Growth and dynamics of Econophysics: A bibliometric and network analysis
HHighlights
Growth and dynamics of Econophysics: A bibliometric and network analysis
Kiran Sharma, Parul Khurana• The objective of this research is to assess the scientific development of “Econophysics” in terms of the totalnumber of studies carried out over two decades. This study analyses the growth of publications, citations, keydisciplines, journals, nations, organizations, and authors involved in information productivity and disseminationof knowledge. For the analysis, the data has been taken from the Clarivate Analytics Web of Science from2000-2019.• We have shown the dynamics of citations and self-citations with a gap of five-year intervals. Also, the contri-bution of disciplines has been measured from the cited references.• We have identified the disciplines from the cited references that have highly contributed to the development ofthe field.• We have explored the scientific collaborations networks at the micro, meso, and macro-levels to investigate thekey author’s, their affiliations, and corresponding countries, respectively.• We have demonstrated the evolution and growth of co-authorship and institutional collaborations networks overthe years. a r X i v : . [ c s . D L ] N ov rowth and dynamics of Econophysics: A bibliometric andnetwork analysis Kiran Sharma a , ∗ , Parul Khurana b a Chemical & Biological Engineering, Northwestern University, Evanston, Illinois-60208, USA b School of Computer Applications, Lovely Professional University, Phagwara, Punjab-144401, India
A R T I C L E I N F O
Keywords :EconophysicsBibliometric analysisCitations analysisScientific collaborationCo-authorship network
A B S T R A C T
Digitization of publications, advancement in communication technology, and the availability ofbibliographic data have made it easier for the researchers to study the growth and dynamics ofany discipline. We present a study on “Econophysics” metadata extracted from Web of Sciencemanaged by the Clarivate Analytics from 2000-2019. The study highlights the growth and dy-namics of the discipline by measures of a number of publications, citations on publications, otherdisciplines contribution, institutions participation, country-wise spread, etc. We investigate theimpact of self-citations on citations with every five-year interval. Also, we find the contributionof other disciplines by analyzing the cited references. Results emerged from micro, meso andmacro-level analysis of collaborations show that the distributions among authors collaborationand affiliations of authors follow a power law. Thus, very few authors keep producing most of thepapers and are from few institutions. We find that China is leading in the production of a numberof authors and a number of papers; however, shares more of national collaboration rather thaninternational, whereas the USA shares more international collaboration. Finally, we demonstratethe evolution of the author’s collaborations and affiliations networks from 2000-2019. Overallthe analysis reveals the “small-world” property of the network with average path length 5. Asa consequence of our analysis, this study can serve as an in-depth knowledge to understand thegrowth and dynamics of Econophysics network both qualitatively and quantitatively.
1. Introduction
Scientific collaborations have seen considerable growth in recent times and have emerged as an important factor forproductive and qualitative research. The citation analysis of the scientific publications have become a tool to analyzethe individual’s performance, journal’s impact as well as the discipline’s growth (Zeng, Shen, Zhou, Wu, Fan, Wangand Stanley, 2017; Radicchi, Weissman and Bollen, 2017). Bibliometrics analysis not only makes a decision on the re-searcher’s growth, in fact, it also measures the growth of a discipline. Many new interdisciplinary and multidisciplinaryfields have arisen over time which in turn have increased and strengthened the interdisciplinary collaborations (Ama-ral, Cizeau, Gopikrishnan, Liu, Meyer, Peng and Stanley, 1999; Stanley, Amaral, Canning, Gopikrishnan, Lee andLiu, 1999; Chakraborti, Raina and Sharma, 2016). One such interdisciplinary field is “Econophysics” which wascoined by H. Eugene Stanley in 1995 (Stanley and Mantegna, 2000; Chakrabarti, Chakraborti and Chatterjee, 2006;Rosser, 2008). Initially, physicists and economists contributed together to start this field and started applying theo-ries and methods of physics to address problems in economics and stock markets (Carbone, Kaniadakis and Scarfone,2007; Roehner, 2010; Chakraborti, Toke, Patriarca and Abergel, 2011; Pereira, da Silva and Pereira, 2017; Abergel,Chakrabarti, Chakraborti, Deo and Sharma, 2019). Later on, with the acceptance of the idea, scholars from other disci-plines started contributing. Before the term Econophysics was coined, many people from different branches of sciencehad worked and applied their knowledge in the field of economics leading to the evolution of Econophysics (Dash,2014).Citations play a significant role in understanding the link between scientific works (Tahamtan and Bornmann,2019). Nowadays, most of the research publications are created by teams of researchers instead of single individ-uals (Guimera, Uzzi, Spiro and Amaral, 2005). To investigate the patterns and trends of scientific collaboration, re-searchers have been working on publications data for a long time. There are different methods available in the literatureto study collaborations and among them investigating the co-authorship network is the popular one (Sun and Rahwan, ∗ Corresponding author [email protected] (K. Sharma); [email protected] (.P. Khurana)
