution of Indonesian scholars to the advancement of knowledge [3]. Bibliometric research can be used to advance knowledge of science and technology development in relation to social and policy issues [4]. Some of these are citation analysis for assessment of research performance and co-word analysis for mapping science and producing visualization of field of science [5]. Several bibliometrics and scientometrics research carried out in Mathematics and related areas. For example, Arunachalam [6] described mathematics research in India, and Asadi [3] explored the research trend in information theory using a bibliometrics approach. Bibliometrics and Scientometrics approaches are used in a large body of research in order to measure the productivity of scholars in a subject area at a country or international level. Nadhiroh et al. [7] conducted a scientometric study using social network analysis methods to explore central actors and institutions involved in Indonesia scientific publication in Chemistry.


Introduction
As the fourth most populous country in the world, Indonesia has great potential because around 43% of its 250 million people are young or under 25 years old [1] and participation in formal education (higher education level) in 2017 increased 113.78% compared to 2005 [2].Indonesian scholars also have published a numbers of articles in numerous international journal, but in fact, it still lacking in publications compared with other ASEAN countries such as Singapore, Malaysia, and Vietnam.Bibliometrics studies can identify and measure the contribution of Indonesian scholars to the advancement of knowledge [3].Bibliometric research can be used to advance knowledge of science and technology development in relation to social and policy issues [4].Some of these are citation analysis for assessment of research performance and co-word analysis for mapping science and producing visualization of field of science [5].Several bibliometrics and scientometrics research carried out in Mathematics and related areas.For example, Arunachalam [6] described mathematics research in India, and Asadi [3] explored the research trend in information theory using a bibliometrics approach.Bibliometrics and Scientometrics approaches are used in a large body of research in order to measure the productivity of scholars in a subject area at a country or international level.Nadhiroh et al. [7] conducted a scientometric study using social network analysis methods to explore central actors and institutions involved in Indonesia scientific publication in Chemistry.
Arunachalam [6], Van Raan [5], and Asadi [3] in their studies only discussed research trends using bibliometric analysis.The study using SNA has been done by Nadhiroh et al. [7] in chemistry but only

Descriptive Data
In total, 426 publications were retrieved.Duplicate records were excluded; 690 authors from 306 institutions.Table 1 shows the yearly distribution of publications production and the number of authors in mathematics or statistics area of study with Indonesian affiliation.The number of authors grew significantly (110%) in 2013 then grew even higher in 2015 (283%) but with a decline back to the average growth rate of publications and authors (Fig. 1).Bandung Institute of Technology (ITB) was the affiliation with the highest number of publications and number of authors.The second and third affiliation with the highest number of publications are Gadjah Mada University (UGM) and Sepuluh November Institute of Technology.Even though, number of authors of UGM is less than number of authors of Sepuluh November Institute of Technology (  Table 2 shows the number of author and articles from ITB are much higher than other institutions, 18.3% from total number of authors and 32.4% from total number of articles, and therefore the highest author/article ratio of 1.85.ITB was the first university with a mathematics faculty in Indonesia and may have affected the quality of human resource and network connection of scholars.Table 3 shows the domination of ITB in the international publication of mathematics and statistics related area in Indonesia.Eight of the top 10 authors are from ITB. Edy T Baskoro (ITB) is author with the highest number of articles (30), followed by his ITB colleagues ANM Salman (15).

