WORKSHOP Analisi delle Reti Sociali per conoscere uno strumento uno strumento per conoscere

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1 Università di Salerno WORKSHOP Analisi delle Reti Sociali per conoscere uno strumento uno strumento per conoscere The scientific collaboration network of the University of Salerno Michele La Rocca, Giuseppe Giordano, Maria Prosperina Vitale DiSES, Università di Salerno Fisciano, 30 novembre 2007

2 Outline Scientific Collaboration and Social Network Analysis (SNA) Some Statistical Remarks A Case study: the co-authorship network of the Economics and Statistics Department at the University of Salerno Data structure e Matrix definition Net characteristics of scientific collaboration Collaborative Groups and style of co-authorship Some concluding remarks and further developments

3 The Theme Co-autorship in a Scientific Community The Data The Framework Affiliation Matrix; Adjacency Matrix Attribute Matrix; Contingency Table The Aims to detect patterns in the Net structure where the researchers are connected according to the number of papers published together. to discover homogeneous groups of Authors characterized by different styles in the scientific collaboration. to describe the degree distributions of the papers per authors, and authors per paper

4 The scientific collaboration and SNA The study of the collaboration networks is one of the traditional areas of interest in SNA (Krichel et al., 1996; Newman, 2001a, b, c, 2004; Barabasi et al., 2002). The current literature focuses on the effectiveness of the network to define models and examine patterns of cooperation in the scientific community and to describe the various roles of researchers in a network. It has long been realized that the co-authorship of articles in learned journals provides a window on patterns of collaboration within the academic community. (Newman, 2004) The time evolution of coauthorship networks has also been investigated by several authors dealing with the preferential attachment" hypothesis. (Vazquez, 2003 )

5 The scientific collaboration: collect data Two points of view to collect data from a scientific community: Co-authorship patterns (i.e., two scientists are connected if they have coauthored a paper together). The nodes in a co-authorship network represent authors and two authors are connected by a line if they have coauthored one or more papers. Co-citation patterns (i.e., connections between authors established via the citation of their works in the same literature). The nodes in a citation network are papers, and the links are citations (Newman, 2004)

6 Looking at the co-authorship network distance between authors to assess the attitude to collaborate and to identify the peculiar styles of collaborations (Batagelj, Mvar, 2000; Chirita et al., 2005; Said, 2007). existence and size of a giant component degree distribution of the quantities including the numbers of papers per authors, numbers of authors per paper, numbers of collaborators per author to model the overall mechanism of growing in the network, especially in the Physical Sciences, the Power-Law Degree Distribution has been considered existence and shape of a particular growth mechanism Preferential Attachment (BA model, Barabasi 20002)

7 The scientific community at the University of Salerno Electronic Data base: Archive of the published papers produced by the 59 researchers in the Economics and Statistics Department of the University of Salerno. Period: Number of the papers: 681 Relational Data Structure: Affiliation Matrix Paper*Authors Descriptive measures: Numbers of papers per author, Number of authors per paper.

8 Relational Data Structure Affiliation Matrix: Paper Author Adjacency Matrix: Author Author (two scientists are connected if they have coauthored a paper) In particular, we know - how many papers each pair of scientists has published during the period under observation n1 n2 n3. ni... ng n1 n2 n3. ni... ng E1 E2 Ej Eh n1 n2 n3. ni... ng Vertices in the net: Authors Edge/Tie: writing a paper together

9 Data Pre-treatment and Coding Drawbacks: two authors may have the same name; authors may identify themselves in different ways on different papers; Kind of publication can be reported differently by co-authors (Newman, 2001) External Attribute Information: Scientific Field; Academic Position; Department and Faculty membership How to deal with Outers Authors Shrink Component

10 Centrality Measures of centrality, such as closeness, betweenness, Inside the circle= high value of centrality index On the circle = low value of centrality index Betweenness centrality Accademic Position Red = Assistant Professor Blue = Associate Professor Yellow = Full Professor the betweenness of an actor i, is an indicator of who the most influential people in the network are, the ones who control the flow of information between most others.

11 Centrality Measures of centrality, such as closeness, betweenness, Inside the circle= high value of centrality index On the circle = low value of centrality index Closeness centrality Accademic Position Red = Assistant Professor Blue = Associate Professor Yellow = Full Professor The closeness centrality analyzes centrality structure of a network based on geodesic distances among the nodes. Closeness centrality is measured by the inverse of the sum of distances from a node to all the other nodes.