ORCID (s):
K Sharma et al.:
Preprint submitted to Elsevier
Page 1 of 13017). A co-authorship network is a social network built on scientific collaborations, and thus it is amenable to socialnetwork analysis (Barabási et al., 2016; Singh, Vasques Filho, Jolad and O’Neale, 2020). With the development ofcomplex network theory, researchers have been using network science to re-investigate the structural properties of co-authorship networks (Price, 1965; Newman, 2001, 2003; Newman, Barabási and Watts, 2006; Zheleva, Sharara andGetoor, 2009).Over time many such networks have been studied in different domains of social aspects like the author’s collab-orations (Newman, 2001; Andrikopoulos, Samitas and Kostaris, 2016), author’s affiliations collaborations (Zhelevaet al., 2009), and countries collaborations networks (Ortega and Aguillo, 2013). Finding communities inside net-work (Good, De Montjoye and Clauset, 2010) and calculating centralities have been a major focus of social networkanalysis (Freeman, 1977; Valente, Coronges, Lakon and Costenbader, 2008). It identifies critical pointers in the net-work and often used to equate popularity and leadership. The above-mentioned social networks are either directed orundirected where nodes act as authors and edges represent the collaboration among authors. The author’s collaborationanalysis is a micro-level study however, such interactions among authors also give rise to institutional collaborationsat meso-level and cross-country collaborations at the macro-level. Investigating the co-authorships network can helpto identify entrants, leading researchers, and new collaborations. Co-authorship, institutional, and cross-country col-laboration networks jointly reveal scientific collaboration and its growth (Chakrabarti and Chakraborti, 2010; Ghosh,2013; Sinatra, Wang, Deville, Song and Barabási, 2016). This way we captured the changes in network structure atthe microscopic, mesoscopic, and macroscopic levels and identified the key leaders at all levels.The scholars have studied the econophysicists collaboration network earlier (Fan, Li, Chen, Gao, Di and Wu, 2004;Li, Wu, Fan and Di, 2007), however, to the best of our knowledge, no one has performed systematic empirical researchhighlighting the patterns in data, key disciplines by cited references, and the patterns of collaborations at micro, meso,and macro-levels. At the micro-level, an author’s collaboration, at the meso-level author’s affiliation, and at macro-level countries’ collaboration networks have been analyzed that demonstrate the in-depth knowledge of the growth ofthe discipline. This is the first time we are showing the detailed analysis of Econophysics through bibliometric andnetwork analyses which cover the gap of the previous studies accomplished on it. It demonstrates the current state ofEconophysics and provides researchers and practitioners with up-to-date knowledge. Thus, the objective of this studyis to appraise the scientific evolution of Econophysics through various factors involved in information productivity anddiffusion of knowledge.To demonstrate the progress, growth and dynamics of Econophysics, the study is organized as follows: Section 2provides the data description. Section 3 highlights the results which are further divided into three subsections: Subsec-tion 3.1 discusses the results on dynamics of citation patterns in the data and the key disciplines of the cited references.Subsection 3.2 presents a detailed discussion on the collaboration networks at micro- (3.2.1 and 3.2.2), meso- (3.2.3)and macro- (3.2.4) levels. Subsection 3.3 shows the growth of co-authorship and institutional networks over years.Section 4 concludes this study and discusses the limitations and future directions.
2. Data description
We collected the data from Web of Science managed (WoS) by Clarivate Analytics. The data mining API ( https://apps.webofknowledge.com/ ) of WoS is used to fetch the records (Bacis, 2019). We searched for the papers thatmatch the keyword
Econophysics published during 2000-2019. During 1995-1999 significant publication count is notavailable in WoS, so we could not perform the analysis since 1995. A total of 1458 records are retrieved including alldocument types. We further filtered the data based on the
Document Type and included papers which are:
Articles,Reviews, Proceedings, Editorial Material, and Book Chapter as these categories are having a sufficient number ofpapers. Hence, we finally filtered 1437 records. All records contain the full description of the paper like author name,affiliation, citations, publication journals, references, etc.To retrieve the disciplines of the cited references of each paper, first, we extracted the title of each reference andthen searched for that title in the WoS database. Not all cited references are listed in the WoS and this allowed us tomatch of the references. This way we get the list of relative disciplines of all cited references in 1437 papers. Toget the list of author’s collaborations, we identified the author’s unique ID provided by WoS (DAIS number) as therecould be two authors with the same name. Similarly, corresponding to the author’s ID, we identified the institutions.The corresponding author’s location information is extracted from the reprinting address in the paper. Many scholarshave studied the economy and the stock market behavior by using the methods of statistics, mathematics, computerscience, etc. However, the focus of our study is to select papers where physics concepts have been used to study the
K Sharma et al.:
Preprint submitted to Elsevier
Page 2 of 13 conomy and stock market behavior.