Collaboration Network
The average ratio of authors by article during 2009-2017, is 3.1 (Table 1), meaning that there were, on average, three authors of every article.Only 40 articles (9%) have one author, the rest are articles with multiple authors.on the other hand, 84% (359) of all articles produced are by collaboration works between Indonesian affiliation scholars and non-Indonesian scholars.Only 16% (67) articles were produced by Indonesian affiliation scholars without international collaboration which showed the high dependency of Indonesian affiliation scholars on foreign scholars to publish their work in international journals.Percentage of collaboration articles increased in the past five years parallel with the increase of number of articles (Fig. 2).
A deep comprehension of the dynamics of scientific collaboration in Mathematics and Statistics related studies of Indonesian affiliation scholars can be carried out using Social Network Analysis.This analysis will portray the links of each scholar and the relative adjacency of other scholars.Abbasi and Altmann [9] conclude that using SNA can help people understand how to share the knowledge via the social network and evaluate the performance in the individual, group, or entire networks.The node of the graph represents the actor, whereas, in this study, node represents the author [10].In this article, edge is the co-authorship relationship between the authors in these studies.SNA has been widely used to explore the co-authorship network in scientific publications at both country and/or area level.For example, Glanzel & Schubert [11] analyzed scientific networks through co-authorship.Mena-Chalco et al. [12] studied the co-authorship network in Brazil.Alhaider et al. [13] studied the co-authorship network in the Pharmacy area in United Arab Emirate.Sorensen et al. [14] studied the co-authorship network in the research of Alzheimer disease.Li & Li [15] examined the pattern and evolution of co-authorship in China's humanities and social sciences.Yan et al. [16] mapped co-authorship networks in library and information science in China.
SNA metrics measure different levels within a network.Macro-level metrics used to identify the global character of the network [16] and micro-metrics that measure sub-networks of such as individuals (e.g.journals or scholars) and groups (e.g.scholars within a specific institution or a specific group of scholars within an institution).Table 6 shows the network description of co-authorship network of Indonesian affiliation scholars in three networks: all authors in the network, ITB network as a subset of all authors and a network of a big cluster of ITB authors.Network description uses metrics such as network density (ND), degree centrality (DC), closeness centrality (CC) and betweenness centrality (BC).The mean degree centrality reflects the average number of authors that have co-authors in the network.
The Network Density (ND) describes the portion of the potential connection in a network that are actual connections.A potential connection is a connection that could potentially exist between two nodes-regardless of whether or not it actually does.By contrast, an actual connection is one that exists.The network density of all authors is 0.7%, the analysis showed that the total number of potential connections between these authors is 475,410.Of those potential connections, there are only 3,084 actual connections, therefore the network density was 0.7%.The network density of ITB sub-network was 2% and the big cluster of ITB network was 5.4%.
The mean Degree Centrality (DC) of the 3 networks was 5 or 4, which means that co-authorship of Mathematics and Statistics related studies of Indonesian affiliation scholars is very low.As a comparison, this result is quite similar with Grossman [17] and Newman [18] found, the average number of coauthors the co-authorship network of Mathematical Review Journal during 1940-2009, had a DC 2.9 or 3 co-authors per each author.Meanwhile, Brunson et al. [19] examined the co-authorship network of Mathematical Review Journal during 1985-2009 and they found the mean number of co-authors in the co-authorship network had a DC of 4.1.The standard deviation of DC reflects the variation in the number of authors that have co-authors in the network.The Closeness Centrality metric (CC) is based on the geodesic distances between nodes in a network map and is the average geodesic distance that a node is from all other nodes as shown in the network map.CC measures the closeness between the actors/nodes and a measure of how fast information spreads from a given node to other reachable nodes in the network The initial idea of this measure is referred to as a central actor of a network if it can interact with other actors more easily and quickly.Associated with the flow of information, a central actor, who has close relations with other actors, will be more productive as the actor can access the information due to the shorter lines of communication.The mean CC reflects closeness between the actors.If we compare the value of CC in three networks, network with the best closeness was the network with the lowest CC's score.Smaller CC indicates the better network; means between actors in the co-authorship relation tend to be closer to each other.There is one big cluster consisting of many authors with a relatively close distance between authors (Fig. 4).This network cluster shows that the members mostly come from ITB.Where ITB's coauthorship network consists of one big cluster and several small clusters.There are 60 ITB scholars in their co-authorship network in the Mathematics and Statistics related studies area.The big cluster consists of three central authors, Baskoro E.T., Salman, A.N.M., and Miller Minka.The clusters consist of 98 authors with 510 ties of co-authorship.Each central author is connected with the other networks within this cluster.There are three authors, Ryan, J., Maryanti, T.K., and Baca, Martin, that have direct connection with all of the central author.Ten authors in the network have direct connection with Baskoro and Salman.While another big cluster in ITB's network was made up of (Pudjaprasetya, S, R) (Gunawan, Hendra) as the central authors.Those cluster is quite big with more than 10 members of authors in each cluster and the others clusters are small with 2 to 5 members.6 shows the co-authorship network where ITB is the central affiliation in the Indonesian affiliation network.ITB has direct relation with several big institution such as IPB, Airlangga University, University of Indonesia, etc.Meanwhile, ITB not have direct relation with UGM (Gadjah Mada University).In general, there are two big network in the institutional level in Indonesia, the one that centered by ITB and the others is centered by UGM.Fig. 7 shows the keyword density from an analysis of publications of Indonesian affiliation scholars.Keywords were taken from the indexed keyword of the articles.Keyword density was produced by the co-word analysis approach.Co-word analysis is on the assumption that two keywords co-occurring within different articles are an indication of a link between the articles Wu & Leu [22] and the assumption that they have the same meaning.Co-word analysis is widely used as a methodological approach to explore knowledge discovery in several fields of study.Surjandari et al. [23] mapped research themes of published articles by the top eight universities of Indonesia using co-word analysis.