12 Exploring the scientific network Co-authors Net Yellow = Statistics Red = Mathematics Blue = Economics Green = Other disciplines Working by alone Outer Collaborative Group Brokers Group High inner specialised collaborative groups High collaborative group

13 Looking for structures in the net: groups Clustering of the Authors based on the Adjacency Matrix Three Main groups Outer Collaborative Group and Working by alone High collaborative group High inner specialised collaborative group

14 Looking for a productivity index The Equivalence Regular (REGGE) explores the role-set structure of a network based on the similarity of tie-profiles among its nodes. Lower productivity Higher productivity

15 Looking for a productivity index The Equivalence Regular (REGGE) explores the role-set structure of a network based on the similarity of tie-profiles among its nodes. Scientific Field Yellow = Statistics Red = Mathematics Blue = Economics Green = Other disciplines Lower productivity Higher productivity

16 Looking for association structures (1) Paper classification and Scientific Fields Grafico simmetrico (assi F1 e F2: %) SECS-S/05 SECS-P/12 SECS-S/06 Altro SECS-P/10 SECS-P/05 F2 (27.36 % 0 SECS-S/03 Proceedings SECS-S/01 no dises SECS-P/01 Articolo su rivista -0.5 SECS-P/02 M-GGR/02 Articolo su libro M onografia SECS-S/04 AGR/01 SECS-P/06 Curatele SECS-P/ F1 (48.28 %)

17 Looking for association structure (2) Academic position and year of Publication of the papers Grafico simmetrico (assi F1 e F2: %) 0.2 F2 (23.23 % Ordinario no dises Associato 2000 Ricercator 2004 Strao rdinario F1 (62.07 %)

18 Looking for association structure (3) Year of publication of the papers and Paper classification Grafico simmetrico (assi F1 e F2: %) Altro M onografia Articolo su rivista 2005 F2 (35.67 % Proceedings Articolo su libro Curatele F1 (45.30 %)

19 Degree Distribution: Preliminary Results The Theory of the SMALL WORLD In general, real networks are characterised by a small average minimum path distance and a large clustering coefficient We can reach every vertex in the graph by crossing a small number of edges (Watts & Strogatz) The Theory of Barabasi-Albert Growing nature and preferential attachment lead to power-law degree distribution

20 Mean Papers per Author (DiSES) = 15,8 Preliminary Results degree distributions of the authors per paper Mean Authors per Paper = 1,8 degree distributions of the papers per author Papers per author Papers per author (group I) Ricercatori Papers per author (group II) Associati Papers per author (group III) Ordinari Mean Papers per Author= 11,0 Mean Papers per Author= 15,7 Mean Papers per Author= 21,2

21 Concluding Remarks & Further Developments Highlight differences in the patterns of scientific collaboration in others Departments of the University of Salerno Departments in the same University In different University How do we model the evolution of the network? What if we experience clustering hierarchy? We suggest to use mixture distribution to model degree

22 References Barabasi A.L., Jeonga H., Neda Z., Ravasza E., Schubert A., Vicsekb T. (2002), Evolution of the social network of scientific collaborations, Physica A, 311, Batagelj V., Mrvar A. (2000), Some analyses of Erdos collaboration graph, Social Networks, 22, Chirita P.A., Damian A., Nejdl W., Siberski W. (2005), Search Strategies for Scientific Collaboration Networks, in Proceedings of the P2P Information Retrieval Workshop, 14th ACM International Conference on Information and Knowledge Management (CIKM), Bremen, Germany. Dorogotsev S.N., Mendes J.F.F. (2000), Evolution of networks with aging of sites, Phys. Rev. E, 62, Krichel T., Bakkalbasi, N. (2006), A social network analysis of research collaboration in the economics community, in Proceedings the International Workshop on Webometrics, Informetrics and Scientometrics & Seventh COLLNET Meeting, Nancy (France). Newman M. E. J. (2001a), The structure of scientific collaboration networks, Proc. Natl. Acad. Sci. USA 98, pp Newman M. E. J. (2001b), Scientific collaboration networks. I. Network construction and fundamental results, Physical Review E, 64, Newman M. E. J. (2001c), Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality, Physical Review E, 64, Said, Y.H. Wegman, E.J. Sharabati, W.K., Rigsby J.T. (2007), Implications of Co-author Networks on Peer Review, in Proceedings of Classification and Data Analysis, EUM Edizioni Università di Macerata. Vazquez, A. (2003), Growing network with local rules: Preferential attachment, clustering hierarchy, and degree correlations, Physical Review E, vol. 67, Issue 5,