Modelling of Scientific Collaboration based on Graphical Analysis Veslava Osinska 1 , Grzegorz Osinski 2 and Wojciech Tomaszewski 2 1 wieo@umk.pl Nicolaus Copernicus University, Institute of Information Science and Book Studies ul. Bojarskiego 1, 87-100 Torun (Poland) 2 grzegorz.osinski@wsksim.edu.pl; wojciech.tomaszewski@wsksim.edu.pl Institute of Computer Science, College of Social and Media Culture sw. Jozefa 23/35, 87-100 Torun (Poland) Introduction An analysis of the interrelationships between elements within dynamic structure typically involves perturbation methods based on the minimum energy. In result, the researchers use minimum distance-based algorithms and therefore the shortest path between the various components of the system. However, the history of science development shows that collaboration between the researchers in different disciplines becomes effective and fruitful when scientific explorations do not follow the “shortest possible” roads. In current work authors present a novel approach, how to analyse and evaluate the possible collaborations ways in a small team of researchers (number of nodes is less than 100) participating in the project network KnowEscape COST Action. 1 Data, metrics and assumption Analysed dataset consists of 83 records characterized each member of COST network. Input data organized in 83x83 matrix, describe two years collaboration within such activities as: mobility, events organization, publishing (also for former years) and project management. The dataset was gathered using KnowEscape website (knowescape.org), ResearchGate and Mendeley services. To describe the mutual relationships between members the graph based on Mycielski concept was constructed (Larsen, Propp & Ullman, 1995). The authors identified graphically four attractors of maximum energy. The clique represents each researcher’s pair, and arbitrarily large chromatic number means any combination of disciplines. Presented visualisation (Fig. 1) was generated by using the Poincare section (PS) of the 3D space which is defined by all ties between team’s members (Tamassia, 2000). The main problem concerns identification subgroups categories with regard to scientific activity. The matrix was generated using selected 1 This research is sponsored by National Science Center (NCN) under grant 2013/11/B/HS2/03048/ Information Visualization methods in digital knowledge structure and dynamics study. nodes and links through Poincare projection (Clifford, Azuaje, & McSharry, 2006). Figure 1. An iterated visualization of discrete distance routes. Obtained iterated visualization of discrete distance routes is shown on Figure 1. As a final result we observe four clear clusters. All participants were divided on four groups by describing appropriate roles in social network: leaders, connectors, performers and outliers. This approach was tested using algorithms adopted from medical data analysis for time series (Swierkocka-Miastkowska & Osinski, 2007, Mazur, Osinski, Swierkocka, 2009). The authors evaluate also the dynamics of total activity by using fractal dimension (FD) of each PS image. FD is the measure of nonclassical geometry shapes and can be used as a pattern’s complexity parameter (Osinska 2012). Fractal dimension was obtained by Higuchi algorithm, so the resulting maps help to discover possible opportunities for further development of cooperation between the scientists. Visual results All members’ activities represented by matrixes are summarized and full collaboration is weighted by appropriate real numbers. Popular application Gephi allows finding collaboration groups and revealing the scientists with basic roles: leader, 5 10 15 20 10 20 30 40 50 60 70 80 4 group 3 group 2 group 0,000 3,750 7,500 11,25 15,00 18,75 22,50 26,25 30,00 1 group Members quantity Topological dimension D 1257