3. Results
We have presented the characterization of number of publications, citations, self-citations, etc. in Fig.1. Thenumber of papers published from 2000-2019 are reported in Fig.1(a). To show the growth of the citations and self-citations we randomly selected a few papers published from 2000-2015. The citations received by each paper over theyears since its publication is plotted cumulatively in Fig.1(b). The color code depicts the publication year. The inset ofthe figure shows the growth of self-citations received by the same set of papers over years since its publication. Fig.1(c)represents the median number of citations received by all papers published over years. The numeric value inside thebox plot represents the count for the total number of papers published in the respective year. The median number ofcitations received by papers published as
Articles , Reviews , Book Chapter , etc. is shown in Fig.1(d) and correspondingmedian self-citations is shown in Fig.1(e). The numeric value inside the plot is the number of papers published. Thebars are arranged according to the median number of citations rather than the number of publications. For example,papers published as
Articles and
Proceedings have received equal median number of citations; however, the number ofpublications as
Articles are higher than
Proceedings . On the other hand,
Review papers are less published as comparedto other document types but have received the highest median number of citations. The median self-citations receivedby
Reviews and
Articles are almost same.Fig.2 represents the dynamics of citations and self-citations over the years. Fig.2(a) shows the average age ofa paper when it has received the first citation which is not a self-citation during 2000-2019. Similarly, the averageage of a paper when it has received first self-citation is shown in Fig.2(b). On an average, the paper receives firstcitation and self-citation within the first two years after its publication. Fig.2(c) shows the overall citations and self-citations received by papers from 2000-2019. Higher the number of citations, the higher the self-citations. Duringthe first five years of a publication, the count of self-citations has increased with the increase of citations as shown inFig.2(d) (Fowler and Aksnes, 2007). This shows that during the initial year’s authors tend to cite their papers quite oftento maintain the visibility of the papers. This association decreases with the increase of the time interval (Fig.2(e-f)).
To understand which disciplines have contributed more to the growth of Econophysics, we analyzed the referencescited by each paper. We retrieved the disciplines of all the cited references and analyzed the contribution of disciplines.Fig.3(a) highlights the disciplines according to the number of cited references (in % ). It is evident that major referenceswere quoted from Physics followed by
Economics which clearly represents the true nature of Econophysics. Theproportion of physics references also revealed the major contribution of physicists’ in the field. Fig.3(b) highlightsthe journals based on the median number of citations received by the papers. The bars are arranged according tothe median of citations rather than the number of citations.
Physica A has published more papers (739) than
PhysicsReview E (34); however,
Physics Review E has received higher the median number of citations (20) than
Physica A (10). The first few journals are also physics-based journals where papers have gained higher citations.
Here we presented the scientific collaborations at micro, meso, and macro-level.
In the co-authorship network (Fan et al., 2004), we have constructed an undirected weighted network consistsof 1834 nodes and 4590 edges (3137 unique edges) as shown in Fig.4(a), where nodes correspond to authors andedges represent the collaboration (when two or more authors write a paper together). Single-authored articles areexcluded from the data set since they do not contribute to the co-authorship network. The first five largest connectedcomponents of the network are colored differently. The giant component (colored in purple) contains the of thetotal nodes of the network. The giant component is further elaborated in Fig.5. The second-largest component (coloredin green) contains nodes, and so on (see network statistics table in Fig.4). It is often perceived that certain authorsare actively engaged in collaboration than others. Fig.4(b-c) shows the complementary cumulative density function(CCDF) of the degree of the nodes and edges strength which represents the author’s collaborations and the strengthof the collaboration. The power-law behavior of CCDF shows that there are few authors who share a large number K Sharma et al.:
Preprint submitted to Elsevier
Page 3 of 13a) (b)(c)(d) (e)
Figure 1: Characterizing publications, citations, and self-citations. (a) Total number of papers published during 2000-2019. (
Inset ) Probability density of the number of papers. (b) Yearly citations growth for a few randomly selected paperspublished between 2000 and 2015. (Inset)
Cumulative plot of the number of self-citations received. The color codecorresponds to the publication year of each paper. (c) Citations received by papers published over years. The numberinside the box shows the publication count corresponding to years. (d) The median number of citations received by differentdocuments published during 2000-2019. The numeric value inside the box is the total number of published papers in thatdocument category. (e) The fraction of self-citations received by each document category. of collaborations. The CCDF’s of the cluster size or connected components are shown in Fig.4(d). The power-lawbehavior of the cluster size distribution clearly shows that only one component contains a large number of nodes. Inthe network, of nodes have clustering coefficient 1, and have 0. The highest clustering coefficient representshow well the nodes are connected to their neighbors. The highest average clustering coefficient (0.87) shows thatalmost everyone is connected to others in the network. Fig.4(e) shows the relation between the number of authors andthe number of papers published by them. A few authors have published more than 10 papers, whereas a large numberof authors have published less than 10 papers. Also, how big is the team size of authors is studied in Fig.4(f). Themajority of the papers are either published as a single author or two authors. There are few papers that have beenwritten by 7 to 8 authors which is also the largest team size. Fig.4(g) shows the evolution of team size in scientificcollaborations (Guimera et al., 2005). Over the years the team size fluctuates from an average of 2 to an average of 3.
