The collaboration network of the Brazilian Symposium on Databases

For a more complete study, we consider both publication statistics and co-authorship social perspectives. Therefore, our dataset comprises bibliographic data of SBBD’s 30 editions from 1986 to 2015, which includes for each paper: its title, year of publication, list of authors with their respective affiliations, and the language the paper was written. As each SBBD edition is unique in terms of its program and aiming at a more robust analysis, we consider only full papers actually presented at the symposium (i.e., our dataset disregards short papers, demos and tools, tutorials and keynotes, and workshop papers).

To ensure continuity, the dataset analyzed by Procópio et al. [31], comprising SBBD’s first 25 years, was extended with data from the remaining 5 years (2011–2015) as collected from BDBComp¹, the Brazilian Digital Library of Computing [15]. For consolidating our dataset and keeping data consistency, we have also performed name disambiguation to avoid splitting the publications of one person under two different author names.

Note that, from 2010 to 2014, SBBD full papers were published as articles in the Journal of Information and Data Management - JIDM², whereas the SBBD proceedings included short papers, demos and workshop papers. Then, the 2015 edition published full papers in the proceedings (mostly in Portuguese) and articles in JIDM as well. JIDM has also published full versions of invited SBBD short papers, as well as invited papers from other conferences such as the Brazilian Symposium on Geoinformatics (GeoInfo), the Symposium on Knowledge Discovery, Mining and Learning (KDMiLe), and the Brazilian Symposium on Multimedia and the Web (WebMedia). Thus, seeking a more round analysis, for the 2010–2015 period, we consider only full papers from SBBD proceedings and all SBBD-related papers from JIDM (both regular articles and invited full versions of short papers). Selected papers from the other conferences are not considered, as they do not reflect publications from the SBBD community, the focus of our study.

Following Maia et al. [22], in this study, we also represent the SBBD network as a temporal graph G _y =(V _y ,E _y ), where V _y is the set of vertices, E _y is the set of edges, and y is the year a network refers to. The graph G _y =(V _y ,E _y ) is an undirected weighted graph, where the vertices represent authors, and the edges indicate that two authors have published together in or before the year y. In addition, each edge has a corresponding weight based on the weighted collaboration network proposed by Newman [27]: the weight for each edge is discounted by the size of the collaboration, according to the formula \(w = \sum _{p} \frac {1}{N_{p}-1}\), where N _p is the number of authors of paper p. For instance, given a,b,c,d∈V _y and assuming that a and b wrote a single paper with no other co-author, and b and c have a joint co-author d. Then, the weight of the edge (a,b) is 1.0, while the weight of the edges (b,c), (c,d), and (b,d) is 0.5, as the weights among nodes are calculated by the number of authors for each paper. Figure 1 shows the complete SBBD network as viewed in 2015, representing 30 years of history.

The complete SBBD collaboration network, built from all papers published in its 30 editions, has a total of 1034 authors (vertices) and 2299 collaborations (edges), comprising a total of 674 papers. The largest connected component (LCC) (the largest subgraph in which any pair of nodes is connected by paths) has 781 nodes, representing 75.53% of the whole community. Then, 162 nodes compose smaller components containing three to seven authors. Finally, there are 80 nodes that form pairs of authors, and 11 nodes that correspond to sole authors.

The average number of papers per year is 22.47 (with a standard deviation of 4.86), and the average number of authors per year is 60.53 (with a standard deviation of 17.53). Finally, the average number of papers per author is 1.98 (with a standard deviation of 3.21), while the average number of authors per paper is 3.04 (with a standard deviation of 1.47).

Several metrics characterize and enable to investigate collaboration networks as the one studied here. This section summarizes the definition and applicability of the metrics used in this work.

The degree of a vertex is the number of its adjacent edges. Hence, authors who have high number of papers with different co-authors also have high degree. The degree distribution is the probability distribution of these degrees over the whole network. The network density is calculated by dividing the number of edges by the number of nodes present in the graph. The assortativity measures the similarity of connections in the graph with respect to the node degree. High coefficient means that authors of high degree tend to connect to authors of high degree (assortative network).

A connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths. The size of such a component is given by dividing the number of its nodes by the total number of vertices of the graph. The average path length is the average number of steps along the shortest paths for all possible pairs of network nodes. The graph diameter is the length of the longest shortest path between all pair of vertices.

Betweenness and closeness regard the centrality of nodes in the network. The former is equal to the number of shortest paths from all vertices to all others that pass through a given node, whereas the latter measures how close a vertex is to all other vertices in the graph. The clustering coefficient CC(x) of a vertex x is the ratio between the number of edges among the neighbor-set of x and the total possible number. The clustering coefficient of the whole network is the average CC(x) over all x. Finally, homophily is the tendency of authors to interact with others with similar features. We refer to Albert and Barabási [1] and Costa et al. [6] for further information and complete definitions of all these network metrics.

The SBBD network has a high global clustering coefficient of 65.6%, indicating dense groups of authors who publish together (PODS, for example, achieved only 35% in its 30th edition in 2011 [2]), indicating that there is a stronger triadic closure effect [12] in SBBD. Even though the number of authors in the network has substantially increased, new authors tend to collaborate with coauthors that maintain previous collaborations, establishing triangle network motifs. In other words, previous collaborations increase the chance of a pair of authors establishing a collaboration with a newcomer in the network⁴.

Figure 14 shows the evolution of the average shortest path length and the clustering coefficient of SBBD, as well as their equivalent random networks. A high clustering coefficient (compared to its equivalent random network) and a small average shortest path (as low as its equivalent random network) characterize the SBBD network as a small-world network [25]. This phenomenon has long been subject of scientific studies and is typical in social networks [35].

Table 5 shows the size (number of vertices) of the two SBBD largest connected components over the years, and Fig. 15 the evolution of their relative sizes. The LCC for the 30 editions has 2004 edges, with a relative size of 87.17%. It grows with an average of approximately 26 new nodes yearly over the 30 years, 32 over the last 20 years, and 41 over the last 10 years, reaching 75.53% of all nodes in 2015 (13.06% in 1995 and 36.07% in 2005). These values confirm that most of the SBBD authors are connected through a single component, with the second largest connected component (SLCC) having only 22 edges, with a relative size of 0.96%. The remaining cases correspond to smaller components and authors who did not collaborate with other authors. There are only 11 cases of sole authors (see Fig. 1), whose papers were published between 1986 and 2003 (see Fig. 10). It is worth noticing that most of such papers are short communications describing projects developed by large technology companies (e.g., Telebrás and Embratel) or present results of their authors’ thesis or dissertation.

Decomposing a complex network into groups (sets of highly connected nodes) is very important, as it may help to understand a-priori unknown features and properties of the network. In this section, we focus on discovering and analyzing collaboration groups inside SBBD.

Specifically, we use the k-clique algorithm [30] that relaxes the notion of clique and has shown great success in detecting clusters on a large scale. A collaboration group is then defined as the maximal union of k-cliques that can be reached from each other by a series of adjacent k-cliques (they are adjacent if they share k-1 nodes). The k-clique algorithm returns a large number of groups inside SBBD, thus showing that collaboration has greatly increased over the years. According to Fig. 16, there are currently 148 (with k = 3), 116 (with k = 4), and 75 (with k = 5) groups formed.

Despite the high number of groups, they do not include many authors. In fact, most of them are really small groups: 51.4% of the 3-cliques have only three authors. The largest 3-clique has 230 nodes and contains the biggest 4-clique inside it (61 nodes). Considering 5-cliques, the number of authors in the largest, second largest, and third largest groups are respectively 18, 12, and 12.

Using the top three groups found by the k-clique algorithm with k = 4, which only uses topological features of the graph, there are clusters in which most authors belong to one or at most two distinct institutions, as shown in Table 6. The largest group found is composed by authors from the states of Minas Gerais and Amazonas (due to a longstanding collaboration between Alberto H. F. Laender from UFMG and Altigran S. da Silva from UFAM). On the other hand, the second and third largest groups are mainly composed by authors from the states of São Paulo and Rio de Janeiro, respectively. This indicates that the geographical location and the affiliation of an author is a strong factor to determine which group this author belongs to in the SBBD community.