# Co-Authorship Networks Analysis to Discover Collaboration Patterns among Italian Researchers
## 4 Inside the Data
### Structure of the Networks  
As detailed in the previous sections, we have built the co-authorship networks using the list of Italian academic researchers from four different \"academic disciplines\" as seeds: for each discipline, we build three subnetworks where we include all the researchers separated by up to one, two, or three degrees of collaborations. As shown in Table 2, reporting the number of nodes and edges of the three datasets, the networks built at different depths have different size. This is expected, since the networks may also include researchers from other institutions or countries. We also extract the Giant Connected Component (GCC, also known as Largest Connected Component, LCC) of the networks, i.e., the largest cluster of connected nodes, capturing the largest group of researchers that have a finite degree of separation from each other. The sizes of such components are shown in Table 3.  
We also plot the GCC of the depth-one networks (for the sake of readability, as the larger networks would be unintelligible) in Figure 2 that highlights the Italian researchers. Let us note that the co-authorship networks of ING-INF/05 and INF/01 disciplines show similar collaboration patterns, which is expected considering the large overlap in research interests and topics between them. In Table 4, we report some topological characteristics of the depth-two networks, describing their size, edge density, and connection patterns. As the Reader may notice, although the computer science-related fields have comparable size, the networks show a very different number of nodes and edges among academic fields. On the other hand, the average degree, strength, and link weight are comparable. Another interesting difference among the disciplines is in the average local clustering coefficient and in the transitivity, which shows that the researchers in computer science-related fields are more prone to collaborate. We also compute the degree and strength assortativity, as defined in [39; 40]. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Academic Discipline**} & \multicolumn{2}{c}{**Depth-Zero**} & \multicolumn{2}{c}{**Depth-One**} & \multicolumn{2}{c}{**Depth-Two**} \\ \cline{2-7}  & **Vertices** & **Edges** & **Vertices** & **Edges** & **Vertices** & **Edges** \\ \hline MAT/05 & 679 & 1990 & 7891 & 13,764 & 338,475 & 1,042,750 \\ SECS-P/01 & 674 & 784 & 10,736 & 13,404 & 727,060 & 2,512,882 \\ ING-INF/05 & 784 & 3759 & 46,879 & 84,127 & 1,900,424 & 6,897,383 \\ INF/01 & 966 & 4327 & 43,339 & 78,283 & 1,824,553 & 6,666,596 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Italian co-authorship networks size of the academic disciplines under analysis. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Academic Discipline**} & \multicolumn{2}{c}{**Depth-Zero**} & \multicolumn{2}{c}{**Depth-One**} & \multicolumn{2}{c}{**Depth-Two**} \\ \cline{2-7}  & **Vertices** & **Edges** & **Vertices** & **Edges** & **Vertices** & **Edges** \\ \hline MAT/05 & 613 & 1970 & 7712 & 13,599 & 338,462 & 1,042,745 \\ SECS-P/01 & 458 & 752 & 9309 & 12,042 & 727,028 & 2,512,863 \\ ING-INF/05 & 758 & 3758 & 46,851 & 84,101 & 1,900,413 & 6,897,354 \\ INF/01 & 929 & 4318 & 43,324 & 78,271 & 1,824,552 & 6,666,596 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Giant Connected Components size of the Italian co-authorship networks of the academic disciplines under analysis. Figure 2: These figures highlight the core of co-authorship networks (orange/clear) with respect to direct coauthors (blue/darker).