Fig.5(a) shows the zoomed-in view of the giant component of the co-authorship network extracted from Fig.4(a).A modularity maximization algorithm is used to find out the communities inside the giant component (Chen, Kuzminand Szymanski, 2014). Different colors represent different communities in the giant network. There is a total of 17
K Sharma et al.:
Preprint submitted to Elsevier
Page 4 of 13a) (b) (c)(d) (e) (f)
Figure 2: Dynamics of citations and self-citations over the years. (a) Average age of the paper when it has received firstcitations which is not a self-citation during 2000-2019. (b) The average age of the paper when it has received the firstself-citation. (c) A number of citations and self-citations received by papers from 2000-2019. (d) Relationship betweenthe citations and self-citations received by each paper in the first five years after publication. (e-f) Five-five years’ timeinterval behavioral change in citations and corresponding self-citations.(a) (b)
Figure 3: Key disciplines by cited references and publication journals. (a) Bar plot shows the number of times (in % )a reference has been cited from a discipline. of the references are cited from physics discipline and are fromeconomics, which clearly depicts the true nature of Econophysics. (b) The median number of citations received by differentjournals that published Econophysics papers. The numeric value inside the box is the total number of published papers.The bars are arranged according to the median of citations rather than the number of citations. The majority of the papersare published in physics journals. communities in the network and the node with the highest number of connections is labeled with the author’s name.Also, the average path length of the network is 5.3 which reveals the “small-world” property of the network (Wattsand Strogatz, 1998). In the community of econophysicists’, everyone is connected to others in ≈ K Sharma et al.:
Preprint submitted to Elsevier
Page 5 of 13a) (b) (c) (d)(e) (f) (g)
Figure 4: Co-authorship network. (a) An undirected weighted co-authorship network having 1834 nodes and 4590 edges(3137 unique edges). The nodes represent authors and edges represent the collaboration among authors. We have filteredthe self-loops in the network representation. The size of the node corresponds to the weighted degree of the node and thewidth of the edge represents the strength of the collaboration. Different colors represent the first five largest connectedcomponents. The giant component (colored in purple) contains 547 nodes which are of the total nodes of the network.(b-d) The statistical properties of the network as complementary cumulative density functions (CCDF’s): weighted degree,edge weight, and cluster size, respectively. (e) Number of papers published by authors represents the contribution ofauthors in the field. A few authors have published a large number of papers. (f) Papers published by teams of varyingsizes. (g) Time evolution of the typical number of team members. The red line represents the average team size. Thetable shows the network statistics. The network is constructed in
Gephi 0.9.2 . After the institutionalization of Econophysics in 1995, many reputed institutes have initialized research on it andsome institutes have started courses on it (Dash, 2015; Ortega and Aguillo, 2013). To investigate the contribution ofdifferent institutions, an undirected weighted authors’ affiliations (institutions) network is constructed (see Fig.6 (a)).The network consists of 1059 institutions/universities and shows 2817 possible collaborations between institutionsacross the globe. Self-loops are removed while plotting the network, however, included in the analysis. The giantcomponent (colored in dark pink) contains of the network nodes shown in Fig.6(b) as CCDF of cluster size.Fig.6(c-d)) show the CCDF’s of nodes degree and edges strength, respectively. Fig.6 (e) shows the number of authors
K Sharma et al.:
Preprint submitted to Elsevier
Page 6 of 13a) (b)(c) (d) (e)
Figure 5: A giant component of the co-authorship network. (a) A zoomed-in view of the giant component. A modularitydetection algorithm has been used to detect the communities among the network. The node with the largest connectivityis labeled by the author’s name. (b) Degree versus the average local clustering coefficients of the nodes. On an averagenodes of higher degrees exhibit lower local clustering. (c) Degree versus average betweenness centrality of the nodes.Nodes with higher betweenness centrality represent the potential key authors and nodes with higher degree represent hubsin the network. It highlights that the nodes with the highest degree act as the bridge to compute the shortest-path amongall nodes in the network. (d) Degree versus average closeness centrality of the nodes. On an average, nodes of higherdegrees share a low closeness. (e) Degree versus average eigencentrality of the nodes. The eigencentrality measures theprestige of the node in the network. On an average, nodes of higher degrees have higher prestige. The table shows thenetwork statistics. The network is constructed in
Gephi 0.9.2 . corresponding to the number of institutions working on Econophysics. A large number of authors belong to a fewinstitutions. The top two institutions in terms of the number of authors and collaborations are East China Universityof Science and Technology (ECUST) and
Boston University . ECUST produces a large number of authors, whereasBoston University shares a large number of collaborations (see Table 2 for institutions details).