Conclusion
Based on nine years data-set of international publications from Indonesian affiliated scholars in Mathematics and Statistics studies area, this research conducted a bibliometrics and scientometrics approach to examine the performance of Indonesian affiliation scholars in that area.This study showed some significant information about the performance of Indonesian affiliation authors and Indonesia academic institutions.Number of articles produced by Indonesian affiliated scholars are still low, only 426 articles during 2009-2017.Forty percent of authors are not affiliated with an Indonesia institution.ITB is the most productive institution with 138 publications from 255 authors.The most productive and efficient author has 30 articles and 79-degree centrality.
Based on macro-level measure of Social Network Analysis, co-authorship network from Indonesia affiliated scholars is a small-world network, where the network was sparse and fragmented.It was also dependent on several central authors to maintain the entire connection within the network.Based on degree distribution, the network is a scale-free network that indicates that some central authors have many connections with other authors while a majority of authors only collaborate with few authors.Coauthorship network in the Indonesian affiliation level shows there are two big cluster, ITB is the biggest network cluster, and UGM's cluster, as the second best-performed institution.Unfortunately, this two big institution are not have direct relation with each other.Co-word analysis found that there are four big cluster of keyword.

Fig. 1 .
Fig. 1.Growth rate of number of articles and authors

Fig. 2 .
Fig. 2. Distribution of articles produced by collaboration works between Indonesian affiliation scholars and foreign affiliation scholars

Fig. 4 .
Fig. 4. Co-authorship network of all Indonesian affiliation scholars published on the Mathematics and Statistics studies area Fig. 5 give the clear picture of co-authorship network for ITB scholars.There are 96 ITB scholars in their co-authorship network in the Mathematics and Statistics related studies area.Those scholars build a co-author relation with 210 scholars from 91 institutions around the world.The ITB's co-authorship network consist of one big cluster and several small clusters.

Fig. 5 .
Fig. 5. Co-authorship network of ITB's scholar published on the Mathematics and Statistics studies area

Fig.
Fig.6shows the co-authorship network where ITB is the central affiliation in the Indonesian affiliation network.ITB has direct relation with several big institution such as IPB, Airlangga University, University of Indonesia, etc.Meanwhile, ITB not have direct relation with UGM (Gadjah Mada University).In general, there are two big network in the institutional level in Indonesia, the one that centered by ITB and the others is centered by UGM.

Fig. 6 .
Fig. 6.Co-authorship affiliation network of ITB Indonesian scholars published on the Mathematics and Statistics studies area

Fig. 7 .
Fig. 7. Keyword density for Indonesian affiliation scholars published on the Mathematics and Statistics studies area

Fig. 7
Fig. 7 is the visualization of co-word analysis using VosViewer software.Red color indicates high intensity of occurrence of the keyword.In general, there are 4 big hotspots that consist of many of keyword that are correlated.In first hotspot consist of keyword that related to consistency test.The second hotspot is hyper-invariant subspace.Third is Shallow-water equation, and Helmholtz equation.Forth hotspot is related with, such as, Boxcox transformation, Newton-Raphson, Genetic Algorithm, and Mathematical model.

Table 1 .
Number of articles and authors in Mathematics/Statistics scientific publication of authors with Indonesian affiliation
Nadhiroh et.al (Mathematics and statistics related studies in indonesia using co-authorship network analysis)

Table 2 .
Number of authors and articles by affiliation (The Big 10), year 2009-2017

Table 3 .
Top 10 number of articles by Indonesian affiliation scholars, year 2009-2017

Table 4 .
Research area of Indonesian affiliation scholars articles in Mathematics and Statistics related are of studies, year 2009-2017

Table 5
shows that 12% of all articles in the Mathematics and Statistics studies area, by Indonesian affiliation scholars, were published in International Journal of Applied Mathematics 7 Statistics (19%) and JP Journal of Algebra Number Theory and Applications (3%).

Table 5 .
Journals used by Indonesian affiliation scholars to publish two or more articles in Mathematics and Statistics related area of studies, year 2009-2017

Table 6 .
Network statistics descriptive for three co-authorship networks of Indonesian affiliation scholars in Mathematics and Statistics related studies

Table 7 .
Top 10 author centrality measures for co-authorship network of Indonesian affiliation scholars (in all networks) in Mathematics and Statistics related studies