To visualize the expansion of the econophysicists’ across the globe we have studied the geolocations of authors.Fig.7(a) represents the number of authors in different countries’ (in % ) working on Econophysics. The violet-coloredbars represent the corresponding authors who lead the projects and cyan colored bars represent the co-authors of thepapers. Here, we displayed results only for few countries’ as per the number of corresponding authors. China is leadingin terms of the number of corresponding as well as co-author’s participation. Fig.7(b) highlights the number of paperspublished by the number of authors in the respective countries. The results are presented in 71 countries. The trendreveals the signature of scaling behavior in terms of the author’s publications across the globe. Further, an undirectedweighted network of countries’ with 71 nodes and 1716 edges is constructed in Fig.7(c). There are self-loops presentin the network which correspond to either a single author paper or collaboration among the same country. The size ofthe node represents the number of authors in the respective country and the edge width represents the number of timesa collaboration occurred. Results highlight a strong collaboration between the USA and France; however, the number K Sharma et al.:
Preprint submitted to Elsevier
Page 7 of 13a) (b)(c) (d) (e)
Figure 6: Author’s affiliations network. (a) An undirected weighted network of institutions having 1059 nodes and2817 edges (1924 unique edges) where nodes represent the institutions and edges represent the collaboration among theinstitutes across the globe. The giant component (colored in dark pink) comprises of the nodes. The instituteswith strong collaborations are labeled with the names. There is an isolated institution in the network that correspondsto within institution collaboration; however, we have filtered the self-loops in the network representation. The size of thenode represents the weighted degree and the width of the edge represents the collaboration strength. (b) CCDF of clustersize. (c) CCDF of nodes degree. (d) CCDF of edges strength. (e) A number of authors corresponding to a number ofinstitutions. A large number of authors correspond to a few institutions. The table shows the network statistics. Thenetwork is constructed in
Gephi 0.9.2 . of authors is higher in the USA rather than in France which shows there might be a small but active communityof researchers in the field. We also find that the within-country collaboration is more active as compared to cross-country. Hence, China, the USA, Italy, Japan, Germany, France, etc. have a large number of authors, a large numberof publications, and strong connectivity/ collaboration among them (self-loops not shown in-network). We can saythat these leading countries’ are driving the discipline, however, other countries are also contributing to the growth ofthe discipline and getting connecting to the leading countries. Fig.7(d) shows the evolution of the cumulative growthof international and national collaborations. Results highlights that national collaboration is higher than internationalcollaborations. China shares more nationals, whereas the USA shares more international collaborations. There is adip in the international collaborations trend during 2007-2008, this was the time when the stock market crashed dueto the bankruptcy of Lehman Brothers. The evolution of fundamental statistical properties of the scientific collaboration networks in terms of the averagedegree of the nodes ( < 𝑘 > ), average clustering coefficient ( < 𝑐𝑐 > ), and size of the giant component (GC(%)) during2000-2019 is shown in Fig.8. The evolution of the co-authorship network is shown in Fig.8(a) where the time seriesof network growth and a number of connected components shares a high amount of correlation (0.94). Similarly, theevolution of the author’s affiliation network is shown in Fig.8(b) where the time series of network growth and a numberof connected components also shares a high amount of correlation (0.87). The evolution of the network’s average
K Sharma et al.:
Preprint submitted to Elsevier
Page 8 of 13a) (b)(c) (d)
Figure 7: countries collaborations network. (a) Number of papers published as a corresponding author (colored violet)and as one of the authors (colored cyan) listed for few countries. The countries are arranged in descending order based onthe number of corresponding authors. (b) Scattered plot for 71 countries representing the number of papers published byauthors. (c) An undirected weighted network of countries corresponding to the author’s location contains 71 nodes and1716 edges (310 unique edges) where nodes represent countries and edges represent the scientific collaboration. There area few isolated countries too. For simplicity, we filtered the self-loops from the network representation which correspond towithin the country collaboration. The size of the node represents the weighted degree and the color gradient of the nodesvaries according to the degree. The edge width represents the number of connections/collaborations among the nodes.The cross-country network shows the countries that have strong ties among them. (d) The evolution of the cumulativegrowth of international and national collaborations. The table shows the network statistics. The network is constructedin
Gephi 0.9.2 . degree, average clustering coefficient, and size of the giant component (in%) are shown for both the co-authorship andaffiliations networks in Fig.8(c-e), respectively. On an average, the degree of the co-authorship network varies between2 to 3, and the clustering coefficient varies between 0.6 to 0.8. Similarly, on an average, the degree of the affiliationsnetwork varies between 1 to 3 and the clustering coefficient varies between 0.2 to 0.6 over years. The average pathlength of the network lies between 2 to 3 which reveals the “small-world” behavior of the network at every time step.A higher average clustering coefficient shows that nodes are grouped into communities.
4. Discussion and conclusion
We have presented the detailed analysis of “Econophysics” in terms of the evolution and structure of collabo-rations networks from 2000-2019. We have performed a systematic empirical research highlighting the patterns indata, key disciplines by cited references, and the patterns of collaborations at micro, meso, and macro-levels. The key
K Sharma et al.:
Preprint submitted to Elsevier
Page 9 of 13a) (b)(c) (d) (e)
Figure 8: Network growth over the years. (a-b) Size of the network and number of connected components of co-authorshipand institutional networks over years, respectively. The time series of network size evolution is highly correlated with thetime series of the evolution of the number of connected components for both the networks. (c-e) Growth of co-authorshipnetwork and affiliation network over years: (c) average degree, (d) average clustering coefficient, and (e) size of the giantcomponent (in %). findings of the study are: (i) The impact of self-citations on citations reveals that in first few years the publicationshave received more self-citations and this trend goes down with time. Also, on an average a paper has received firstself-citations in first two years after the publication. (ii) The disciplines extracted from cited references from all pub-lished papers highlights the higher contribution of physics and second highest of economics . The higher contributionof physicists’ towards the growth of Econophysics reveals the true nature of the discipline. (iii) The co-authorshipnetwork at micro-level identifies the key authors and their contributions as an individual or in group. Also, the numberof papers contributed by teams of varying sizes and the evolution of the team size over time is presented. We identi-fied communities inside the giant component of the network and presented the relationships among nodes degrees andcentrality measures (betweenness, closeness and eigencentrality). (iv) We also explored the authors’ affiliations andcountry collaborations at meso and macro level. Results highlight that large number of authors are affiliated to a fewnumbers of institutions and China and USA has produced the higher authors as well as institutions. In terms of nationaland international collaborations, China share more national and USA shares more international collaborations. (v) Fi-nally, the author’s collaborations and affiliations networks are explored in terms of average degree, average clusteringcoefficient, average path length, size of giant component, etc. to study the networks evolution with a yearly resolution.To conclude further, our study has provided an integrated view of citation dynamics and the growth of scientificcollaborations networks of Econophysics metadata from 2000-2019. Our study justified the highest contribution ofphysicists’ towards the field and to spread the visibility of the discipline, we suggest authors should publish more ininterdisciplinary journals. However, the low number of publications reported under the Econophysics domain in Webof Science points out as a limitation of the study which further leads to the absence of the significant contribution offew authors. A possible future direction to extend the study is to integrate temporal data and quantify the evolutionprocess of the co-authorship network and affiliations network (Börner, Maru and Goldstone, 2004). This could revealhow the importance of an author varies with time at different stages in his/her career.
Acknowledgment
This work greatly benefited from discussions with and comments from A. Chakraborti and H. K. Pharasi. Thiswork uses Web of Science data by Thomson Reuters provided by the Northwestern University.
K Sharma et al.:
Preprint submitted to Elsevier
Page 10 of 13 able 1
List of 50 authors based on the degree (collaboration). The table shows the Author name. country, affiliation, number ofcollaboration ( 𝑘 ), and clustering coefficient ( 𝑐𝑐 ). S.No.
Country Author Affiliation 𝑘 𝑐𝑐
S.No.
Country Author Affiliation 𝑘 𝑐𝑐 USA Stanley, HE Boston University 56 0.07 China Gu, GF East China University ofScience & Technology 15 0.45 China Zhou, WX Chinese Academy of Sciences 39 0.13 South Korea Jung, WS Pohang University ofScience & Technology 15 0.34 Japan Takayasu, H Sony ComputerScience Laboratories 31 0.13 USA Johnson, NF University of Miami 15 0.16 Italy Mantegna, RN University of Palermo 26 0.17 England Schinckus, C University Leicester Finance 14 0.26 China Ren, F E China University ofScience & Technology 25 0.22 China Jiang, XF Collaborat InnovatCtr Adv Microstruct 13 0.32 Belgium Ausloos, M University of Liege 24 0.10 China Zheng, B Collaborat InnovatCtr Adv Microstruct 13 0.26 England Di Matteo, T Kings College London 23 0.13 China Zhang, W Tianjin University 13 0.59 Switzerland Sornette, D Swiss Finance Institute 22 0.10 Croatia Podobnik, B University of Rijeka 13 0.24 Japan Takayasu, M Tokyo Institute of Technology 22 0.19 England Preis, T University College London 13 0.33 Japan Kaizoji, T Int Christian University 21 0.20 India Chakrabarti, BK Saha Institute of Nuclear Physics 13 0.24 USA Yakovenko, VM University of Maryland 21 0.18 Ireland McCauley, JL NUI Galway 13 0.26 China Qiu, T Nanchang Hangkong University 20 0.24 Japan Mizuno, T University of Tsukuba 13 0.33 Ireland Richmond, P Univ Dublin Trinity College 19 0.17 South Korea Kim, SY Korea Advance Institute ofScience & Technology 13 0.24 Italy Gallegati, M Univ Politecn Marche 19 0.22 Australia Aste, T Australian National University 12 0.21 South Korea Lee, JW Inha University 19 0.15 China Wang, GJ Hunan University 12 0.26 Canada Li, SP University of Toronto 17 0.20 China Xie, C Hunan University 12 0.30 China Jiang, ZQ East China University ofScience & Technology 17 0.33 South Korea Yang, JS Korea University 12 0.36 China Huang, JP Fudan University 17 0.23 South Korea Moon, HT Korea Advance Institute ofScience & Technology 12 0.41 China Xiong, X Tianjin University 17 0.40 Germany Mimkes, J University of GesamthschPaderborn 11 0.36 Japan Takahashi, T University of Tokyo 17 0.15 South Korea Kim, S Korea Advance Institute ofScience & Technology 11 0.29 China Zhong, LX Dianzi University 16 0.33 South Korea Oh, G Pohang University ofScience & Technology 11 0.31 China Chen, W Shenzhen Stock Exchange 16 0.42 USA Amaral, LAN Northwestern University 11 0.46 England Scalas, E University of Sussex 16 0.15 China Yang, G Fudan University 10 0.49 Italy Lillo, F Scuola Normale Super Pisa 16 0.37 China Zhang, YJ Tianjin University 10 0.51 Japan Fujiwara, Y University of Hyogo 16 0.30 India Chakraborti, A Jawaharlal Nehru University 10 0.29
CRediT authorship contribution statement
Kiran Sharma:
Conceived and designed the analysis; Collected the data; Contributed data or analysis tools;Performed the analysis; Writing - original draft.
Parul Khurana:
Collected the data; Contributed data or analysistools; Performed the analysis; Writing - review.
References
Abergel, F., Chakrabarti, B.K., Chakraborti, A., Deo, N., Sharma, K., 2019. New Perspectives and Challenges in Econophysics and Sociophysics.Springer.Amaral, L.A., Cizeau, P., Gopikrishnan, P., Liu, Y., Meyer, M., Peng, C.K., Stanley, H., 1999. Econophysics: can statistical physics contribute tothe science of economics? Computer Physics Communications 121, 145–152.Andrikopoulos, A., Samitas, A., Kostaris, K., 2016. Four decades of the journal of econometrics: Coauthorship patterns and networks. Journal ofeconometrics 195, 23–32.Bacis, E., 2019. enricobacis/wos. URL: https://github.com/enricobacis/wos .Barabási, A.L., et al., 2016. Network science. Cambridge university press.Börner, K., Maru, J.T., Goldstone, R.L., 2004. The simultaneous evolution of author and paper networks. Proceedings of the National Academy ofSciences 101, 5266–5273.Carbone, A., Kaniadakis, G., Scarfone, A.M., 2007. Where do we stand on econophysics?Chakrabarti, B.K., Chakraborti, A., 2010. Fifteen years of econophysics research. arXiv preprint arXiv:1010.3401 .Chakrabarti, B.K., Chakraborti, A., Chatterjee, A., 2006. Econophysics and sociophysics: trends and perspectives. John Wiley & Sons.Chakraborti, A., Raina, D., Sharma, K., 2016. Can an interdisciplinary field contribute to one of the parent disciplines from which it emerged? TheEuropean Physical Journal Special Topics 225, 3127–3135.Chakraborti, A., Toke, I.M., Patriarca, M., Abergel, F., 2011. Econophysics review: I. empirical facts. Quantitative Finance 11, 991–1012.Chen, M., Kuzmin, K., Szymanski, B.K., 2014. Community detection via maximization of modularity and its variants. IEEE Transactions onComputational Social Systems 1, 46–65.Dash, K.C., 2014. Evolution of econophysics, in: Econophysics of Agent-Based Models. Springer, pp. 235–285.
K Sharma et al.:
Preprint submitted to Elsevier
Page 11 of 13 able 2
List of 50 institutes based on the degree (collaboration). The table shows the institute name, number of collaborations( 𝑘 ) and number of authors ( S.No.
Institutes 𝑘 S.No.
Institutes 𝑘 Boston University, USA 56 30 University of Evora, Portugal 14 3 East China University ofScience & Technology, China 36 38 CNRS, France 13 3 University of Palermo, Italy 34 13 Saha Institute of NuclearPhysics, India 13 10 University Buenos Aires, Argentina 26 5 Sony Compter Science Labs, Japan 13 2 University of Tokyo, Japan 25 17 Swiss Federal Institute ofTechnology, Switzerland 13 6 Int Christian University, Japan 23 2 Trinity College Dublin, Ireland 13 6 University of Leicester, England 23 8 Federal University ofRio Grande do Sul, Brazil 13 6 Santa Fe Institute, USA 22 9 University of Pavia, Italy 13 3 UCL, England 21 8 Artemis Capital AssetManagement GmbH, Germany 12 1 Kyoto University, Japan 19 7 Kings College London, England 12 10 Tokyo Institute of Technology, Japan 19 13 Korea University, South Korea 12 3 Aalto University, Finland 18 7 Peking University, China 12 9 Ist Nazl Fis Nucl, Italy 18 2 Tel Aviv University, Israel 12 6 Korea Advance Institute ofScience & Technology, South Korea 18 11 University of Catolica Brasilia, Brazil 12 3 University of Wroclaw, Poland 18 7 University of ElectronicScience and Technology, China 12 7 University Maryland, USA 17 5 University of Fed Alagoas, Brazil 12 8 Bar Ilan University, Israel 16 4 University of Kiel, Germany 12 3 University Cologne, Germany 16 6 University of Piemonte Orientale, Italy 12 2 Kanazawa Gakuin University, Japan 15 2 University of Politecn Madrid, Spain 12 6 National University of Singapore 15 5 University of Porto, Portugal 12 6 University of CaliforniaLos Angeles, USA 15 1 Budapest University ofTechnology & Economics, Hungary 11 7 University Politecn Marche, Italy 15 2 Pohang University ofScience & Technology, South Korea 11 5 Complexity Science HubVienna, Austria 14 3 University of Adelaide, Australia 11 2 Consejo Nacl InvestCient & Tecn, Argentina 14 3 University of Liege, Belgium 11 1 ETH, Switzerland 14 6 Zhejiang University, China 11 27
Dash, K.C., 2015. Judging the impact of ‘econophysics’ through response to questionnaire, in: Econophysics and Data Driven Modelling of MarketDynamics. Springer, pp. 327–348.Fan, Y., Li, M., Chen, J., Gao, L., Di, Z., Wu, J., 2004. Network of econophysicists: a weighted network to investigate the development ofeconophysics. International Journal of Modern Physics B 18, 2505–2511.Fowler, J., Aksnes, D., 2007. Does self-citation pay? Scientometrics 72, 427–437.Freeman, L.C., 1977. A set of measures of centrality based on betweenness. Sociometry , 35–41.Ghosh, A., 2013. Econophysics research in india in the last two decades. IIM Kozhikode Society & Management Review 2, 135–146.Good, B.H., De Montjoye, Y.A., Clauset, A., 2010. Performance of modularity maximization in practical contexts. Physical Review E 81, 046106.Guimera, R., Uzzi, B., Spiro, J., Amaral, L.A.N., 2005. Team assembly mechanisms determine collaboration network structure and team perfor-mance. Science 308, 697–702.Li, M., Wu, J., Fan, Y., Di, Z., 2007. Econophysicists collaboration networks: Empirical studies and evolutionary model, in: Econophysics ofMarkets and Business Networks. Springer, pp. 173–182.Newman, M.E., 2001. Scientific collaboration networks. i. network construction and fundamental results. Physical review E 64, 016131.Newman, M.E., 2003. The structure and function of complex networks. SIAM review 45, 167–256.Newman, M.E., Barabási, A.L.E., Watts, D.J., 2006. The structure and dynamics of networks. Princeton university press.
K Sharma et al.:
Preprint submitted to Elsevier
Page 12 of 13 rtega, J.L., Aguillo, I.F., 2013. Institutional and country collaboration in an online service of scientific profiles: Google scholar citations. Journalof Informetrics 7, 394–403.Pereira, E.J.d.A.L., da Silva, M.F., Pereira, H.d.B., 2017. Econophysics: Past and present. Physica A: Statistical Mechanics and its Applications473, 251–261.Price, D.J.D.S., 1965. Networks of scientific papers. Science , 510–515.Radicchi, F., Weissman, A., Bollen, J., 2017. Quantifying perceived impact of scientific publications. Journal of Informetrics 11, 704–712.Roehner, B.M., 2010. Fifteen years of econophysics: worries, hopes and prospects. arXiv preprint arXiv:1004.3229 .Rosser, J.B., 2008. Econophysics .Sinatra, R., Wang, D., Deville, P., Song, C., Barabási, A.L., 2016. Quantifying the evolution of individual scientific impact. Science 354.Singh, C.K., Vasques Filho, D., Jolad, S., O’Neale, D.R., 2020. Evolution of interdependent co-authorship and citation networks. Scientometrics ,1–20.Stanley, H.E., Amaral, L.A.N., Canning, D., Gopikrishnan, P., Lee, Y., Liu, Y., 1999. Econophysics: Can physicists contribute to the science ofeconomics? Physica A: Statistical Mechanics and its Applications 269, 156–169.Stanley, H.E., Mantegna, R.N., 2000. An introduction to econophysics. Cambridge University Press, Cambridge.Sun, L., Rahwan, I., 2017. Coauthorship network in transportation research. Transportation Research Part A: Policy and Practice 100, 135–151.Tahamtan, I., Bornmann, L., 2019. What do citation counts measure? an updated review of studies on citations in scientific documents publishedbetween 2006 and 2018. Scientometrics 121, 1635–1684.Valente, T.W., Coronges, K., Lakon, C., Costenbader, E., 2008. How correlated are network centrality measures? Connections (Toronto, Ont.) 28,16.Watts, D.J., Strogatz, S.H., 1998. Collective dynamics of ‘small-world’networks. nature 393, 440–442.Zeng, A., Shen, Z., Zhou, J., Wu, J., Fan, Y., Wang, Y., Stanley, H.E., 2017. The science of science: From the perspective of complex systems.Physics Reports 714, 1–73.Zheleva, E., Sharara, H., Getoor, L., 2009. Co-evolution of social and affiliation networks, in: Proceedings of the 15th ACM SIGKDD internationalconference on Knowledge discovery and data mining, pp. 1007–1016.
K Sharma et al.: